A radiation detector records the following counts from a sealed radioactive source:…

PHYSICS · Subjective · A Level · Physics · Nuclear physics · Nuclear physics

Problem

A radiation detector records the following counts from a sealed radioactive source: Count in the first

10\,\text{min}

interval:

C_1 = 1.20\times10^{5}

disintegrations Count in the next successive

10\,\text{min}

interval:

C_2 = 1.10\times10^{5}

disintegrations (a) Show that the decay constant

\lambda

of the source can be expressed in terms of

C_1

C_2

and the time interval

\Delta t

\lambda = \frac{1}{\Delta t}\,\ln\left(\frac{C_1}{C_2}\right).

(b) Using the given data, calculate

\lambda

and the corresponding half-life of the nuclide.