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A radioactive sample contains 10^(-3)kg ...

A radioactive sample contains `10^(-3)`kg each of two nuclear species A and B with half-life 4 days and 8 days, respectively. The ratio of the amounts of A a nd B after period of 16 days is

A

`1:2`

B

`4:1`

C

`1:4`

D

`2:1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given half- life of species
A = 4 days
Half- life of species B = 8 days
For species A, N =`N_(0)(1/(2))^(n),n=16/(4)=4`
Now, `N_(1)=N_(0)(1/(2))^(4)` …(i)
Similarly, for species B
`N_(2)=N_(0)(1/(2))^(2)` …(ii)
On dividing Eq. (i) from Eq. (ii), we get
`N_(1)/(N_(2))=(2)^(2)/((2)^(4))rArrN_(1)/N_(2)=1/(4)`
`rArrN_(1):N_(2)=1:4`
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