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Question

The rate at which a particular decay process occurs in a radioactive sample, is proportional to the number of radioactive nuclei present. If N is the number of radioactive nuclei present at some instant, the rate of change of N is dNdt=λN.

The number of nuclei of B will first increase then after a maximum value, it will decreases, if

A
λ1>λ2+λ3
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B
λ1=λ2=λ3
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C
λ1=λ2+λ3
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D
For any values of λ1,λ2 and λ3
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Solution

The correct option is A λ1>λ2+λ3
If we assume option C to be correct, then rate of decay of A to B is same as rate of decay of B to X plus rate of decay from B to Y which means number of nuclei of B will not increase and rather remain same. So clearly option C is correct.

If we assume option B to be correct, then rate of decay of A to B is same as rate of decay of B to X and rate of decay from B to Y which means in due time course number of nuclei of B will decrease.

Now, clearly when λ1>λ2+λ3, number of nuclei of B will first increase but after a maximum value when A is decayed completely, B will start decreasing. So, option A is correct.


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