The half-life of a radioactive substance is `48` hours. How much time will it take to disintegrate to its `(1)/(16) th` parts ?

Options

A. About 2/3 of the substance
B. About 90% of the substance
C. Almost all the substance
D. About 1/3 of substance

Answer

A

Explanation

For a radioactive substance , `N=N_0 e^(-lamdat)`
it is given that t = mean life `(tau) = 1/lamda`
` therefore N = N_0e^(-lamdaxx1/lamda) = (N_0)/(e ) = (N_0)/(2.71) = 0.37N_0`
`0.37N_0` is the amount of radioactive substance left after time `tau` .
`therefore` The amount disintegrated in time `tau`
`=N_0 - 0.37 N_0 = 0.63 N_0 = 2/3 N_0`