7 Radioactivity and particles

Method: first identify the measured quantity, then choose a sensible unit and convert all values to a common unit before calculating. Write the symbol after the value: for example, an activity of 450 Bq, a source-detector distance of 3.0 cm, or a counting time of 60 s. A duration of 2 h 30 min is 150 min or 9000 s.

X is the element symbol, Z is the number of protons, and A is the total number of protons and neutrons. The number of neutrons is A - Z. For carbon-14, ¹⁴₆C, the nucleus contains 6 protons and 8 neutrons; a neutral atom also has 6 electrons.

Example: carbon-12 and carbon-14 both have Z = 6, so both contain 6 protons and are carbon. Their neutron numbers are 12 - 6 = 6 and 14 - 6 = 8, so they are different isotopes.

Ionising radiation transfers enough energy to remove electrons from atoms or molecules. The affected particles become ions; removing an electron leaves a positive ion. This ability to ionise is why radiation can change or damage matter.

Radioactive decay is random: it is impossible to predict exactly which unstable nucleus will decay next or the exact time it will decay. For a large collection of nuclei, however, the overall rate follows a predictable statistical pattern.

Strong ionisation makes alpha lose energy rapidly, so it travels the shortest distance. Gamma interacts less often, so it penetrates farther. Penetration and ionisation therefore show an inverse pattern across these three radiations.

Method: 1. Use a Geiger-Müller tube and counter to measure background count for a fixed time. 2. Place the source at a fixed distance and measure the count for the same time. 3. Put an absorber between source and detector, changing only its material or thickness. 4. Repeat readings and calculate means. 5. Subtract the background count rate, then compare the corrected rates.

A lower corrected count rate means more radiation was absorbed. Identify the radiation by the pattern: paper stops alpha, aluminium stops beta, while gamma requires thick lead or concrete for a large reduction.

If Z changes, the daughter nucleus is a different element. Alpha and beta-minus emission therefore change the element; gamma emission does not, and neutron emission leaves the same element but a different isotope.

Method: 1. Add the upper A values on each side. 2. Add the lower Z values on each side. 3. Use the difference to find a missing number or particle. 4. Check both totals; balancing A alone is not enough.

In the example, mass numbers balance because 238 = 234 + 4, and atomic numbers balance because 92 = 90 + 2. The element symbol of the daughter must match its resulting atomic number.

A GM reading should be taken over a stated time, repeated when precision matters, and corrected by subtracting the background count rate. A larger corrected count rate means more ionising events were detected, not necessarily that every emitted particle reached the tube.

Background level varies with location. It can be higher in areas with radioactive rocks or radon, and cosmic exposure increases at high altitude because there is less atmosphere above to absorb the radiation.

As time passes, unstable nuclei decay and are not replaced in a closed sample. Fewer undecayed nuclei remain, so fewer decays occur per second and the activity decreases. The decrease is not linear: equal time intervals do not remove the same fixed number of nuclei.

A detector's count rate is usually lower than the source activity because it detects only some emissions. Correct the reading for background, and use a stated detection fraction when estimating activity. For example, 840 counts/s at 5% detection corresponds to 840 ÷ 0.05 = 16,800 Bq.

After one half-life, one-half remains; after a second, one-quarter remains; after a third, one-eighth remains. Each halving starts from the amount present at that time, not from the original amount.

Different radioactive isotopes have different half-lives. For a particular isotope, half-life is a characteristic statistical timescale: individual nuclei still decay randomly, but a large sample follows the repeatable halving pattern.

A₀ is initial activity, A is remaining activity, t is elapsed time, T₁/₂ is half-life and n is the number of half-lives. Use consistent time units before dividing.

Example: a sample starts at 120 kBq and has a half-life of 12 years. After 48 years, n = 48 ÷ 12 = 4, so 120 → 60 → 30 → 15 → 7.5 kBq.

From a decay graph, choose an activity on the curve, halve it, then read the time difference between the two points. Repeat with another pair to check the estimate. Use a smooth decreasing curve and background-corrected activity or count rate.

Food exposed to gamma rays is irradiated, not contaminated, if the sealed source never contacts it. The radiation can kill microorganisms, but switching off or removing the source ends the exposure and does not make the food radioactive.

Radioactive waste may remain hazardous for many half-lives. Ionising radiation can damage people, while leaked radioactive material can contaminate soil or water. Long-lived waste therefore needs isolation for very long periods rather than ordinary disposal.

Reduce the risk by immobilising and sealing waste in strong corrosion-resistant containers, adding shielding, and storing it in a secure, monitored, geologically stable site away from groundwater. Records, controlled access and continued monitoring are needed so containment failure can be detected and managed.

The nuclear energy store decreases as energy is transferred to the reaction products and surroundings. A power station can ultimately transfer this energy into thermal energy and then electrical energy, while a star's fusion energy reaches space as radiation.

U-235 absorbs a neutron → an unstable U-236 nucleus forms → the unstable nucleus splits into two smaller daughter nuclei → neutrons and energy are released. The energy is carried mainly as kinetic energy of the fast-moving fission products.

The daughter nuclei repel and move apart at high speed. Their kinetic energy is transferred by collisions to surrounding material, increasing its thermal energy; a reactor uses that heating to help generate electricity.

The total nucleon number and total proton number are conserved across a complete fission equation. The exact daughter isotopes can vary, but the defining product pattern remains two daughter nuclei plus a few neutrons.

1. A U-235 nucleus absorbs a neutron and undergoes fission. 2. The fission releases two or three neutrons. 3. Some of these neutrons are absorbed by other U-235 nuclei. 4. Those nuclei split and release still more neutrons. 5. The repeating process forms a chain reaction.

If, on average, one neutron from each fission causes one further fission, the reaction continues at a steady rate. If more than one succeeds, the rate grows; if fewer than one succeeds, the chain reaction dies away.

Lowering control rods farther into the core absorbs more neutrons and reduces reactor power. Raising them absorbs fewer neutrons and allows the rate to increase. Their position is adjusted so the reactor produces the required steady output.

Fission products and radioactive daughter nuclei can emit penetrating radiation, including gamma rays and high-energy neutrons. Without shielding, this radiation could escape, ionise body tissue and increase the risk of cell damage, mutation and cancer.

The total mass of the fusion products is slightly less than the total mass of the original nuclei. This loss of mass corresponds to energy released by the reaction; the energy appears as kinetic energy of products and radiation.

A common fusion pattern joins light hydrogen nuclei into a helium nucleus. The product is larger than either starting nucleus, but its mass is less than the combined starting mass, so energy is released.

In a main-sequence star such as the Sun, hydrogen nuclei ultimately combine to form helium nuclei. Each set of fusion reactions releases energy because the products have slightly less mass than the starting nuclei.

Energy transferred from the core moves through the star and is eventually emitted into space as electromagnetic radiation and carried by particles. This sustained release makes a star hot and luminous.

At low temperature, nuclei move too slowly to overcome the repulsive effect. At low pressure, they are too far apart and collide too rarely. With both conditions high, some collisions bring nuclei close enough for fusion to occur.