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Question

Two radioactive material X1 and X2 have decay constant 10λ and λ respectively. Initially, they have the same number of nuclei. The ratio of the number of nuclei X1 to that of X2 will be 1e after time,

A
1100λ
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B
111λ
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C
110λ
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D
19λ
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Solution

The correct option is D 19λ

For X1, N1=N0eλ1t
For X2, N2=N0eλ2t
Here, λ1=10λ, λ2=λ

N1N2=N0eλ1tN0eλ2t

1e=eλ1teλ2t

e1=e(λ1λ2)t

1=(λ1λ2)t

t=1λ1λ2=110λλ=19λ

Hence, (D) is the correct answer.

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