Half-lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively. If, initially a sample has an equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

 

  • Option 1)

    3 : 8

  • Option 2)

    1 : 8

  • Option 3)

    8 : 1

  • Option 4)

    9 : 8

 

Answers (1)

 

Number of nuclei in terms of half life -

N=\frac{N_{0}}{2^{t/t_{1/2}}}

- wherein

Very useful to determine number of nuclei in terms of half life

 

 

  A B
t_{1/2} 10 m 20 m
t 60 m 60 m
  =6 t_{1/2}

=3 t_{1/2}

after 60 minutes.

undecay N_{A}=\frac{N_{0}}{2^{t/t_{1/2}}}=\frac{N_{0}}{2^{6}}=N_{B}=\frac{N_{0}}{2^{3}}

undecay  N^{1}_{A}=N_{0}-\frac{N_{0}}{2^{6}}=\frac{63N_{0}}{64}

            N^{1}_{B}=N_{0}-\frac{N_{0}}{8}=\frac{7N_{0}}{8}

So,  \frac{N^{1}_{A}}{N^{1}_{B}}=\frac{63}{64}\times \frac{8}{7}=\frac{9}{8}

\Rightarrow N_{A}^{1}:N_{B}^{1}=9:8


Option 1)

3 : 8

Option 2)

1 : 8

Option 3)

8 : 1

Option 4)

9 : 8

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