P4 Atomic structure

Atoms are extremely small, with a radius of about 1 × 10⁻¹⁰ m. An atom has a tiny, positively charged central nucleus surrounded by negatively charged electrons.

The nucleus is very small compared to the whole atom — its radius is less than 1/10 000 of the atom's radius. However, it contains almost all of the atom's mass.

Electrons are arranged at specific distances from the nucleus, in what are called energy levels or shells.

If an electron absorbs electromagnetic radiation, it moves to a higher energy level, which is further away from the nucleus.

If an electron emits electromagnetic radiation, it drops to a lower energy level, which is closer to the nucleus.

Left: an electron absorbs EM radiation and moves out to a higher energy level. Right: an electron drops to a lower energy level and emits EM radiation. Dashed circles show where each electron moves to.

The nucleus of an atom has a radius of 3 × 10⁻¹⁵ m. The nucleus radius is less than 1/10 000 of the atom's radius. What is the smallest the atom's radius could be?

The atom's radius is more than 10 000 (10⁴) times the nucleus radius, so multiply.

Smallest atom radius = 3 × 10⁻¹⁵ × 10⁴ = 3 × 10⁻¹¹ m.

Check: multiplying by 10⁴ makes the power of ten 4 bigger (−15 + 4 = −11).

A factor of 10⁴ means 10 000 times bigger, not 4 times bigger.

Remember that the nucleus is positively charged. The negative electrons are in the energy levels outside it.

Because the nucleus is so tiny compared to the whole atom, most of an atom is just empty space.

Electrons must absorb radiation to move further out, and they emit radiation to drop closer in.

The atomic number of an atom is the number of protons in its nucleus. Every atom of a given element has the same atomic number.

The mass number of an atom is the total number of protons and neutrons in its nucleus.

Isotopes are atoms of the same element that have different numbers of neutrons. This means they have the same atomic number but different mass numbers. They have the same nuclear charge but different masses.

In a neutral atom, the number of negative electrons equals the number of positive protons, so the atom has no overall electrical charge. If an atom loses one or more outer electrons, it becomes a positive ion.

Nuclide notation shows the mass number at the top left of the chemical symbol and the atomic number at the bottom left.

An atom of uranium-235 is written as . How many protons, neutrons and electrons does a neutral atom of uranium-235 contain?

The bottom number is the atomic number, so there are 92 protons.

In a neutral atom, electrons equal protons, so there are 92 electrons.

The top number is the mass number (protons + neutrons). Number of neutrons = mass number − atomic number = 235 − 92 = 143 neutrons.

The top number is the mass number. Do not confuse it with the atomic number or use it directly as the number of neutrons.

To find the number of neutrons, always subtract the bottom number from the top number.

Ions are formed by gaining or losing electrons only. The nucleus (protons and neutrons) does not change.

Models change when new evidence does not fit them.

Solid sphere: before electrons were discovered, atoms were tiny spheres that could not be divided.

Plum pudding model: a ball of positive charge with negative electrons embedded in it.

Nuclear model: alpha particle scattering showed the mass is concentrated in a tiny, positive nucleus, with electrons outside it.

Bohr: electrons orbit at specific distances (energy levels); his calculations agreed with experiments.

Protons and neutrons: the nuclear charge is a whole number of identical positive particles, protons. About 20 years after the nucleus was accepted, James Chadwick showed neutrons exist.

Most alpha particles pass far from the nucleus and go almost straight through; a few pass close and are deflected; a very few head almost straight at it and bounce back.

A very small number of alpha particles bounced back from the gold foil. Explain why this means the positive charge and mass of an atom are packed into a tiny region.

Alpha particles are positive and fast, so turning one round needs a very large repelling force.

Positive charge spread through the whole atom (plum pudding) would give only a weak force and small deflections.

A very large force needs the charge concentrated, so the alpha particle can get very close to it. It bounced back rather than pushing the target aside, so the target is much more massive than the alpha particle.

So few bounced back because the nucleus is a tiny target.

The plum pudding model has no nucleus and no empty space.

Alpha particles are repelled by the positive nucleus, not by electrons.

Details of Bohr's and Chadwick's experiments are not needed.

An unstable nucleus gives out nuclear radiation as it changes to become more stable. This is radioactive decay.

Decay is random — you cannot predict which nucleus will decay next or when.

Activity is the rate at which unstable nuclei decay, measured in becquerels (Bq). 1 Bq means 1 decay per second.

Count-rate is the number of decays recorded each second by a detector. It is smaller than the activity.

Types of nuclear radiation:

Alpha: 2 protons and 2 neutrons (helium nucleus). Strongly ionising, travels a few centimetres in air, stopped by paper.

Beta: high-speed electron from the nucleus. Moderately ionising, passes through paper, stopped by a few millimetres of aluminium.

Gamma: electromagnetic radiation. Weakly ionising, long range in air, only reduced by thick lead or concrete.

Neutron: also emitted from some unstable nuclei.

Alpha is stopped by paper, beta passes through paper but is stopped by aluminium, and gamma is reduced by thick lead.

A factory makes steel sheets about 1 cm thick. Which radiation should a thickness gauge use, and why?

Alpha and beta would be stopped completely by 1 cm of steel, so the detector would read nothing whatever the thickness.

Gamma passes through, and a little more is absorbed when the sheet is thicker. So use a gamma source: the count-rate falls if the steel gets too thick.

Count-rate is what the detector measures, which is always less than the source's total activity.

Ionising means knocking electrons off atoms to form ions.

