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A point source emitting alpha particles ...

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 `6.0xx10^16`active nuclei and the counter records a rate of 50000 counts//second, find the decay constant. Assume that the source emits alpha particles fall nearly normally on the window.

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The correct Answer is:
A
Count received per `cm^(3)`
` = 50000 Counts / se `
`N = no of active nuclei= 6 xx 10^(16) `
Total count radited from the source
` Total surface area xx 50000 counts/cm^(2) `
` = 4 xx 3.14 xx 1 xx10 ^(4) xx 5 xx 10^(4) `
` 6.28 xx 10^(9) Counts = (dN)/(dt) `
` We know (dN)/(dt) = lambda t `
` or lambda = (628 xx 10^(9))/(6 xx 10^(16)) `
` = 1.0467 xx 10^(-7) `
` = 1.05 xx 10^(-7) s^(-1) `
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