A-level Chemistry/WJEC/Module 1/Atoms

The Atom

The word atom comes from the Greek for "indivisible". An atom is the smallest particle of a chemical element that retains the chemical properties of the element. Atoms are composed of subatomic particles, and to understand the behaviour of an atom we must first understand its constituent particles.

An atom is made of electrons, which "orbit" a central nucleus. The nucleus consists of protons and neutrons.

Electrons

Electrons are tiny, electrically-charged particles. They have a negative charge, very little mass and they exist in the empty space surrounding the nucleus of the atom which contains all the other particles. In their elemental states atoms are not charged and will have the same number of electrons as they have protons. Electrons can behave as particles and also as waves; this is known as the wave-particle duality of matter. It is only significant for things which are of similar size to atomic particles. Electrons exist in different energy levels or orbitals, filling the lowest energy levels first.

Protons

Protons are much larger than electrons. They are 1836 times heavier than an electron and they have a positive charge equal and opposite to that of an electron.

Neutrons

Neutrons were the last of the nuclear particles to be discovered. They have no charge so they are not deflected by a magnetic field. They are almost the same weight as protons (1839 times heavier than an electron), and normally there are more neutrons than protons in a nucleus of an atom.

• A few light atoms have equal numbers of protons and neutrons. Calcium-40 (4020Ca) is the heaviest stable atom with equal numbers of protons and neutrons.

• Hydrogen-1 (11H) is the only atom with no neutrons. Helium-3 (32He) is the only other stable atom with fewer neutrons than protons.

Atomic Number, Mass Number and Charge

Atoms are normally described in terms of two key numbers, their atomic number and their mass number.

Atomic Number (Z)

The number of protons in the nucleus is the most important aspect of an atom. This number determines which element an atom belongs to. The atomic number of an atom can tell you:

• The number of protons in the nucleus of the atom
• The number of electrons in the atom when it is neutral
• The atom's position in the periodic table

Mass Number (A)

Nearly all of an atom's mass comes from the nucleus. Since we know that the mass of a proton is almost equal to that of a neutron, we can measure the mass of an atom in terms of the number of particles in its nucleus. The mass number can tell you:

• The total number of particles in the nucleus
• The number of neutrons in the nucleus (remember to subtract the atomic number)
• The relative atomic mass of an atom

Charge (Q)

An atom, strictly speaking, has no electrical charge. This means that the number of electrons must be equal to the number of protons.

If there are more, or fewer, electrons than protons, then the atom has an electrical charge and we call it an ion.

Positive ions are called cations. Negative ions are called anions.

The electrical charge (Q) is the number of protons (Z) minus the number of electrons (E)

Q = Z - E

It is useful to rearrange this to find the number of electrons: E = Z - Q

Summary Table

Particle Name	Relative Mass (unified atomic mass unit)	Mass (kg)	Relative Charge
Electron	1/1836	9.11 x 10-31	-1
Proton	1	1.67 x 10-27	+1
Neutron	1	1.67 x 10-27	0

Isotopes

Isotopes are Atoms with the same atomic number but different mass number

Isotopes are shown like this:

AZX^Q

Where A is the mass number, Z is the atomic number, Q is the charge on the atom and X is the symbol for that element.

Isotopes Of Hydrogen

For example, hydrogen has three isotopes.

Name	Protium	Deuterium	Tritium
Symbol	11H	21H	31H
Protons	1	1	1
Neutrons	0	1	2

Isotope Calculations

It is fairly simple to work out the number of each sub-atomic particle from an isotope's symbol:

4020Ca²⁺

The number of protons is equal to Z = 20

The number of neutrons (sometimes called N) is equal to A - Z = 40 - 20 = 20

The number of electrons in an atom/ion is equal to Z - Q = 20 - (+2) = 18

Using these rules, you should be able to work out that a calcium-40 ion has 20 protons, 20 neutrons and 18 electrons.

3717Cl^–

The number of protons is equal to Z = 17

The number of neutrons is equal to A - Z = 37 - 17 = 20

The number of electrons in an atom/ion is equal to Z - Q = 17 - (-1) = 18

Using these rules, you should be able to work out that a chloride-37 ion has 17 protons, 20 neutrons and 18 electrons.

Radioactivity

Only some combinations of protons and neutrons will make a stable nucleus. If the protons and neutrons are in the wrong proportions, the nucleus will eject or capture a subatomic particle and become a new nucleus.

Plotting proton number against neutron number shows which atoms are stable (black) and which are unstable until they change the ratio of protons to neutrons.

Alpha emission

21084Po → 20682Pb + 42α

Notice how A and Z balance: A = 210 = 204 + 4 and Z = 84 = 82 + 2

Beta emission

146C → 147N + 0-1β

Notice again how A and Z balance: A = 14 = 14 + 0 and Z = 6 = 7 - 1

For radioactive particles, we use Z to mean "charge" and not simply "number of protons".

