# 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

As we learnt in

Number of nuclei in terms of half life -

- wherein

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

A  (T1/2 = 20 minutes)

B  (T1/2 = 40 minutes)

at t = 80 min.

at t = 80 min.

Decayed number of

Decayed number of

Ratio

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.

3

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

1

4:1

Option 3

Option 3)  1:4

4)5:4

option 1

4)5:4

4:1

S

4:1

S

4:1

4:1

1:4

1:4

1:4 Option 3

Option 3)1:4

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