THE BASIC THEORY OF ELECTRICITY IN PHYSICS

Application of electricity


There is no denying the fact that electricity is an important topics in Physics with which a person may learn for education on science and technology. A direct current (DC) is a flow of charges around a circuit in the same direction all the time. Batteries supply DC and most appliances need DC to function. Alternating current (AC) is a flow of charges around a circuit that reverses its direction at regular intervals, usually many times a second.Household electrical power is supplied in the form of AC which usually needs to be rectified to DC before use.


Electrical Symbols


Circuit diagrams are essential part of the study of current electricity and are often drawn symbolically. In circuit diagrams, various circuit elements are represented by standard electric symbols.


The mass (m) of a body of matter is quantitative measure of its inertia, i.e., its resistance to a change in the state of rest or motion of the body, when a force is applied.
Standard International of mass is the kilogram (kg). It is a scalar quantity
The greater the mass of a body, the smaller the rate of change in motion.


Matter is the material substance that constitutes the observable universe and, together with energy, forms the basis of all objective phenomena. The basic building blocks of matter are atoms. The atoms themselves comprise of nucleus and electrons.


Series Circuits


Series circuits has the same current through each circuit components BUT different potential difference across each circuit components.


Same Current
In a series circuit, the flow of charges has only one path to follow. The flow of charge passes through each component in turn.
Therefore, in a series circuit, the current at every point is the same.
Adding a new component to the series circuit reduces the current flow throughout because of the added resistance of the new component.


Different potential difference
Potential difference (p.d.) between two points in a circuit is caused by the energy dissipation in the circuit elements connected between those two points. Energy is a scalar quantity. It can be added to get the total energy dissipation in a circuit.
In a series circuit, the sum of the potential difference across the sinks (i.e. the bulbs) is equal to the sum of the e.m.f.s across the sources (i.e. the battery).
In a series circuit, the sum of the potential difference across the bulbs is equal to the potential difference across the battery.
In a series circuit, the highest potential difference occurs across a component with the largest resistance. (Disregarding the potential difference across the battery)
The potential difference between the ends of any of the pieces of connecting wire is effectively zero because there is almost no loss of potential energy.


Parallel Circuits


Parallel circuits has the different current through each branch (same current through the circuit components within the branch) BUT same potential difference across each branch. (different potential difference across the circuit components within the branch)


Different currents
Instead of wiring components in series, they can be connected in parallel. Parallel connection offers different paths for the flow of charges, but the total flow of charges from the source remains unchanged.
Therefore, in a parallel circuit, the current from the source is the sum of the currents in the separate branches.
In the parallel circuit shown, if one lamp is removed, the others still light up. This is why most household lighting circuits are connected in parallel.
In a parallel circuit, the largest current will pass through the branch with the smallest effective resistance.
At a junction in a circuit, the total current entering a junction is equal to the total current leaving the junction. This is the conservation of charge.


Same potential difference
In a parallel circuit, two or more components are connected between two points of the circuit. The potential difference across a component is the potential difference between the two points and is equal to the potential difference of any other component connected in between.
Therefore, the potential difference across separate branches of a parallel circuit is the same.


Amount Of Substance


Although mass is defined in terms of inertia, it is conventionally interpreted as:


The mass (m) of a body of matter is a measure of its amount of substance in the body.
Under ordinary circumstances, matter does not change. Hence, the amount of substance in the body can be assumed to be quantitatively equal to its mass. If the amount of substance divides itself, we can assume that its mass also halved.
Mass can be measured with a beam balance or an electronic balance.


Note: As we might recall in , the base SI unit for amount of substance is mol.


Circuit Diagrams


A simple circuit, with a cell (if a series of cells is used, it is called a battery) and a resistor or bulb.


Circuit diagram showing the measurement of current in the circuit and potential difference across a circuit element (e.g. the resistor).
An ammeter is used to measure the current flowing in the circuit and must be inserted in series with the circuit element as shown.
A voltmeter measures the potential difference between two points in a circuit and must be connected in parallel to the circuit element as shown.


Note that:
An ideal ammeter has zero resistance so that when inserted into a circuit, it does not reduce the current that was previously flowing.
An ideal voltmeter has infinite resistance so that it takes no current. A finite resistance causes it to take current from the circuit, and to lower the potential difference between the points to which it is connected.


________________
Variable resistor can be used as a rheostat to control current or as a potential divider to control voltages.
The fuse is a short piece of thin wire which overheats and melts to break the circuit if current of more than its rated value flows through it. A fuse is connected in series to protect devices in the circuit.
Resistance of a thermistor (thermally sensistive resistor) decreases rapidly as its surrounding temperature rises.
Resistance of light dependent resistor (LDR) decreases with increasing surrounding light intensity.
A light emitting diode (LED) allows current to flow in only one direction. When current is allowed to pass, it shines brightly with only a small voltage across it. LED is used as on/off indicator in many electronic devices such as televisions, computers.
A earth connector is a conductor that connects directly to earth.


The mass (m) of a body of matter is quantitative measure of its inertia, i.e., its resistance to a change in the state of rest or motion of the body, when a force is applied.
Standard International of mass is the kilogram (kg). It is a scalar quantity.
The greater the mass of a body, the smaller the rate of change in motion.


Note:


Matter is the material substance that constitutes the observable universe and, together with energy, forms the basis of all objective phenomena. The basic building blocks of matter are atoms. The atoms themselves comprise of nucleus and electrons.


Amount Of Substance


Although mass is defined in terms of inertia, it is conventionally interpreted as:


The mass (m) of a body of matter is a measure of its amount of substance in the body.
Under ordinary circumstances, matter does not change. Hence, the amount of substance in the body can be assumed to be quantitatively equal to its mass. If the amount of substance divides itself, we can assume that its mass also halved.
Mass can be measured with a beam balance or an electronic balance.


Note: As you might recall in Base quantities, the base SI unit for amount of substance is mol.


Any two bodies in the universe attract each other with a force. This spectacle is called the gravitational attraction. This force of attraction is known as the gravitational force or force due to gravity.


A force field is a region in which a body experiences a force as a result of the presence of some other body or bodies.
A force field is thus a method of representing the way in which bodies are able to influence each other.


A gravitational field is a region in which a mass experiences a force due to gravitational attraction.
A gravitational field is a region of space surrounding a body that has the property of mass. In this region, any other body that has mass will experience a force of attraction.
All bodies near the surface of Earth experience gravitation attraction exerted by Earth.
You experience weight on Earth due to the Earth exerting gravitational force on you. The formula to calculate weight is stated below.


