Half-lives of two radioactive elements A and B are 20 minutes and 40 minutes, respectively.  Initially, the samples have equal number of nuclei.  After 80 minutes, the ratio of decayed numbers of A and B nuclei will be :

  • Option 1)

    1 : 16

     

  • Option 2)

    4 : 1

     

  • Option 3)

     1 : 4

     

  • Option 4)

    5 : 4

     

 

Answers (20)

As we learnt in

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  (T1/2 = 20 minutes)

B  (T1/2 = 40 minutes)

N_{A}=\frac{N_{0}}{2^{t/T_{1/2}}}

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

at t = 80 min.

N_{A}=\frac{N_{0}}{2^{4}}=\frac{N_{0}}{16}

at t = 80 min.

N_{B}=\frac{N_{0}}{2^{2}}=\frac{N_{0}}{4}

Decayed number of  A=\frac{N_{0}-N_{0}}{16}=\frac{15}{16}N_{0}

Decayed number of B=\frac{3N_{0}}{4}

Ratio =\frac{\frac{15}{16}N_{0}}{\frac{3}{4}N_{0}}=\frac{5}{4}

Correct option is 4


Option 1)

1 : 16

 

This is an incorrect option.

Option 2)

4 : 1

 

This is an incorrect option.

Option 3)

 1 : 4

 

This is an incorrect option.

Option 4)

5 : 4

 

This is the correct option.

Option 1

After 80 minutes 1/16th part of initial nuclei of element A is left and  1/4th part of initial nuclei of element B is left 

So  the decayed number of nuclei of element A will be 15/16th of initial nuclei and that of element B will be 3/4th of initial nuclei

Hence the ratio of decayed number of A and B nuclei after 80 minutes will be 5/4.

Thank you

OPTION 4

Option 3

 

Option 3)  1:4

4)5:4

4)5:4

4:1

 

S Sami

4:1

 

S Sami

4:1

4:1

1:4

A A.teja
1:4 Option 3

Option 3)1:4

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