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Question

Half life of radium is 1620 years. How many radium nuclei decay in 5 hours in 5 gm radium? (Atomic weight of radium =223).

A
9.1×1012
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B
3.15×1015
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C
1.72×1020
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D
3.3×1017
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Solution

The correct option is B 3.15×1015

Given,

Half-life, T12=0.693λ

λ=0.6931620×365×24hr1

In time (t=5hours), λt=0.693×51620×365×24=2.44×107

No=mNAMo=5×(6.023×1023)233=1.292×1022nuclei

Number of radium nuclei decay in 5 hours is

(NoN)=N0(1eλt)

(NoN)=1.292×1022(1e2.44×107)

(NoN)=3.15×1015

Number of radium nuclei decay in 5 hours is 3.15×1015nuclie


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