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 , `"dN"/"dt"` = Total surface area × 50000 counts/cm²

= `4 xx 3.14 xx 1 xx 10^4 xx 5 xx 10^4`

= `6.28 xx 10^9` Counts

We know
`"dN"/"dt" = lambdaN`
Here, λ = 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`