Positron emission

189F → 188O + 0+1β

This process is not taught at GCSE. A positron is the antiparticle of the electron. It is just like an electron except it has a positive charge. Molecules containing fluorine-18 are injected into patients for medical scans.

If a positron meets an electron, they annihilate one another and release pure energy:

0+1β + 0-1e → 2 00γ

Electrons are very common, so this annihilation usually occurs very soon after the positron is emitted.

The γ rays from this process can be detected outside the body, in a scan called positron emission tomography (PET).

Electron capture

4823V + 0-1e → 4822Ti

This is another process not taught at GCSE. It is the only process we need to know where the nucleus captures a particle. Notice that we call the particle an electron (0-1e) when it is captured, but we call it a β-particle when it is emitted (0-1β). It is the same particle, though!

Electron capture causes the same change of nucleus as positron emission, and some nuclei can react in both ways:

189F → 188O + 0+1β

189F + 0-1e → 188O

Gamma emission

111m48Cd → 11148Cd + 00γ

Gamma emission releases excess energy from the nucleus, but does not alter A or Z. Nuclei with excess energy are called "nuclear isomers" and are given the "meta" symbol "m".

Gamma emission usually happens at the same time as another radioactive process:

24195Am → 23793Np + 42α + 00γ

Summary

Effect of three major radioactive transformations on the mass number and atomic number. Electron capture has the same effect as positron (0+1β⁺) emission.

Half-life

Radioactive decay processes follow a pattern defined by a constant half-life (t_½). The half-life is the time taken for 50 % of the radioactive atoms to decay. This is also the time it takes for the radioactivity to decrease to 50 % of its original value.

x is the number of half-lives that have passed.

• After 1 half-life (x = 1), 50 % (¹/₂) of radioactive atoms remain.
• After 2 half-lives (x = 2), 25 % (¹/₄)of radioactive atoms remain.
• After 3 half-lives (x = 3), 12.5 % (¹/₈) of radioactive atoms remain.
• After 4 half-lives (x = 4), 6.25 % (¹/₁₆) of radioactive atoms remain.

The fraction of atoms that remain is 2^-x. For example, after 3 half-lives (x = 3), 2^-3 = ¹/₈ = 12.5 % of radioactive atoms remain.

To find the fraction from the percentage, divide 100 % by the percentage of radioactive atoms remaining. For example, 6.25 % = 100 % / 6.25 % = 16 = 2⁴, so x = 4 half-lives.

Each radioactive isotope has its own half-life. For example, t_½ for ²⁴¹Am is 432.6 y (years), t_½ for ²¹⁰Po is 138.376 d (days) and t_½ for ¹⁸F is 109.734 m (minutes).

Questions take three forms, asking you to find either the half-life, the fraction of radioactive atoms remaining, or the time taken.

A sample of ¹⁸F decays to 12.5 % of its original radioactivity after 329.202 minutes. What is its half-life?

12.5 % is ¹/₈ = 2^-3, so x = 3 half-lives.

If 329.202 minutes is 3t_½ then t_½ = 109.734 minutes.

²⁴¹Am has a half-life of 432.6 y. How long will it take before its radioactivity drops to 25 % of its original rate?

25 % is ¹/₄ = 2^-2, so x = 2 half-lives.

t_½ = 432.6 y so 2t_½ = 865.2 years.

²¹⁰Po has a half-life of 138.376 days. A sample is stored for 553.504 days. What percentage of the original ²¹⁰Po will be left?

553.504 days is 553.504 / 138.376 = 4 half-lives. (i.e. x = 4 half lives)

The fraction left is 2^-4 = ¹/₁₆ = ^100 %/₁₆ = 6.25 %

In WJEC Chemistry questions, x will always be a whole number, and the fractions will always be ¹/₂, ¹/₄, ¹/₈, ¹/₁₆, etc. In real life (and exams in Physics and Maths), x is a continuous variable and is not restricted to whole numbers.

Electronic Configurations

Electrons in Atoms

Most of the way that atoms behave is governed by the interactions of their electrons. When you sit on a chair the force that stops you from moving through it is the repulsion between the electrons in the atoms that make up the chair and those that make up your body.

In order to understand chemical reactions, you must understand how electrons exist in atoms. Much about what we know of electrons comes from quantum theory, which states that electrons can be described by four quantum numbers. The only one you need to know about is the principal quantum number, which describes the energy level of an electron.

