Radioactive decay

Nuclear & Particle Physics - OCR A-Level Physics

Key Definition

Radioactive decay
The spontaneous and random disintegration of an unstable nucleus, emitting radiation (alpha, beta, or gamma) to become more stable.

Spontaneous: not affected by external conditions (temperature, pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻²., chemical state).
Random: impossible to predict when a specific nucleus will decay, but for large numbers, the average rate is predictable.
The decay constantThe probability of decay of a nucleus per unit time. Measured in s⁻¹. λ is the probability of a nucleus decaying per unit time.
The half-lifeThe time taken for half the number of radioactive nuclei in a sample to decay, or for the activityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. to halve. $t_{1/2}$ is the time for half the nuclei in a sample to decay.

N = N_0 e^{-\lambda t}

t_{1/2} = \frac{\ln 2}{\lambda}

ActivityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. $A = λN = A_0 e^{-λt}$. ActivityThe number of nuclear decays per unit time. Measured in becquerels (Bq), where 1 Bq = 1 decay per second. is the number of decays per second, measured in becquerelsThe SI unit of radioactive activity. 1 Bq = 1 nuclear decay per second. (Bq).
A graph of N (or A) against t is an exponential decayA process where the quantity decreases by a constant fraction in each equal time interval: N = N₀e^(−λt). curve.
A graph of ln N against t gives a straight line with gradient -λ.