Half life of `Ra^(226)` is 1620 years. Find how many atoms of radium decayed in 1 second ?

Options

A. `3.6xx10^(10)`
B. `7.2xx10^(10)`
C. `1.8xx10^(10)`
D. `9.97xx10^(10)`

Answer

A

Explanation

Number of atoms in 1 gm of radium
`=(1)/(226)xx6.02xx10^(23)=2.66xx10^(21)`
decay constant `lambda = (0.693)/(T_(1//2))=(0.693)/(1620xx(3.16xx10^(7)))`
`=1.35xx10^(-11)` per second
Number of decayed nuclie per second `= Delta N`
`=lambda N.Delta t`
`=1.35xx10^(-11)xx2.66xx10^(21)xx1`
`=3.6xx10^(10)`