Gravitational Field Strength


ALL objects set up a gravitational field around itself. If a second body is placed at distance X from the first body, it will experience a gravitational attractive force towards the first body.


The gravitational field strength (g) at any point in a gravitational field is the gravitational force per unit mass exerted on any body placed at that point.
SI unit of gravitational field strength is newton per kilogram. (N kg-1)
Fg=mg, where Fg = gravitational force (unit is N), m = mass (unit is kg), g = gravitational field strength
Its direction is towards the massive body, such as Earth, that sets up the force field.
The gravitational field strength on Earth is approximately 10 N kg-1, while the gravitational field strength on the Moon is only 16 of that on Earth. Hence, you will only feel 16 of your weight on the Moon.


Example: Gravitational force on a 5 kg object is 5×10=50N


All bodies of matter near the surface of Earth experience gravitational force due to Earth’s gravitational field. This gravitational pull is commonly referred to as the weight.


The weight of a body is the gravitational force exerted on it by Earth.
SI unit of weight is newton (N). It is a vector quantity.
Its direction is towards the centre of the Earth or commonly referred to as vertically downwards.
Weight is measured using a newton-meter.
Your weight does change slightly from place to place on Earth – at the north pole, one would weigh about 3 N heavier than one near the equator. This is due to the gravitational field strength being slightly DIFFERENT at different places on Earth. Normally, you neglect this difference in your calculations. (If you want to ask why heavier at the poles, it is due to the Earth being slightly flattened at the poles.)



Mass

Weight


It is amount of substance in a body

It is the pull of gravity on the body


Scalar quantity

Vector quantity


SI unit is kilogram (kg)

SI unit is newton (N)


Constant under ordinary circumstances

Changes and depends on its location


Measured using a beam balance or electronic balance

Measured using a spring or newton-meter



Note:


When a body is placed in a region of free space far away from any massive bodies, it experiences no gravitational pull and thus are considered weightless. When this same body is now placed near the surface of the Earth, the body experiences the pull of gravity. This shows that the weight must come from an external source. Hence, it is an external force.


Example:


The gravitational field strength on the surface of the Moon is one-sixth that of Earth’s. For a body of 60 kg, deduce its mass and weight on the Moon?


Solution:


Mass of body on Moon = 60 kg. (Mass don’t change)


Earth’s gravitational field strength, gEarth=10ms−2


Weight of body on moon = m×gMoon=(60)(106)=100N










The electric charges in motion is called electric current and it forms the basis of current electricity. Static electricity, or electrostatics, on the other hand involves charges at rest.


Electric current (I) is the rate of flow of charges.(Q)
SI unit: Ampere (A)
Can be measured by an ammeter (must be connected in SERIES to the circuit)


I=Qt


A current of one ampere is a flow of charge at the rate of one coulomb per second.


For electric current in a metal conductor (a solid), the charge carriers are electrons. For historical reasons, the direction of the conventional current is always treated as the opposite direction in which electron effectively moves.
Current in gases and liquid generally consists of a flow of positive ions in one direction together with a flow of negative ions in the opposite direction.


Electric current generates a magnetic field. The strength of the magnetic field depends on the magnitude of the electric current.


Current electricity consists of any movement of electric charge carriers, such as subatomic charged particles (e.g. electrons having negative charge, protons having positive charge), ions (atoms that have lost or gained one or more electrons), or holes (electron deficiencies that may be thought of as positive particles)
If the direction of the current (charge flow) is fixed, it is known as a direct current. If the motion of the electric charges is periodically reversed; it is called an alternating current.


Analogy to river:


In order to help you understand the concept of current better, you can think of a river. Current in an electric circuit is similar to water flowing through the river.


Examples:


An electric current in a wire involves the movement of
electrons
atoms
molecules
protons


The lower part of a cloud has a positive charge. The cloud discharges in a flash of lightning. In which direction do electrons and conventional current flow?


A battery moves a char


A charge of 60 C around a circuit at a constant rate in a time of 20 s. What is the current in the circuit?






Electromotive Force (e.m.f.) of a source is the energy converted from non-electrical to electrical form when one coulomb of positive charge passes through the source.
SI unit: Volt (V)


E=WQ, where E = e.m.f., W = work done by source, Q = amount of positive charges


Potential difference between two points is defined as the energy converted from electrical to other forms when a coulomb of positive charge passes between the two points.
SI unit: Volt (V)


V=WQ, where V = potential difference, W = work done in driving the charge between the two points, Q = amount of positive charges


IMPORTANT: There can be e.m.f. without a closed circuit. BUT there cannot be a potential difference without a closed circuit.


Analogy to waterfalls:


In order to help you understand the concept of potential difference better, you can think of a waterfall. In the case of a waterfall, the water flows due to a height difference. In electric circuits, current flows between two points due to the existence of potential difference between the two points. No potential difference = no current.


When two or more sources are arranged so that the positive terminal of one is connected to the negative terminal of the next, they are said to be in series and their e.m.f.s add up.


This arrangement gives increased e.m.f. because, the charge flowing round a circuit will pass through more than one source and gains electrical potential energy from each of them.


Note:

Cells can also be arranged in parallel. In this, all the positive terminals are connected together and all the negative terminals are connected together. The combined e.m.f. in parallel connection will not increase like in the series connection. But the battery will last longer before going flat.


When a torch bulb is connected to a battery, the torch bulb gets lit. The battery converts chemical energy into electrical energy and is therefore a source of electrical energy. The torch bulb converts electrical energy into heat and light and is therefore a sink of electrical energy.
Dissipation of electrical energy between two points (e.g. across torch bulb) in an electrical circuit causes potential difference (p.d.) between those two points.


The potential difference (p.d.) between two points in a closed circuit is defined as the energy converted from electrical to other forms when a unit positive charge passes between the two points.
SI unit of p.d. is the volt (V). It is the same as that of e.m.f.. (Both are measures of electrical potential energy, e.m.f. is gained electrical energy while potential difference is lost electrical energy.)
V=WQ


By increasing p.d. across the ends of a conductor, current flow can be increased. But the increase in the amount of current flow depends on the conducting ability of the conductor. Some conductors offer some resistance to current flow than others.


Resistance (R) of a conductor is defined as the ratio of potential difference (V), across the conductor to the current (I), flowing through it.
SI unit of resistance is the ohm Ω.
V = IR


Ohm’s law states that, the current flowing in a metallic conductor is directly proportional to the potential difference applied across its ends, provided that all other physical conditions, such as temperature, are constant. Comparing with V=IR, thus, R must be constant for a metallic conductor under steady physical conditions.


