The half-life of `Ra^(226)` is 1620 years. Then the number of atoms decay in one second in 1 g of radium(Avogadro number = `6.023xx omega xx 10^(23)`).

Options

A. `4.23 xx 10^(9)`
B. `3.16 xx 10^(10)`
C. ` 3.61 xx 10^(10)`
D. `2.16 xx 10^(10)`

Answer

C

Explanation

The number of atom decay , `dN/dt = lambdaN`
`lambda = 0.693/t_(1/2)= 0.693/1620 xx 365 xx 86,400`
`N = 6.023 xx 10^(23)/M = 6.023 xx 10^(23)/226`
`dN/dt = 0.693/(1620 xx 365 xx 86,400)xx(6.023 xx 10^(23))/226 = 3.61 xx 10^(10)`