Radioactive disintergation always follow `I` order kinetics and is independent of all external factors and is represented by the relation `N = N_(0) e^(-lambda t)` where `lambda` is decay constant and `N` atoms are left at time `t`. The radioactive nature of element is expressed in terms of average life numerically equal to decay constant `(1//lambda)` however all the radioactive do not lose their radioactive nature in thier average life. The radioactive emission involves `alpha, beta` particles as well as `gamma-` rays.The penertrating power order is `alpha lt beta lt gamma`. The emissions can perntrate even thick steel walls but are however unable to penttrate `Pb` blocks. The `S` unit fo rate of decay is `dps`.
The mass of `.^(14)C` with `t_(1//2) = 5730` year having activity equal to `1` curies si:

Options

A. `0.0043g`
B. `2.243g`
C. `22.43g`
D. `224.3g`

Answer

`a`

Explanation

Rate `= lambda.N`
`1xx3.7xx10^(10) = (0.693xx N)/(5730xx365xx24xx60xx60)`
`:. N = 9.65xx10^(21)` atoms
`:.` Mass `= (9.65xx10^(21)xx14)/(6.023xx10^(23)) = 0.2243g`