Besides temperature, experimental results shows that the resistance (R of a given conductor) also depends on the composition and size.


Resistance, R is found to be:
directly proportional to its length, L
inversely proportional to its cross-sectional area
dependent on the type of material


From experimental results, we can show that:


R=ρLA


,where


R = resistance in ohm (Ω)

A = cross-sectional area of conductor in metre2 (m2)

L = length of conductor in metre (m), and

ρ = resistivity of material in ohm-metre (Ωm)


In many situations, several electrical devices are connected to the same power supply. There are two basic methods of connecting resistors or other devices together. They are called series and parallel connections.


The derivation of the formula for effective resistance for series and parallel resistors can be found at the end of this post.
Effective Resistance Of Resistors
Resistors In Series


If individual resistors are connected from end to end, the resistors are said to be connected in series. The effective resistance, R, of three resistors of resistances R1, R2; and R3 connected in series (shown in the figure) is given by:


R=R1+R2+R3


In general, if there are n resistors in series, the effective resistance R is given by:


R=R1+R2+….+Rn


Note: In a series connection, the effective resistance, R, is always larger than the largest of the individual resistances.
Resistors In Parallel


If each end of individual resistors are connected together to one another as one, the resistors are said to be connected in parallel.


The effective resistance, R, of three resistors of resistances R1, R2and R3 connected in parallel is given by:


1R=1R1+1R2+1R3


In general, if there are n resistors in parallel, the effective resistance R is given by:


1R=1R1+1R2+….+1Rn


Note: In a parallel connection, the effective resistance, R, is always smaller than the smallest of the individual resistances.


Next: I/V Characteristic Graphs


Previous: Resistivity


Back To Current Electricity
Derivation of effective resistance for series and parallel resistors
Series Resistors


When the resistors are in series, the current through each resistor is the same. We shall denote the current as I. Each resistor will have its own voltage. If the resistance of the resistors are different (R1≠R2≠R3≠…), the voltage drop across each resistor will be different (V1≠V2≠V3≠…).


We know that resistance is given by R=VI.


Hence the effective resistance of the whole stretch of resistor is given by:


Reff=VtotalI


However, we know that


Vtotal=V1+V2+V3+…


Substitute that into the effective resistance equation, we have:


Reff====VtotalIV1+V2+V3+…IV1I+V2I+V3I+…R1+R2+R3+…
Parallel Resistors


When the resistors are in parallel, the voltage drop across each resistor is the same. We shall denote the voltage as V. Each resistor will have its own voltage. If the resistance of the resistors are different (R1≠R2≠R3≠…), the current through each resistor will be different (I1≠I2≠I3≠…).


We know that resistance is given by R=VI.


Hence the effective resistance of the whole stretch of resistor is given by:


Reff=VItotal


However, we know that


Itotal=I1+I2+I3+…


Substitute that into the effective resistance equation, we have:


ReffReff1Reff1Reff1Reff=====VItotalVI1+I2+I3+…I1+I2+I3+…VI1V+I2V+I3V+…1R1+1R2+1R3+…


In order to prevent excessive currents flowing into the home circuit, electrical appliances and its cables, fuses and circuit breakers are wired into the live wire and used as safety devices.
A fuse is usually made up of a tin-coated copper wire. When current exceeds its design rating value. The wire will overheat and melt, thus opening the electrical circuit. It will prevent further damage to the appliance or user. It cannot be reused.
A circuit breaker is usually made up of a reusable spring-loaded type of switch. The function of the circuit breaker is similar to that of the fuse. If current exceeds its breaking setting, it will spring open and break the circuit as in a fuse. The device can be reused by resetting the spring-loaded switch.


It is correct to fix the fuse or circuit breaker at the live wire before the appliance. When the circuit is loaded with excessive current, the fuse or circuit breaker will break and open the circuit. It will prevent overloading, burning or damaging the appliance.
Connecting the fuse or circuit breaker to the neutral wire is incorrect, i.e., even when the circuit is opened due to excessive currents, the appliance may still be at live potential, creating possibility of an electric shock.


The current limit through the fuse (fuse rating) can be controlled by varying the thickness of the tin-coated copper wire. Thicker the wire, the larger the heating effect needed to melt the connection, thus permitting larger current to flow.
Different fuse ratings and circuit breaker settings are used in different appliances according to their power requirements. The rating limits used is normally slightly higher than the normal current needed by the appliance.
Switch is used to open or close the electrical circuit.
Open the switch = NO current is flowing through the circuit.
Close the switch = Current can flow through the circuit.
The switch should be connected to the LIVE wire and not the neutral or earthing wire. If you connect the switch to the neutral wire, even if the switch is opened, the appliance will still be connected to the live wire. This increases the possibility of an electric shock.
The switch should be connected BEFORE the appliance. (There’s no way for you to connect after the appliance.)


Earthing is the act of connecting the metal casing of the appliance to earth via a wired connection to the bare ground. Earthing wires are usually have a green and yellow bands around them. Why do you need earthing? Consider this scenario:
The live wire is frayed and touched the metal casing of the appliance. (Another phrase for this is: The metal casing of the appliance becomes live.)
The appliance do not have an earthing cable.
YOU touched the metal casing of the appliance.
Your body would have completed the circuit → electricity will pass through your body.
The current is not high enough to trigger the breaking of fuse in the power plug.
You get electrocuted.


If you have earthing (connecting the metal casing to the ground), the current will have two paths to take to complete the circuit:
The low resistance earthing wire
Your body (Note that your body have a high resistance when compared to the earthing wire)


The current will obviously travel through the low resistance earthing wire instead of your body. Hence, the earthing will divert the current into the earth by providing an alternate path to the large current flow via the earth wire, rather than through the user’s body.


Double Insulation


There are some appliances which do NOT have an earth wire. They have another way to protect the user: double insulation. Double insulation protects the user of the appliance from an electrical shock by preventing any possibility of the external casing becoming live (the live wire can not touch the casing even if wires inside become loose), thus eliminating the need for an earth connection. The two layers of insulation are:
First insulation: Insulating electrical cable from the internal component of the appliance.
Second insulation: Insulating internal metal part which could become live from the external casing.


Note: If the external casing is plastic, there’s no way the external casing can become live.


