5. Nuclear physics

A neutral atom has equal total positive and negative charge. Its nucleus is still positive and its electrons are still negative; neutral describes the combined charge of the whole atom.

Diagrams are models and are not drawn to scale. The nucleus is much smaller than the atom, while the electron region accounts for the atom's overall size.

Lose negative electrons → become positive. Gain negative electrons → become negative. The sign follows the imbalance left after the electron transfer.

A magnesium atom that loses two electrons forms Mg²⁺. A chlorine atom that gains one electron forms Cl⁻.

An alpha particle passing far from a nucleus is nearly undeflected. Passing closer produces stronger repulsion and a larger bend. A near head-on approach can send it back along or near its incoming path.

Together, the results support a nuclear atom: a tiny positively charged nucleus containing most of the mass, surrounded by mostly empty space.

A proton and an electron have equal charge magnitude but opposite signs. A neutron is uncharged; it is not a negatively charged particle.

The charge of a collection of particles is the sum of their relative charges. Protons add positive charge, electrons add negative charge and neutrons add none.

For chlorine-35 with Z = 17: protons = 17, neutrons = 35 − 17 = 18, and a neutral atom has 17 electrons.

A platinum nucleus with 78 protons and 118 neutrons has A = 196 and is written ¹⁹⁶₇₈Pt.

Carbon-12 and carbon-14 both have Z = 6, so both contain 6 protons. Carbon-14 has two more neutrons and a greater nucleon number.

Both processes can release energy. In each energy-releasing reaction, the total mass of the products is slightly smaller than the total mass before the reaction; the mass decrease corresponds to released energy.

Fission pattern: ¹₀n + ²³⁵₉₂U → two smaller nuclei + further ¹₀n particles + energy. The exact product nuclei can vary, but both number sums must balance.

Fusion example: ²₁H + ³₁H → ⁴₂He + ¹₀n + energy. Upper numbers balance 5 = 4 + 1 and lower numbers balance 2 = 2 + 0.

For a neutral atom, Z electrons outside the nucleus supply total charge −Z and balance the nuclear charge +Z.

A helium-3 nucleus has relative mass about 3; a helium-4 nucleus has relative mass about 4. Their charge is the same because both have Z = 2.

A detector can therefore record counts before an experimental source is introduced or after it is removed. This persistent reading is a real environmental contribution, not automatically a detector zero error.

The measured background level depends on the place, surroundings and measuring interval, so it should be measured for the experiment rather than assumed to be zero.

Radon and rocks/buildings are terrestrial sources, food and drink contribute internally after intake, and cosmic rays come from beyond Earth.

A count is one registered detection event. The detector-counter reading does not necessarily equal the number of particles emitted by the source because not every emission reaches or is registered by the detector.

If 360 counts are recorded in 3 minutes, the count rate is 360 ÷ 3 = 120 counts/minute. In seconds, 3 minutes is 180 s, so the same result is 2 counts/s.

Keep the count and time interval together. To compare rates, first express both using the same time unit; 60 counts/minute equals 1 count/s.

Background counts of 170, 164 and 185 in separate 10-minute intervals average to 173 counts in 10 minutes, or 17.3 counts/minute. If the total rate with the source is 949 counts/minute, the corrected rate is 949 − 17.3 ≈ 932 counts/minute.

A corrected decay curve lies below the uncorrected curve by the background rate. An uncorrected curve approaches the background level; a correctly background-subtracted curve approaches zero.

The emission is random. The exact nucleus that will emit next and the exact time of its emission cannot be predicted, so repeated detector readings naturally fluctuate.

The direction is also random. Emissions from many nuclei leave in different directions rather than following one preferred direction.

Although one event is unpredictable, a large sample can show a stable statistical pattern when counts are collected over suitable time intervals.

The radiation that ionises most strongly loses energy most rapidly in matter, so it travels the shortest distance and has the lowest penetrating ability. Gamma interacts less frequently and is therefore the most penetrating.

