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Question

4grams of radioactive substance A left 1/2 gm after some time. 1 gram of another radioactive substance B left 1/4 gm in the same period. If half life of B is 2 hours, the half life of A is

A
3/4 hours
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B
4/3 hours
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C
1/4 hours
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D
1/2 hours
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Solution

The correct option is B 4/3 hours
From integrated rate law, half life of B =2hours
So, λ=ln22
For B, 14=eln2t2

ln(14)=tln222ln=t2ln2
t=4 seconds
For A, after same period,

From rate law:
12=4eλ4ln(18)=4λ3ln24=λ
Half life =4ln23ln2=43hours=43hrs

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