Radioactivity

Radioactive decay is the spontaneous emission of radiation from an unstable nucleus. The process is random, it is impossible to predict when any particular nucleus will decay, but for a large sample, the average rate of decay follows a predictable exponential pattern.

The Three Types of Radiation

Property	Alpha ( $\alpha$ )	Beta ( $\beta$ )	Gamma ( $\gamma$ )
Nature	Helium-4 nucleus ( ${}^{4}_{2}\text{He}$ )	Fast electron	High-energy electromagnetic wave
Charge	+2	−1	0
Mass (relative)	4	~0	0
Speed	Slow (~5% of $c$ )	Fast (up to ~90% of $c$ )	$c$ (speed of light)
Ionising ability	Very high (dense ionisation)	Medium	Low
Penetrating ability	Stopped by 5 cm of air or a sheet of paper	Stopped by 3-5 mm of aluminium	Reduced by several cm of lead or metres of concrete
Deflection by electric field	Toward negative plate	Toward positive plate	Not deflected
Deflection by magnetic field	Yes (using left-hand rule for positive charge moving)	Yes (in opposite direction to alpha)	Not deflected

Diagram showing the penetrating ability of alpha, beta, and gamma radiation: alpha particles are stopped by a sheet of paper, beta particles are stopped by a few millimetres of aluminium, and gamma rays are only partially attenuated by a thick block of lead

Nuclear Equations

In a nuclear equation, both the mass number (A) and the atomic number (Z) must be conserved.

Alpha Decay

An alpha particle ( ${}^{4}_{2}\text{He}$ ) is emitted. A and Z both decrease:

${}^{A}_{Z}\text{X} \rightarrow {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}$

Example: Ra-226 undergoes alpha decay:

${}^{226}_{88}\text{Ra} \rightarrow {}^{222}_{86}\text{Rn} + {}^{4}_{2}\text{He}$

Beta Decay

A beta particle (electron, ${}^{0}_{-1}\text{e}$ ) is emitted. A stays the same; Z increases by 1 (a neutron converts to a proton):

${}^{A}_{Z}\text{X} \rightarrow {}^{A}_{Z+1}\text{Y} + {}^{0}_{-1}\text{e}$

Gamma Emission

A gamma ray ( $\gamma$ ) is emitted. A and Z are unchanged, only the nucleus loses energy.

Half-Life

The half-life ( $t_{1/2}$ ) of a radioactive substance is the time taken for the activity (or the number of undecayed nuclei) to fall to half of its initial value.

Half-life is a characteristic of each isotope and does not change with temperature, pressure, chemical form, or sample size.

After $n$ half-lives, the fraction of activity remaining is $\left(\frac{1}{2}\right)^n$ .

Exponential decay curve: activity halves in each successive half-life. Starting at 80 Bq with a 1-hour half-life, activity is 40 Bq after 1 hour, 20 Bq after 2 hours, etc.

ExampleHalf-life from a graph (2016 Paper 02, Q1)

Activity data for a sample:

Time (h)	Activity (disintegrations/s)
0	80.0
1	50.0
2	34.5
3	20.0
4	13.0
5	7.5
6	5.0

From the smooth decay curve: activity falls from 80 to 40 between $t = 0$ and approximately $t = 1.5$ h. Activity falls from 40 to 20 between $t \approx 1.5$ h and $t \approx 3$ h.

Both intervals give approximately the same half-life: $t_{1/2} \approx 1.5$ h.

Time for activity to reach 10 disintegrations/s: Read from the graph, at $A = 10$ , $t \approx 3$ h.

The decay is not a perfectly smooth curve because radioactive decay is random, individual decays occur by chance, producing statistical fluctuations in the measured activity.

Applications of Radioisotopes

Application	Radioisotope used	Reason for choice
Medical imaging (thyroid scan)	Iodine-123 ( ${}^{123}_{53}$ I)	Absorbed by thyroid; short half-life minimises patient dose
Cancer treatment (radiotherapy)	Cobalt-60, gamma knife	High-energy gamma kills tumour cells
Carbon dating	Carbon-14 ( ${}^{14}_{6}$ C), half-life 5730 years	Living organisms maintain constant C-14 level; ratio to C-12 decreases after death
Industrial thickness gauging	Beta emitters	Absorption through material gives thickness measurement
Sterilisation of medical equipment	Gamma sources	Gamma penetrates packaging to kill bacteria

Exam Tip

In a half-life calculation: if the activity falls to 1/16 of its original value, that is $(1/2)^4$ , so four half-lives have passed. Divide the total elapsed time by 4 to find one half-life.

