The decay constant of `Hg_80^197`(electron capature to `Au_79^197`)is `1.8xx10^-4 s^-1`.(a) What is the half-life?(b) What is the average-life ?(c ) How much time will it take to convert 25% of mercury into gold?

Answer

A, B, C, D

Explanation

(a)` since t_(1/2) = (0.693)/(lambda) `
` [lambda rarr Decey constant]`
` rArr t_(1/2) = (0.693)/(1.8 xx10^(-4)) `
` = 3850 sec = 64 min `
(b) Averge life `= (t_(1/2))/(0.693) `
`=64/(0.693) = 92 min`
` ( c ) 0.75 = e^(-lambdatau)`
` rArr In 0.75 = - lambda t`
` rArr t = (In 0.75)/(-0.00018) `
` = 1598.23 sec` .