#### 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 cm^{2} window. If the source contains 6.0 × 10^{16} 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.

#### Solution

Given:

Counts received per second = 50000 Counts/second

Number of active nuclei, N = 6 × 10^{16}

Total counts radiated from the source, `"dN"/"dt"` = Total surface area × 50000 counts/cm^{2}

= 4 × 3.14 × 1 × 10^{4} × 5 × 10^{4}

= 6.28 × 10^{9} Counts

We know

`"dN"/"dt" = lambdaN`

Here , `lambda` = Disintegration constant

`therefore lambda = (6.28 xx 10^9)/(6 xx 10^16)`

= `1.0467 xx 10^-7`

= `1.05 xx 10^-7 "s"^-1`