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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 3.15×1015Given, Half-life, T12=0.693λ ⇒λ=0.6931620×365×24hr−1 In time (t=5hours), λt=0.693×51620×365×24=2.44×10−7 No=mNAMo=5×(6.023×1023)233=1.292×1022nuclei Number of radium nuclei decay in 5 hours is (No−N)=N0(1−e−λt) (No−N)=1.292×1022(1−e−2.44×10−7) (No−N)=3.15×1015 Number of radium nuclei decay in 5 hours is 3.15×1015nuclie

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