Two radioactive nuclides A and B have half-lives 50 min and 10 min respectively . A fresh sample contains the nuclides of B to be eight times that of A. How much time should elapse so that the mumber of nuclides of A becomes double of B ?

Options

A. 30
B. 40
C. 50
D. None

Answer

C

Explanation

Initial no. of nuclei
`{:(Aoverset(t_(1//2)=50 min)rarrX,,B overset(t_(1//2)=10 min)rarrX),(N_(0),,8N_(0)),(,,),(,,):}`
Let after n `t_(1//2)` of A, no. of nuclei of A becomes double of B.
`N_(A)=(N_(0))/(2^(n)) " " N_(B)=(8N_(0))/(2 ^(5n)) " " ( . :. "in" n t _(1//2) of A, t_(1//2) of B " will " 5n)`
`N_(A)=2 N_(B)`
`(N_(0))/(2^(n))=2 xx (8N_(0))/(2^(5n))`
`2^(4n)=16 = 2^(4) rArr n=1`
After one half life time of A (i.e. 50 min)
No. of nuclei of A will become double of B.