Nuclei - Result Question 74

75. Two radioactive materials X1 and X2 have decay constants 5λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will be 1e after a time

[2008]

(a) λ

(b) 121

(c) 141

(d) e1

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Answer:

Correct Answer: 75. (c)

Solution:

  1. (c) Let the required time be t. Then

N1=N0e111t;N2=N0e12t

Where

N1= number of nuclei of X1 after timet

N2= number of nuclei of X2 after timet

N0= initial number of nuclei of X1 and X2 each.

Now, N1N2=N0e11tN0e12t Here N1N2=1e

λ1=5λ;λ2=λ

1e=e51te1te1=e4λt4λt=1

t=141



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