Please provide solution of this problem

Asked by  | 2nd Feb, 2010, 08:40: AM

Expert Answer:

Assuming all the disintegrations are detected by the counter.

count rate = activity

dN/dt = -λe-λt N0

16000 = -λe-λt N0 .....(1)

After 4 hrs i.e. 240 min,

500 = -λe-λ(t+240) N0 ....(2)

Divide (2) by (1),

500/16000 = et-λ(t+240)

500/16000 = e-240λ

ln (1/32) = -240λ

Use t1/2 = ln2/λ

ln (1/32) = -240(ln2/t1/2)

t1/2 = 240 ln2 / ln32

t1/2 = 240 ln2 / ln32 = 48 min.

Half life of the radioactive material is 48 min.

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Answered by  | 2nd Feb, 2010, 09:38: AM

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