Energy Levels

In your GCSE chemistry you will have come across the principle quantum number in the form of electron shells. The number is given the symbol n, so that if we say 'the electron is in n = 3' what we mean is 'the electron is in the third shell, or energy level'. Each energy level can accommodate a certain number of electrons.

n=	Maximum Electrons
1	2
2	8
3	18

At GCSE, you would have been taught to denote the electronic configuration of that atom like this:

Examples:

Lithium (3): 2,1 Sodium (11): 2,8,1

At AS level we look deeper and divide the shells into a number of subshells. Pairs of electrons are known as atomic orbitals.
s subshells hold 2 electrons (or 1 orbital),
p subshells hold 6 electrons (or 3 orbitals),
d subshells hold 10 electrons (or 5 orbitals),
f subshells hold 14 electrons (or 7 orbitals).

The subshells are arranged in the following order:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, ....

note that the 4s orbital fills before the 3d!!

This sounds daunting but with practice you will learn the correct order. All you have to remember is the order the subshells come in and the number of electrons each shell holds.

To denote the electronic configuration you simply write out that order, raising the number of electrons in each subshell as a superscript.

So Hydrogen-1 (1) is simply 1s¹

Lithium (3) is 1s²2s¹

Sodium (11) is 1s²2s²2p⁶3s¹

Orbitals also have a paired spin, one counterclockwise and one clockwise. You can denote this by drawing a box with an up and down arrow in it. You must remember, if asked to construct a diagram in an exam, that on each shell (say 2p) you always fill in the 3 orbitals first with arrows going in one direction (say fill in all 3 boxes with up arrows before filling in the down arrows). So if there are only meant to be 2 electrons in the 2p subshell, draw 2 up arrows in 2 separate orbitals and don't draw an up and down arrow in just one orbital.

The best evidence chemists have for the existence of the energy levels comes from ionisation energies.

Ionisation energy, E_i

Atoms are ionised when they lose an electron. The energy required to remove the electron is known as the ionisation energy. As each electron is removed from an atom the ionisation energy required increases, so we call the energy required to remove the first electron the first ionisation energy, the energy required to remove the second electron the second ionisation energy and so on. To be more accurate, the first ionisation energy is the amount of energy needed to remove one electron from each atom in one mole of gaseous atoms. The second ionisation energy is the amount of energy needed to remove one electron from each ion in one mole of gaseous ions each of which bear a single positive charge.

Example:

The first ionisation energy of chlorine:

Cl(g) → Cl⁺(g) + e^- E_i = +1251 kJ mol^-1

The Hydrogen Emission Spectrum

The spectral series of hydrogen, on a logarithmic scale.

The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to electrons moving between energy levels in the atom.

Physics

The spectral lines of hydrogen correspond to particular jumps of the electron between energy levels. The simplest model of the hydrogen atom is given by the Bohr model. When an electron jumps ("relaxes") from a higher energy to a lower, a photon of a specific wavelength is emitted.

Electron transitions and their resulting wavelengths for Hydrogen. Energy levels are not to scale.

The spectral lines are grouped into series according to n'.

Series

All wavelengths are given to 3 significant figures.

Lyman series (n′ = 1)

Main article: w:Lyman series

$n$	λ (nm)
2	122
3	103
4	97.2
5	94.9
6	93.7
$\infty$	91.1

The series is named after its discoverer, Theodore Lyman, who discovered the spectral lines from 1906-1914. All the wavelengths in the Lyman series are in the ultraviolet band.

Balmer series (n′ = 2)

Main article: w:Balmer series

$n$	λ (nm)
3	656
4	486
5	434
6	410
7	397
$\infty$	365

Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen. Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen.

The four visible hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right.

Paschen series (n′ = 3)

$n$	λ (nm)
4	1870
5	1280
6	1090
7	1000
8	954
$\infty$	820

Named after the Austro-German physicist Friedrich Paschen who first observed them in 1908. The Paschen lines all lie in the infrared band.

Notice that the limiting wavelengths are related: The ratio 91.1 nm : 365 nm : 820 nm is 1 : 4 : 9

The limits of the first five series are 91.1 nm, 365 nm, 820 nm, 1458 nm and 2297 nm in a 1 : 4 : 9 : 16: 25 ratio.

91.13 nm corresponds to the maximum energy an electron can hold, while still being in a shell of the hydrogen atom. In other words, it measures the ionisation energy (E_i) of hydrogen.

91.13 nm gives 3.00 x 10⁸ m s^-1 / 91.13 x 10^-9 m = 3.292 x 10¹⁵ Hz

f = c / λ

3.292 x 10¹⁵ Hz gives 3.292 x 10¹⁵ Hz x 6.63 x 10^-34 J s = 2.183 x 10^-18 J

E = hf

2.183 x 10^-18 J gives 2.183 x 10^-18 x 6.02 x 10²³ mol^-1 = 1314 kJ mol^-1

E_m = EN_A

In this case, the molar energy is the ionisation energy; E_m = E_i