In nuclear equations, check both the top numbers (A) and the bottom numbers (Z) balance on each side. The most common error is forgetting to adjust Z when writing the daughter nucleus.

The Three Types of Radiation

Property	Alpha ( $\alpha$ )	Beta ( $\beta$ )	Gamma ( $\gamma$ )
Nature	Helium-4 nucleus ( ${}^{4}_{2}\text{He}$ )	Fast electron	High-energy electromagnetic wave
Charge	+2	−1	0
Mass (relative)	4	~0	0
Speed	Slow (~5% of $c$ )	Fast (up to ~90% of $c$ )	$c$ (speed of light)
Ionising ability	Very high (dense ionisation)	Medium	Low
Penetrating ability	Stopped by 5 cm of air or a sheet of paper	Stopped by 3-5 mm of aluminium	Reduced by several cm of lead or metres of concrete
Deflection by electric field	Toward negative plate	Toward positive plate	Not deflected
Deflection by magnetic field	Yes (using left-hand rule for positive charge moving)	Yes (in opposite direction to alpha)	Not deflected

Nuclear Equations

In a nuclear equation, both the mass number (A) and the atomic number (Z) must be conserved.

Alpha Decay

An alpha particle ( ${}^{4}_{2}\text{He}$ ) is emitted. A and Z both decrease:

${}^{A}_{Z}\text{X} \rightarrow {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}$

Example: Ra-226 undergoes alpha decay:

${}^{226}_{88}\text{Ra} \rightarrow {}^{222}_{86}\text{Rn} + {}^{4}_{2}\text{He}$

Beta Decay

A beta particle (electron, ${}^{0}_{-1}\text{e}$ ) is emitted. A stays the same; Z increases by 1 (a neutron converts to a proton):

${}^{A}_{Z}\text{X} \rightarrow {}^{A}_{Z+1}\text{Y} + {}^{0}_{-1}\text{e}$

Gamma Emission

A gamma ray ( $\gamma$ ) is emitted. A and Z are unchanged, only the nucleus loses energy.

Half-Life

The half-life ( $t_{1/2}$ ) of a radioactive substance is the time taken for the activity (or the number of undecayed nuclei) to fall to half of its initial value.

Half-life is a characteristic of each isotope and does not change with temperature, pressure, chemical form, or sample size.

After $n$ half-lives, the fraction of activity remaining is $\left(\frac{1}{2}\right)^n$ .

Exponential decay curve: activity halves in each successive half-life. Starting at 80 Bq with a 1-hour half-life, activity is 40 Bq after 1 hour, 20 Bq after 2 hours, etc.

ExampleHalf-life from a graph (2016 Paper 02, Q1)

Activity data for a sample:

Time (h)	Activity (disintegrations/s)
0	80.0
1	50.0
2	34.5
3	20.0
4	13.0
5	7.5
6	5.0

From the smooth decay curve: activity falls from 80 to 40 between $t = 0$ and approximately $t = 1.5$ h. Activity falls from 40 to 20 between $t \approx 1.5$ h and $t \approx 3$ h.

Both intervals give approximately the same half-life: $t_{1/2} \approx 1.5$ h.

Time for activity to reach 10 disintegrations/s: Read from the graph, at $A = 10$ , $t \approx 3$ h.

The decay is not a perfectly smooth curve because radioactive decay is random, individual decays occur by chance, producing statistical fluctuations in the measured activity.

Applications of Radioisotopes

Application	Radioisotope used	Reason for choice
Medical imaging (thyroid scan)	Iodine-123 ( ${}^{123}_{53}$ I)	Absorbed by thyroid; short half-life minimises patient dose
Cancer treatment (radiotherapy)	Cobalt-60, gamma knife	High-energy gamma kills tumour cells
Carbon dating	Carbon-14 ( ${}^{14}_{6}$ C), half-life 5730 years	Living organisms maintain constant C-14 level; ratio to C-12 decreases after death
Industrial thickness gauging	Beta emitters	Absorption through material gives thickness measurement
Sterilisation of medical equipment	Gamma sources	Gamma penetrates packaging to kill bacteria

Exam Tip

In a half-life calculation: if the activity falls to 1/16 of its original value, that is $(1/2)^4$ , so four half-lives have passed. Divide the total elapsed time by 4 to find one half-life.

In nuclear equations, check both the top numbers (A) and the bottom numbers (Z) balance on each side. The most common error is forgetting to adjust Z when writing the daughter nucleus.