You can identify which appliances have an earth wire by checking the mains plug. If it is a 3-pin plug (all three pins are made of metal), it would have an earthing wire.
Remove a sufficient amount of outer insulation of the three core wires, Live (brown), Neutral (blue) and Earth (green with yellow).
Open the mains plug with a screwdriver and take out the fuse.
Remove about 5 mm of the insulation from three wires and twist the copper strands of each wire together.
Clamp the edge of the removed outer insulation by tightening the two screws that are holding down the outer insulation wire.
Insert each wire to the correct terminal as shown and tighten each screw so that the wires are fixed properly with the terminals.
Fix the fuse back to its position and close the covering of the plug.
Remove a sufficient amount of outer insulation of the three core wires, Live (brown), Neutral (blue) and Earth (green with yellow).
Open the mains plug with a screwdriver and take out the fuse.
Remove about 5 mm of the insulation from three wires and twist the copper strands of each wire together.
Clamp the edge of the removed outer insulation by tightening the two screws that are holding down the outer insulation wire.
Insert each wire to the correct terminal as shown and tighten each screw so that the wires are fixed properly with the terminals.
Fix the fuse back to its position and close the covering of the plug.


Earthing is the act of connecting the metal casing of the appliance to earth via a wired connection to the bare ground. Earthing wires are usually have a green and yellow bands around them. Why do you need earthing? Consider this scenario:
The live wire is frayed and touched the metal casing of the appliance. (Another phrase for this is: The metal casing of the appliance becomes live.)
The appliance do not have an earthing cable.
YOU touched the metal casing of the appliance.
Your body would have completed the circuit → electricity will pass through your body.
The current is not high enough to trigger the breaking of fuse in the power plug.
You get electrocuted.


If you have earthing (connecting the metal casing to the ground), the current will have two paths to take to complete the circuit:
The low resistance earthing wire
Your body (Note that your body have a high resistance when compared to the earthing wire)


The current will obviously travel through the low resistance earthing wire instead of your body. Hence, the earthing will divert the current into the earth by providing an alternate path to the large current flow via the earth wire, rather than through the user’s body.


Double Insulation


There are some appliances which do NOT have an earth wire. They have another way to protect the user: double insulation. Double insulation protects the user of the appliance from an electrical shock by preventing any possibility of the external casing becoming live (the live wire can not touch the casing even if wires inside become loose), thus eliminating the need for an earth connection. The two layers of insulation are:
First insulation: Insulating electrical cable from the internal component of the appliance.
Second insulation: Insulating internal metal part which could become live from the external casing.


Note: If the external casing is plastic, there’s no way the external casing can become live.


You can identify which appliances have an earth wire by checking the mains plug. If it is a 3-pin plug (all three pins are made of metal), it would have an earthing wire.
Remove a sufficient amount of outer insulation of the three core wires, Live (brown), Neutral (blue) and Earth (green with yellow).
Open the mains plug with a screwdriver and take out the fuse.
Remove about 5 mm of the insulation from three wires and twist the copper strands of each wire together.
Clamp the edge of the removed outer insulation by tightening the two screws that are holding down the outer insulation wire.
Insert each wire to the correct terminal as shown and tighten each screw so that the wires are fixed properly with the terminals.
Fix the fuse back to its position and close the covering of the plug.


UNCATEGORIZED
CHEMICAL BONDS IN METALS AND NON-METALS


DECEMBER 22, 2014 LEAVE A COMMENT EDIT






RATE THIS





There is no denying the fact that Forces, Electrons, and Bonds in CHEMISTRY CATEGORIES where atoms are the basic building blocks of all types of matter. Atoms link simultaneously to other atoms through chemicals bonds resulting from the strong attractive forces that exist between the atoms.


It is a region that forms when electrons from different atoms interact with each other. The electrons that participate in chemical bonds are the valence electrons, which are the electrons found in an atom’s outermost shell. When two atoms approach each other these outer electrons interact. Electrons repel each other, yet they are attracted to the protons within atoms. The interplay of forces results in some atoms forming bonds with each other and sticking together.

The two main types of bonds formed between atoms are ionic bonds and covalent bonds. An ionic bond is formed when one atom accepts or donates one or more of its valence electrons to another atom. A covalent bond is formed when atoms share valence electrons. The atoms do not always share the electrons equally, so a polar covalent bond (polar covalent bond is such where the atoms do not share the electrons equally) may be the result. When electrons are shared by two metallic atoms a metallic bond may be formed. In a covalent bond, electrons are shared between two atoms. The electrons that participate in metallic bonds may be shared between any of the metal atoms in the region.

• If the electro negativity values of two atoms are similar.

• Metallic bonds form between two metal atoms.

• Covalent bonds form between two non-metal atoms.

• Non polar covalent bonds form when the electro negativity values are very similar.

Carbon Compounds

There are more carbon compounds than there are compounds of all other elements combined. The study of carbon compounds, both natural and synthetic, is called organic chemistry. Plastics, foods, textiles, and many other common substances contain carbon. Hydrocarbon fuels (e.g., natural gas), marsh gas, and the gases resulting from the combustion of fuels (e.g., carbon monoxide and carbon dioxide) are compounds of carbon. With oxygen and a metallic element, carbon forms many important carbonates, such as calcium carbonate (limestone) and sodium carbonate (soda). Certain active metals react with it to make industrially important carbides, such as silicon carbide (an abrasive known as carborundum), calcium carbide, used for producing acetylene gas, and tungsten carbide, an extremely hard substance used for rock drills and metalworking tools.

Polar covalent bonds form when the electro negativity values are a little further apart different.


The Mole and Avogadro’s Constant


Table of Contents

1. Introduction

2. Applications of the Mole

3. Practice Problems

4. Answers to Practice Problems


THE MOLE

The mole, abbreviated mol, is an SI unit which measures the number of particles in a specific substance. One mole is equal to 6.02214179 × 1023 atoms, or other elementary units such as molecules.

Introduction

The number of moles in a system can be determined using the atomic mass of an element, which can be found on the periodic table. This mass is usually an average of the abundant forms of that element found on earth. An element’s mass is listed as the average of all its isotopes on earth.


Example 1

One mole of oxygen atoms contains 6.02214179×1023 oxygen atoms.

The number 6.02214179×1023 alone is called Avogadro’s number or Avogadro’s constant, after the 19th century scientist Amedeo Avogadro.

Each carbon-12 atom weighs about 1.99265 × 1023 g

therefore, (1.99265×1023 g × 6.02214179×1023 atoms) = 12 g of carbon-12.

Applications of the Mole

The mass of a mole of substance is called the molar mass of that substance. The molar mass is used to convert grams of a substance to moles and is used often in chemistry. The molar mass of an element is found on the periodic table, and it is the element’s atomic weight in grams/mole (g/mol).

