The half-life of radium is 1600 years . Calculate the number atoms that will decay from 1g sample of radium per second (given, atomic weight of radium = 226)

Options

A. `3.6 xx 10^(10)`
B. 7.2 xx 10^(10)`
C. `4.2 xx 10 ^(10)`
D. `14.6 xx 10^(10)`

Answer

A

Explanation

`N_(0)` = `(6.02 xx 10^(23))/ 266` = `2.65 xx 10^(21)`
`lambda` = `(0.693) / (1600 xx 3.16 xx 10^(7))` = `1.37 xx 10^(-11)s^(-1)` We can assume N`=~N_(0)` as the half-life is much larger,
`dN/dt` = `lambdaN_(0)`
dN = (`1.37 xx 10^(-11)) (2.65 xx 10^(21))xx1 =3.6 xx 10^(10)`.