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Two radioactive substances have half-liv...

Two radioactive substances have half-lives T and 2T. Initially, they have equal number of nuclei. After time `t=4T`, the ratio of their number of nuclei is x and the ratio of their activity is y. Then,

A

(a) `x=1//8`

B

(b) `x=1//4`

C

(c) `y=1//2`

D

(d) `y=1//4`

Text Solution

Verified by Experts

The correct Answer is:
B, C
At `t=4T`
Number of half=lives of first `n_1=4` and number of half-lives of second `n_2=2`
`N_1/N_2=x=(N_0(1//2)^4)/(N_0(1//2)^2)=1/4`
`y=R_1/R_2=(lambda_1N_0(1//2)^4)/(lambda_2N_0(1//2)^2)`
`(lambda_1)/(4lambda_2)=(T_2)/(4T_1)`
`=(2T)/(4T)=1/2`
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