If the mass of a substance is known, the number of moles in the substance can be calculated. Converting the mass, in grams, of a substance to moles requires a conversion factor of (one mole of substance/molar mass of substance).

The mole concept is also applicable to the composition of chemical compounds. For instance, consider methane, CH4. This molecule and its molecular formula indicate that per mole of methane there is 1 mole of carbon and 4 moles of hydrogen. In this case, the mole is used as a common unit that can be applied to a ratio as shown below:

2 mol H + 1 mol O = 1 mol H2O

The moles of H and O describe the number of atoms of each element that react to form 1 mol of H2O.

To think about what a mole means, one should relate it to quantities such as dozen or pair. Just as a pair can mean two shoes, two books, two pencils, two people, or two of anything else, a mole means 6.02214179×1023 of anything.

Using the following relation:

1 mole = 6.02214179×1023 is analogous to saying:

1 Dozen = (12 eggs)

It is quite difficult to visualize a mole of something because Avogadro’s constant is extremely large. For instance, consider the size of one single grain of wheat. If all the people who have existed in Earth’s history did nothing but count individual wheat grains for their entire lives, the total number of wheat grains counted would still be much less than Avogadro’s constant; the number of wheat grains produced throughout history does not even approach Avogadro’s Number.


How many moles of potassium (K) atoms are in 3.04 grams of pure potassium metal?

SOLUTION

In this example, multiply the mass of K by the conversion factor:

1 mol K / 39.10 grams K

39.10 grams is the molar mass of one mole of K;

cancel out grams, leaving the moles of K:

3.04 g K × (1 mol K/ 39.10 g K) = 0.0778 mol K

Similarly, if the moles of a substance are known, the number grams in the

substance can be determined. Converting moles of a substance to grams requires

a conversion factor of molar mass of substance/one mole of substance.

One simply needs to follow the same method but in the opposite direction.


Example 2

How many grams are 10.78 moles of Calcium (Ca)?

SOLUTION

10.78 mol Ca × (40.08 g Ca/ 1 mol Ca) = 432.1 g Ca

Multiply moles of Ca by the conversion factor 40.08 g Ca/ 1 mol Ca, with

40.08 g being the molar mass of one mole of Ca, which then allows the

cancelation of moles, leaving grams of Ca.

The total number of atoms in a substance can also be determined by

using the relationship between grams, moles, and atoms. If given the mass

of a substance and asked to find the number of atoms in the substance, one

must first convert the mass of the substance, in grams, to moles, as in

Example 1. Then the number of moles of the substance must be converted to atoms.

Converting moles of a substance to atoms requires a conversion factor of

Avogadro’s constant (6.02214179×1023) / one mole of substance.

Verifying that the units cancel properly is a good way to make sure the correct method is used.

Example 3

How many atoms are in a 3.5 g sample of sodium (Na)?

SOLUTION

3.5 g Na × (1 mol Na/ 22.98 g Na) = .152 mol Na

0.152 mol Na × (6.02214179×1023 atoms Na/ 1 mol Na) = 9.15×1022 atoms of Na

In this example, multiply the grams of Na by the conversion

factor 1 mol Na/ 22.98 g Na, with 22.98g being the molar mass of

one mole of Na, which then allows cancelation of grams, leaving moles

of Na. Then, multiply the number of moles of Na by the conversion factor 6.02214179×1023 atoms Na/ 1 mol Na, with 6.02214179×1023 atoms

being the number of atoms in one mole of Na (Avogadro’s constant),

which then allows the cancelation of moles, leaving the number of atoms of Na.


Applications

Using Avogadro’s constant, it is also easy to calculate the number of atoms or molecules present in a substance. By multiplying the number of moles by Avogadro’s constant, the mol units cancel out, leaving the number of atoms. The following table provides a reference for the ways in which these various quantities can be manipulated:

Known Information Multiply By Result

Mass of substance (g) Molar mass (g/mol) Moles of substance

Moles of substance (mol) Avogadro’s constant (atoms/mol) Atoms (or molecules)

Mass of substance (g) Molar mass ((mol/g) × Avogadro’s constant (atoms/mol)) Atoms (or molecules)


Example 1A

Convert to moles: 3.00 grams of potassium (K)

SOLUTION

= 3.00 g K × (1 mol K/ 39.10 g K) = 0.076726 mol K

In this example, multiply the mass of K by the conversion factor:

1 mol K / 39.10 grams K

39.10 grams is the molar mass of one mole of K. Grams can be canceled,

leaving the moles of K.

Example 1B

Convert to grams: 10.00 moles of calcium (Ca)

SOLUTION

This is the calculation in Example 1A performed in reverse.

Multiply moles of Ca by the conversion factor 40.08 g Ca/ 1 mol Ca,

With 40.08 g being the molar mass of one mole of Ca. The moles cancel,

leaving grams of Ca:

10.00 mol Ca × (40.08 g Ca/ 1 mol Ca) = 400.8 grams of Ca

The number of atoms can also be calculated using

Avogadro’s Constant (6.02214179×1023) / one mole of substance.


Example 1C

How many atoms are in a 3.0 g sample of sodium (Na)?

SOLUTION

3.0 g Na × (1 mol Na/ 22.98 g Na) = .130548 mol Na

0.130548 mol Na × (6.02214179×1023 atoms Na/ 1 mol Na) = 7.86179×1022 atoms of Na

Practice Problems

1) Using a periodic table, give the molar mass of the following:

a. H

b. Se

c. Ne

d. Cs

e. Fe


For problems 2-4, convert to moles and find the total number of atoms.

