Question

A point source emitting alpha particles is placed at a distance of 1 m from a counter which records any alpha particle falling on its 1 cm² window. If the source contains 6.0 × 10¹⁶ active nuclei and the counter records a rate of 50000 counts/second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.

Answer 1

Given:
Counts received per second = 50000 Counts/second
Number of active nuclei, N = 6 × 10¹⁶
Total counts radiated from the source, $\frac{dN}{\mathrm{dt}}$ = Total surface area × 50000 counts/cm²
= 4 × 3.14 × 1 × 10⁴ × 5 × 10⁴
= 6.28 × 10⁹ Counts
We know
$\frac{dN}{dt}=\lambda N$

Here, λ = Disintegration constant
$$\begin{gathered} \therefore \lambda =\frac{6.28\times {10}^9}{6\times {10}^{16}} \\ =1.0467\times {10}^{-7} \\ =1.05\times {10}^{-7}{\mathrm{s}}^{-1} \end{gathered}$$