Give answer! 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 :

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 (T_1/2 = 20 minutes)

B (T_1/2= 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.

Posted by

perimeter

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JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Posted by

Suchitra Nair

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Option 1

Posted by

Anant Jain

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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

Posted by

Rachita pandey

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OPTION 4

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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)

Posted by

perimeter

JEE Main high-scoring chapters and topics

Posted by

Suchitra Nair

Posted by

Anant Jain

Posted by

Rachita pandey

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Rohit Gavali

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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