2) 5.06 grams of oxygen 3) 2.14 grams of K 4) 0.134 kg of Li

Convert the following to grams

5) 4.5 moles of C 6) 7.1 moles of Al 7) 2.2 moles of Mg

How many moles are in the product of the reaction

8) 6 mol H + 3 mol O →? mol H2O

9) 1 mol Cl + 1 mol Cl →? mol Cl2

10) 5 mol Na + 4 mol Cl → ? mol NaCl


————————————————————————————————–

Answers to Practice Problems

1a. 1.008 g/mol

1b. 78.96 g/mol

1c. 20.18 g/mol

1d. 132.91g/mol

1e. 55.85 g/mol

2. 5.06g O (1mol/16.00g)= 0.316 mol of O

0.316 mols (6.022×1023 atoms/ 1mol) = 1.904×1023 atoms of O

3. 2.14g K (1mol/39.10g)= 0.055 mol of K

0.055 mols (6.022×1023 atoms/ 1mol) = 3.312×1022 atoms of K

4. 0.134kg Li (1000g/1kg)= 134g Li (1mol/6.941g)= 19.3 mols Li

19.3 (6.022×1023 atoms/ 1mol) = 1.16×1025 atoms of Li

5. 4.5 mols of C (12.011g/1mol) = 54.05 g of C

6. 7.1 mols of Al (26.98g/1mol) = 191.56 g of Al

7. 2.2 mols of Mg (24.31g/1mol) = 53.48 g of MG

8. 6 mol H + 3 mol O → 3 mol H20

9. 1 mol Cl + 1 mol Cl → 1 mol Cl2

10. 5 mol Na + 4 mol Cl → 4 mol NaCl + 1 mol Na (excess)

EMPIRICAL AND MOLECULAR FORMULA


This article is about analytical chemistry. For observation rather than theory, see Empirical relationship.

In chemistry, the empirical formula of a chemical compound is the simplest positive integer ratio of atoms present in a compound.[1] A simple example of this concept is that the empirical formula of hydrogen peroxide, or H2O2, would simply be HO.

An empirical formula makes no mention towards arrangement or number of atoms. It is standard for a lot of ionic compounds, like CaCl2, and for macromolecules, such as SiO2.

The molecular formula on the other hand shows the number of each type of atom in a molecule, also the structural formula shows the arrangement of the molecule. It is possible for different types of compounds to have equal empirical formulas.

Examples

• Glucose (C6H12O6), ribose (C5H10O5), acetic acid (C2H4O2), and formaldehyde (CH2O) all have different molecular formulas but the same empirical formula: CH2O. This is the actual molecular formula for formaldehyde, but acetic acid has double the number of atoms, ribose has five times the number of atoms, and glucose has six times the number of atoms.

• The chemical compound n-hexane has the structural formula CH3CH2CH2CH2CH2CH3, which shows that it has 6 carbon atoms arranged in a chain, and 14 hydrogen atoms. Hexane’s molecular formula is C6H14, and its empirical formula is C3H7, showing a C:H ratio of 3:7.

Calculation

Suppose you are given a compound such as methyl acetate, a solvent commonly used in paints, inks, and adhesives. When methyl acetate was chemically analyzed, it was discovered to have 48.64% carbon (C), 8.16% hydrogen (H), and 43.20% oxygen (O). For the purposes of determining empirical formulas, we assume that we have 100 g of the compound. If this is the case, the percentages will be equal to the mass of each element in grams.

Step 1

Change each percentage to an expression of the mass of each element in grams. That is, 48.64% C becomes 48.64 g C, 8.16% H becomes 8.16 g H, and 43.20% O becomes 43.20 g O.

Step 2

Convert the amount of each element in grams to its amount in moles.


Step 3

Divide each of the found values by the smallest of these values (2.7)


Step 4

If necessary, multiply these numbers by integers in order to get whole numbers; if an operation is done to one of the numbers, it must be done to all of them.


Thus, the empirical formula of methyl acetate is C3H6O2. This formula also happens to be methyl acetate’s molecular formula.


Problem


The simplest formula for vitamin C is C3H4O3. Experimental data indicates that the molecular mass of vitamin

C is about 180. What is the molecular formula of vitamin C?


Solution


First, calculate the sum of the atomic masses for C3H4O3. Look up the atomic masses for the elements from the Periodic Table. The atomic masses are found to be: H is 1.01, C is 12.01, O is 16.00

Plugging in these numbers, the sum of the atomic masses for C3H4O3 is:

3(12.0) + 4(1.0) + 3(16.0) = 88.0

This means the formula mass of vitamin C is 88.0. Compare the formula mass (88.0) to the approximate molecular mass (180). The molecular mass is twice the formula mass (180/88 = 2.0), so the simplest formula must be multiplied by 2 to get the molecular formula:

molecular formula vitamin C = 2 x C3H4O3 = C6H8O6.

answer:C6H8O6


An approximate molecular mass is usually sufficient to determine the formula mass, but the calculations tend not to work out ‘even’ as in this example. You are looking for the closest whole number to multiply by the formula mass to get the molecular mass.

In chemistry and physics, the Avogadro constant (symbols: L, NA) is defined as the number of constituent particles (usually atoms or molecules) per mole of a given substance, where the mole (abbreviation: mol) is one of the seven base units in the International System of Units (SI). The Avogadro constant has dimensions of reciprocal mol and its value is equal to 6.02214129(27)×1023 mol−1. The constant happens to be quite close to an integer power of two, specifically only about 0.37% less than 279 mol−1, making the latter a useful approximation in nuclear physics when considering chain reaction growth rates.[citation needed]

Previous definitions of chemical quantity involved Avogadro’s number, a historical term closely related to the Avogadro constant but defined differently: Avogadro’s number was initially defined by Jean Baptiste Perrin as the number of atoms in one gram-molecule of atomic hydrogen, meaning (in modern terminology) one gram of (atomic) hydrogen. It was later redefined as the number of atoms in 12 grams of the isotope carbon-12 and still later generalized to relate amounts of a substance to their molecular weight.[4] For instance, to a first approximation, 1 gram of hydrogen, which has a mass number of 1 (atomic number 1), has 6.023×1023 hydrogen atoms. Similarly, 12 grams of carbon 12, with the mass number of 12 (atomic number 6), has the same number of carbon atoms, 6.023×1023. Avogadro’s number is a dimensionless quantity and has the numerical value of the Avogadro constant given in base units.

The Avogadro constant is fundamental to understanding both the makeup of molecules and their interactions and combinations. For instance, since one atom of oxygen will combine with two atoms of hydrogen to create one molecule of water (H2O), one can similarly see that one mole of oxygen (6.022×1023of O atoms) will combine with two moles of hydrogen (2 × 6.022×1023 of H atoms) to make one mole of H2O.

Mole and moles are frequently abbreviated as mol in chemical and mathematic notation.

Revisions in the base set of SI units necessitated redefinitions of the concepts of chemical quantity and so Avogadro’s number, and its definition, was deprecated in favor of the Avogadro constant and its definition. Changes in the SI units are proposed that will precisely fix the value of the constant to exactly 6.02214X×1023 when it is expressed in the unit mol−1 (see New SI definitions, in which an “X” at the end of a number means one or more final digits yet to be agreed upon).