Decay is completely random and cannot be sped up by heating.

A nuclear equation shows a radioactive decay. Each nucleus has its mass number (protons + neutrons) top left and its atomic number (protons) bottom left.

Alpha particle: — a helium nucleus, mass number 4, atomic number 2.

Beta particle: — an electron, mass number 0, atomic number −1.

Balance: the top numbers add up to the same on both sides, and so do the bottom numbers.

Alpha decay: mass number falls by 4 and atomic number by 2.

Beta decay: a neutron turns into a proton, so the mass number is unchanged and the atomic number rises by 1.

Gamma emission: neither number changes (no mass, no charge).

Polonium-210 (atomic number 84) emits an alpha particle. What are the mass number and atomic number of the new nucleus?

Mass number: 210 − 4 = 206. Atomic number: 84 − 2 = 82.

Caesium-137 (atomic number 55) emits a beta particle. Find the new nucleus's numbers.

Mass number stays at 137. Atomic number: 55 + 1 = 56, because 56 + (−1) = 55.

In beta decay the atomic number goes UP by 1: the −1 on the beta particle must be balanced.

In alpha decay take 4 off the mass number but only 2 off the atomic number.

The beta electron comes from the nucleus, not the electron shells.

You do not need to name the new element.

Radioactive decay is random: you cannot predict when a particular nucleus will decay. However, with a very large number of nuclei, a fixed fraction decays in a given time, making the behaviour of the sample predictable.

The half-life of an isotope is the time it takes for the number of unstable nuclei in a sample to halve.

It is also the time it takes for the count-rate (or activity) to fall to half its starting value. Half-life is constant for a given isotope, whatever the starting amount.

A decay curve falls quickly at first, then more slowly, without quite reaching zero. The dashed lines mark where the count-rate has halved once and twice.

Use the decay curve in the diagram to find the half-life of this isotope.

Read the starting count-rate at 0 hours: 800 counts/s.

Halve it: 800 ÷ 2 = 400 counts/s.

Read across from 400 counts/s to the curve, then down to the time axis: 2.5 hours.

Check: it halves again (400 to 200 counts/s) by 5.0 hours, another 2.5 hours. The half-life is 2.5 hours.

Half-life does not mean half the time the source lasts, or that half the mass disappears. It is strictly the time for the number of unstable nuclei to halve.

A radioactive source has not 'all gone' after two half-lives. Its activity halves twice, leaving one-quarter.

Always read the time axis carefully from a graph. The half-life is constant; it does not get shorter as the sample gets smaller.

Contamination: radioactive atoms end up on or inside something where they are not wanted, such as dust on skin or a liquid that has been swallowed. The hazard continues for as long as those atoms keep decaying, and they can be carried elsewhere.

Irradiation: an object is exposed to nuclear radiation from a source outside it. The object does not become radioactive, and the exposure stops when the source is removed or shielded.

Outside the body: alpha is least hazardous (stopped by air or the outer skin); beta and gamma can reach organs.

Inside the body (swallowed or breathed in): alpha is most hazardous. It is strongly ionising and dumps all its energy in a small region of tissue. Most gamma passes out.

Precautions: lead shielding, tongs for distance and short exposure times reduce irradiation; gloves, masks and protective clothing prevent contamination.

A patient swallows a tracer that emits gamma rays, for a scan. Is the patient contaminated, irradiated, or both? What about a nurse standing nearby?

The patient is contaminated: radioactive atoms are inside their body. They are also irradiated by the gamma rays those atoms emit.

The nurse is only irradiated: gamma rays from the patient reach them, but no radioactive atoms get onto them, so the nurse does not become radioactive.

Sterilising equipment with gamma rays is irradiation. It kills bacteria but does not make the equipment radioactive.

Leaving a room stops irradiation from an external source, but contamination on your clothes will stay with you.

Gloves protect against contamination, but do not stop penetrating gamma rays.

Studies of radiation's effects on humans are shared through peer review so other scientists can check the findings, making the conclusions trustworthy.

Half-life is the time for the number of unstable nuclei in a sample to halve, or for the count-rate (or activity) to drop to half.

Higher tier: work out how much is left after a whole number of half-lives, and give the drop as a fraction or ratio.

1. Calculate the number of half-lives by dividing the total time elapsed by the half-life.

2. The fraction of nuclei or activity remaining is (1/2)ⁿ, where n is the number of half-lives.

3. Multiply the initial activity or number of nuclei by this fraction to find the final value.

4. To find the fraction that has decayed, subtract the fraction remaining from 1.

Radon-222 has a half-life of 3.8 days. A sample has an activity of 1600 Bq. What is its activity after 15.2 days?

Number of half-lives = 15.2 ÷ 3.8 = 4

Fraction remaining = (1/2)⁴ = 1/16

Final activity = 1600 ÷ 16 = 100 Bq (a ratio of 1 : 16)

Bismuth-210 has a half-life of 5 days. What fraction of a sample has decayed after 10 days?

Number of half-lives = 10 ÷ 5 = 2

Fraction remaining = (1/2)² = 1/4

Fraction decayed = 1 − 1/4 = 3/4

Do not confuse the fraction that remains with the fraction that has decayed. Read the question carefully.

Remember to raise 1/2 to the power of the number of half-lives (e.g. 2³ = 8). A common mistake is to multiply by 2 instead (2 × 3 = 6).

If you are given the final activity and asked for the initial activity, you must multiply the final activity by 2 for each half-life to work backwards.