An electric field exerts forces in opposite directions on positive and negative charges. Beta bends more because its mass is far smaller than the mass of an alpha particle.

For a magnetic-field diagram, use the beam direction, field direction and the force rule for a positive charge; reverse that force direction for β−. The beta path normally has the tighter curvature because beta has much smaller mass.

A larger electric charge produces a stronger electrical interaction with electrons in nearby atoms. An alpha particle has charge +2, so it interacts more strongly than a beta particle with charge −1; gamma has no charge and interacts less frequently.

Kinetic energy is transferred during interactions that cause ionisation. For the same kinetic energy, the much more massive alpha particle travels more slowly than a beta particle, remains near atoms for longer and produces dense ionisation along a short path.

The change is spontaneous: it occurs without an external trigger. Heating, cooling, pressure and chemical reactions do not select when a nucleus decays.

The change is random: it is impossible to predict which particular nucleus will decay next or the exact time at which it will decay.

For a large sample, the behaviour of many nuclei can form a statistical pattern even though each individual event remains unpredictable.

Alpha emission removes two protons as part of the alpha particle. In beta-minus decay, a neutron changes into a proton and an electron, and the electron is emitted, so the nucleus gains one proton.

Isotopes of one element have the same proton number but different neutron numbers. An isotope with too many neutrons for a stable arrangement can reduce that neutron excess through radioactive change.

A very heavy nucleus contains a large total number of nucleons. The balance of forces can be unstable, so the nucleus may emit radiation and move towards a more stable arrangement.

The electron emitted in beta-minus decay is created by the nuclear change; it is not an orbital electron. Nucleon number stays constant because one nucleon changes type.

Alpha example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Both nucleon numbers balance, 238 = 234 + 4, and both proton numbers balance, 92 = 90 + 2.

Beta-minus example: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. The nucleon number remains 14 and the proton-number total balances because 6 = 7 + (−1).

Gamma example: ᴬ_ZX* → ᴬ_ZX + ⁰₀γ. The asterisk indicates a higher-energy nucleus; emission changes neither A nor Z.

Method: identify the emission, write its A and Z values, conserve both columns, then use the daughter proton number to identify the new element.

Because activity and corrected count rate are proportional to the number of undecayed nuclei, each also halves in one half-life when the same measurement arrangement is used.

For an elapsed time t and half-life T, first find the number of half-lives n = t ÷ T, then halve the starting number, mass, activity or corrected count rate n times. The amount decayed equals initial amount minus amount remaining.

A source has a half-life of 5 days and an initial mass of 400 mg. After 10 days, two half-lives have passed: 400 → 200 → 100 mg, so 100 mg remains and 300 mg has decayed.

Equivalently, the detector reading after one half-life is B + (M₁ − B)/2 = (M₁ + B)/2. It is not usually M₁/2.

If the measured rate starts at 100 counts/min and background is 20 counts/min, the source rate is 80. After one half-life it is 40, so the detector reads 40 + 20 = 60 counts/min. The time for the curve to fall from 100 to 60 is one half-life.

Use more than one halving interval when the data allow it. Similar intervals support the estimate; small differences are expected because radioactive counts fluctuate randomly and graph readings have uncertainty.

For thickness control, alpha would be absorbed by even a very thin sheet, while gamma may pass through with too little change. Beta gives a measurable change in detector count when thickness changes.

A diagnostic tracer must not decay before it reaches the target and measurements are completed, but should decay soon afterwards. Treatment and sterilisation require sufficient penetration and dose, so the source arrangement and service life also matter.

Greater exposure increases the chance and extent of biological damage because more ionising interactions can occur in living tissue.

A sealed source keeps radioactive material contained, but its radiation can still leave the source. It therefore still needs time, distance and shielding controls.

Shielding must match the radiation and be thick enough: paper can stop alpha, aluminium can stop beta, while penetrating gamma generally needs thick lead or concrete.

These principles apply to all ionising radiation. A low-penetration source can still be hazardous at close range or if radioactive material enters the body.