Value of NA[5] in various units

6.02214129(27)×1023 mol−1

2.73159734(12)×1026 (lb-mol)−1

1.707248434(77)×1025 (oz-mol)−1

History

The Avogadro constant is named after the early 19th century Italian scientist Amedeo Avogadro, who in 1811 first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas.[6] The French physicist Jean Perrin in 1909 proposed naming the constant in honor of Avogadro.[7]Perrin won the 1926 Nobel Prize in Physics, largely for his work in determining the Avogadro constant by several different methods.[8]

The value of the Avogadro constant was first indicated by Johann Josef Loschmidt who in 1865 estimated the average diameter of the molecules in air by a method that is equivalent to calculating the number of particles in a given volume of gas.[9] This latter value, the number density of particles in an ideal gas, is now called the Loschmidt constant in his honor, and is related to the Avogadro constant, NA, by


where p0 is the pressure, R is the gas constant and T0 is the absolute temperature. The connection with Loschmidt is the root of the symbol L sometimes used for the Avogadro constant, and German language literature may refer to both constants by the same name, distinguished only by the units of measurement.[10]

Accurate determinations of Avogadro’s number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron in 1910. The electric charge per mole of electrons is a constant called the Faraday constant and had been known since 1834 when Michael Faraday published his works on electrolysis. By dividing the charge on a mole of electrons by the charge on a single electron the value of Avogadro’s number is obtained.[11] Since 1910, newer calculations have more accurately determined the values for the Faraday constant and the elementary charge. (See below)

Perrin originally proposed the name Avogadro’s number (N) to refer to the number of molecules in one gram-molecule of oxygen (exactly 32g of oxygen, according to the definitions of the period),[7] and this term is still widely used, especially in introductory works.[12] The change in name to Avogadro constant (NA) came with the introduction of the mole as a base unit in the International System of Units (SI) in 1971,[13] which recognized amount of substance as an independent dimension of measurement.[14] With this recognition, the Avogadro constant was no longer a pure number, but had a unit of measurement, the reciprocal mole (mol−1).[14]

While it is rare to use units of amount of substance other than the mole, the Avogadro constant can also be expressed in units such as the pound mole (lb-mol) and the ounce mole (oz-mol).

NA = 2.73159757(14)×1026 (lb-mol)−1 = 1.707248479(85)×1025 (oz-mol)−1

General role in science

Avogadro’s constant is a scaling factor between macroscopic and microscopic (atomic scale) observations of nature. As such, it provides the relation between other physical constants and properties. For example, it establishes a relationship between the gas constant R and the Boltzmann constant kB,


and the Faraday constant F and the elementary charge e,


The Avogadro constant also enters into the definition of the unified atomic mass unit, u,


where Mu is the molar mass constant.

Measurement

Coulometry

The earliest accurate method to measure the value of the Avogadro constant was based on coulometry. The principle is to measure the Faraday constant, F, which is the electric charge carried by one mole of electrons, and to divide by the elementary charge, e, to obtain the Avogadro constant.


The classic experiment is that of Bower and Davis at NIST,[15] and relies on dissolving silver metal away from the anode of an electrolysis cell, while passing a constant electric current I for a known time t. If m is the mass of silver lost from the anode and Ar the atomic weight of silver, then the Faraday constant is given by:


The NIST scientists devised a method to compensate for silver lost from the anode by mechanical causes, and conducted an isotope analysis of the silver used to determine its atomic weight. Their value for the conventional Faraday constant is F90 = 96,485.39(13) C/mol, which corresponds to a value for the Avogadro constant of 6.0221449(78)×1023 mol−1: both values have a relative standard uncertainty of 1.3×10−6.

Electron mass measurement[edit]

The Committee on Data for Science and Technology (CODATA) publishes values for physical constants for international use. It determines the Avogadro constant[16] from the ratio of the molar mass of the electron Ar(e)Mu to the rest mass of the electron me:


The relative atomic mass of the electron, Ar(e), is a directly-measured quantity, and the molar mass constant, Mu, is a defined constant in the SI. The electron rest mass, however, is calculated from other measured constants:[16]


As may be observed in the table of 2006 CODATA values below,[17] the main limiting factor in the precision of the Avogadro constant is the uncertainty in the value of the Planck constant, as all the other constants that contribute to the calculation are known more precisely.

Constant Symbol 2006 CODATA value Relative standard uncertainty Correlation coefficient

with NA

Electron relative atomic mass Ar(e) 5.485 799 0943(23)×10–4 4.2×10–10 0.0082

Molar mass constant

Mu 0.001 kg/mol = 1 g/mol Defined —

Rydberg constant

R∞ 10 973 731.568 527(73) m−1 6.6×10–12 0.0000

Planck constant

h 6.626 068 96(33)×10–34 J s 5.0×10–8 −0.9996

Speed of light

c 299 792 458 m/s Defined —

Fine structure constant

α 7.297 352 5376(50)×10–3 6.8×10–10 0.0269

Avogadro constant NA 6.022 141 79(30)×1023 mol−1 5.0×10–8 1

X-ray crystal density (XRCD) methods[edit]


Ball-and-stick model of the unit cell of silicon. X-ray diffraction measures the cell parameter, a, which is used to calculate a value for Avogadro’s constant.

A modern method to determine the Avogadro constant is the use of X-ray crystallography. Silicon single crystals may be produced today in commercial facilities with extremely high purity and with few lattice defects. This method defines the Avogadro constant as the ratio of the molar volume, Vm, to the atomic volume Vatom:

where and n is the number of atoms per unit cell of volume Vcell.

The unit cell of silicon has a cubic packing arrangement of 8 atoms, and the unit cell volume may be measured by determining a single unit cell parameter, the length of one of the sides of the cube, a.[18]

In practice, measurements are carried out on a distance known as d220(Si), which is the distance between the planes denoted by the Miller indices {220}, and is equal to a/√8. The 2006 CODATA value for d220(Si) is 192.0155762(50) pm, a relative uncertainty of 2.8×10−8, corresponding to a unit cell volume of 1.60193304(13)×10−28 m3.

The isotope proportional composition of the sample used must be measured and taken into account. Silicon occurs in three stable isotopes (28Si, 29Si,30Si), and the natural variation in their proportions is greater than other uncertainties in the measurements. The atomic weight Ar for the sample crystal can be calculated, as the relative atomic masses of the three nuclides are known with great accuracy. This, together with the measured density ρ of the sample, allows the molar volume Vm to be determined:


where Mu is the molar mass constant. The 2006 CODATA value for the molar volume of silicon is 12.058 8349(11) cm3mol−1, with a relative standard uncertainty of 9.1×10−8.[19]

As of the 2006 CODATA recommended values, the relative uncertainty in determinations of the Avogadro constant by the X-ray crystal density method is 1.2×10−7, about two and a half times higher than that of the electron mass method.

