A saample of radioactive elements contains `4xx10^(10)` active nuclei. If half-life of element is `10` days, then the number of decayed nuclei after `30` days is

Options

A. `0.5 xx 10^(16)`
B. `2 xx 10^(16)`
C. `3.5 xx 10^(16)`
D. `1 xx 10^(16)`

Answer

C

Explanation

`N_(0)=4 xx 10^(16)`
`T_(1//2)=10` days
t=30 days
`t=nT_(1//2) rArr n=3`
`(N/N_(0))=(1/2)^(n)`
Number of undecayed nuclei `N=N_(0)(1/2)^(3)=N_(0)/8`
Number of decayed nuclei `=N_(0)-N_(0)/8 = 7/8 N_(0)`
`=3.5 xx 10^(16)`