Radioactive Decay and Nuclear Stability

Manual: General · Subject: Physics

Study decay laws, decay modes, and the stability landscape across the chart of nuclides.

Exponential Decay

Decay law

For a radioactive sample, the number of undecayed nuclei follows $N(t)=N_0 e^{-\lambda t}$ , where $\lambda$ is the decay constant. The activity is $A(t)=\lambda N(t)$ .

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Half-life

The half-life is $T_{1/2}=\frac{\ln 2}{\lambda}$ . It is independent of the initial number of nuclei in an ideal pure sample.

Common decay modes

Mode	What changes
Alpha decay	$A$ decreases by $4$ , $Z$ decreases by $2$
Beta minus decay	A neutron becomes a proton
Beta plus decay / electron capture	A proton becomes a neutron
Gamma decay	Nuclear energy decreases without changing $A$ or $Z$

Stability clues

Neutron-rich nuclei

Often decay via

\beta^-

Proton-rich nuclei

Often decay via

\beta^+

or electron capture

Very heavy nuclei

Often undergo

\alpha

decay

Excited nuclei

Often emit

\gamma

rays

If the decay constant doubles, what happens to the half-life?

It doubles It halves It stays the same It becomes zero

Write the exponential decay law for the number of undecayed nuclei.

Which decay changes neither $A$ nor $Z$ ?

Alpha Beta minus Gamma Electron capture

What nuclear quantity measures the rate of disintegrations per unit time?

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Radioactive Decay and Nuclear Stability

Exponential Decay

Decay law