A radioactive element (atomic mass = 90 a.m.u.) has half life of 28 years. The number of disintegration per second is :

Options

A. `5.24xx10^(8)`
B. `5.24xx10^(10)`
C. `5.24xx10^(-10)`
D. `5.24xx10^(12)`

Answer

B

Explanation

Decay rate `=lamdaxxN`
`lamda=(0.693)/(t_(1)//2)=(0.693)/(25xx365xx24xx36000)`
`=7.83xx10^(-10)s^(-1)`
No. of atoms in 1 g of element (N)
`=(1)/(90)xx6.023xx10^(23)`
`=6.69xx10^(19)` atoms
Decay rate `=7.83xx10^(-10)xx6.96xx10^(19)`
`=5.24xx10^(10)`
disintegrations per sec.