The half life of a radioactive substance is 20s. Calculate (i) the decay constant, and (ii) time take by the sample to decay by `7//8th` of its initial value

Answer

b

Explanation

`t_(1//2) = 30s`
(i) `lambda = 0.693/t_(1//2) = 0.693/30 = 0.023 s^(-1)`
(ii) Initial number of atoms `=N_(0)`
Number of atoms left undecayed `=N_(0)`
Number of atoms left undecayed `=N_(0) - 3/4 N_(0)`
`=N_(0)/4`
`N/N_(0) =(1/2)^(n)`
`1/4 = (1/2)^(n)`
`rArr n=2, t=nt_(1//2) = 2 xx 30 s = 60s`