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A sample of 2 gm of Ac (227) with a half life of 21.8 years decay to Fe (223) by emitting  α particles. After what time does the activity reduces to 12.5% of the original activity?

a
60.1 years
b
72.4 years
c
65.4 years
d
21.8 years

detailed solution

Correct option is C

Activity , A=A02-n    here n =tth ⇒12.5=1002n ⇒5103=12n ⇒n=3 ⇒tth=3 ⇒t=3×half life = 3×21.8 = 65.4 years

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