One of the master opticians at the Australian Centre for Precision Optics (ACPO) holding a one-kilogram single-crystal silicon sphere for the International Avogadro Coordination.

The International Avogadro Coordination (IAC), often simply called the “Avogadro project”, is a collaboration begun in the early 1990s between various national metrology institutes to measure the Avogadro constant by the X-ray crystal density method to a relative uncertainty of 2×10−8 or less.[20] The project is part of the efforts to redefine the kilogram in terms of a universal physical constant, rather than the International Prototype Kilogram, and complements the measurements of the Planck constant using watt balances.[21][22] Under the current definitions of the International System of Units (SI), a measurement of the Avogadro constant is an indirect measurement of the Planck constant:


The measurements use highly polished spheres of silicon with a mass of one kilogram. Spheres are used to simplify the measurement of the size (and hence the density) and to minimize the effect of the oxide coating that inevitably forms on the surface. The first measurements used spheres of silicon with natural isotopic composition, and had a relative uncertainty of 3.1×10−7.[23][24][25] These first results were also inconsistent with values of the Planck constant derived from watt balance measurements, although the source of the discrepancy is now believed to be known.[22]

The main residual uncertainty in the early measurements was in the measurement of the isotopic composition of the silicon to calculate the atomic weight so, in 2007, a 4.8-kg single crystal of isotopically-enriched silicon (99.94% 28Si) was grown,[26][27] and two one-kilogram spheres cut from it. Diameter measurements on the spheres are repeatable to within 0.3 nm, and the uncertainty in the mass is 3 µg. Full results from these determinations were expected in late 2010.[28] Their paper, published in January 2011, summarized the result of the International Avogadro Coordination and presented a measurement of the Avogadro constant to be 6.02214078(18)×1023 mol−1

Avogadro’s Number in Practice

How on Earth did chemists settle on such a seemingly arbitrary figure for Avogadro’s number? To understand how it was derived, we have to first tackle the concept of the atomic mass unit (amu). Theatomic mass unit is defined as 1/12 of the mass of one atom of carbon-12 (the most common isotope of carbon). Here’s why that’s neat: Carbon-12 has six protons, six electrons and six neutrons, and because electrons have very little mass, 1/12 of the mass of one carbon-12 atom is very close to the mass of a single proton or a single neutron. The atomic weights of elements (those numbers you see below the elements on the periodic table) are expressed in terms of atomic mass units as well. For instance, hydrogen has, on average, an atomic weight of 1.00794 amu.

Unfortunately, chemists don’t have a scale that can measure atomic mass units, and they certainly don’t have the ability to measure a single atom or molecule at a time to carry out a reaction. Since different atoms weigh different amounts, chemists had to find a way to bridge the gap between the invisible world of atoms and molecules and the practical world of chemistry laboratories filled with scales that measure in grams. In order to do this, they created a relationship between the atomic mass unit and the gram, and that relationship looks like this:

1 amu = 1/6.0221415 x 1023 grams

This relationship means that if we had Avogadro’s number, or one mole, of carbon-12 atoms (which has an atomic weight of 12 amu by definition), that sample of carbon-12 would weigh exactly 12 grams. Chemists use this relationship to easily convert between the measurable unit of a gram and the invisible unit of moles, of atoms or molecules.

Now that we know how Avogadro’s number comes in handy, we need to examine one last question: How did chemists determine how many atoms are in a mole in the first place? The first rough estimate came courtesy of physicist Robert Millikan, who measured the charge of an electron. The charge of a mole of electrons, called a Faraday, was already known by the time Millikan made his discovery.

Dividing a Faraday by the charge of an electron, then, gives us Avogadro’s number. Over time, scientists have found new and more accurate ways of estimating Avogadro’s number, most recently using advanced techniques like using X-rays to examine the geometry of a 1 kilogram sphere of silicon and extrapolating the number of atoms it contained from that data. And while the kilogram is the basis for all units of mass, some scientists want to begin using Avogadro’s number instead, much the way we now define the length of a meter based on the speed of light instead of the other way around.

Atoms and

Molecules


The basic building blocks of the “normal” matter that we see in the Universe are atoms, and combinations of atoms that we call molecules. We first consider atoms and then molecules. However, we shall see that although “normal matter” is composed of atoms and molecules, most of the matter in the Universe is not in the form of atoms or molecules, but rather in the form of a plasma. We discuss plasmas in the next section.

Constituents of Atoms

Atoms are composed of three classes of constituents, as illustrated in the following table.

Constituent Symbol Charge Mass

Electrons e- -1 9.1 x 10-28 g

Protons p+ +1 1836 x electron mass

Neutrons n 0 Approximately that of p+


Thus, most of the mass of atoms resides in the neutrons and protons which occupy the dense central region called the nucleus (see the Bohr atom below).

The number of protons (or the number of electrons) is called the atomic number for the atom. The total number of protons plus neutrons is called the atomic mass number for the atom. Atoms are electrically neutral because the number of negatively-charged electrons is exactly equal to the number of positively-charged protons. The number of neutrons is approximately equal to the number of protons for stable light nuclei, and is about 1-2 times the number of protons for the heavier stable nuclei.

Isotopes of an Element

Atoms having the same number of protons (and therefore the same number of electrons) but different numbers of neutrons are called isotopes of the element in question. Thus, the isotopes of an element have the same atomic number but differ in their atomic mass number. A compact notation for isotopes of an element is illustrated by the following examples.


In this notation the element is represented by its chemical symbol, the atomic number is denoted by a lower left subscript, the number of neutrons is denoted by a lower right subscript, and the atomic mass number is denoted by an upper left superscript (some of these superscripts and subscripts may be omitted, depending on the context).

Thus, the above symbols denote, respectively, the mass-235 and mass-238 isotopes of uranium (symbol U), and the mass-1,-2,and -3 isotopes of hydrogen (symbol H). The mass-2 isotope of hydrogen is also called deuterium and the mass-3 isotope is also called tritium.

Periodic Table of the Elements

The elements have properties that repeat themselves periodically with variation of the number of electrons (atomic number). A chart of the elements arranged to show this periodicity is termed a periodic table (of the elements). Here is a periodic table of the elements which gives the atomic number and symbol for all elements, and the name and basic chemical properties for each of these elements if you click on the element’s symbol in the resulting table.