Carbon (Z=6) with mass number 11 decays to boron (Z=5).(a) Is it a `beta^+` -decay? (b) the half-life of the decay scheme is 20.3 minutes .How much time will elapse before a mixture of 90% carbon-11 and 10% boron-11(by the number of atoms )converts itself into a mixture of 10% carbon-11 and 90% boron -11?

Answer

A, B, D

Explanation

(a) ` P rarr n + e^(-) + v ,`
Hence its is a `beta ^(-)` decay
(b) Let the total no of atoms be `100 N _(1)`
Carbon Boron
Initially 90 N `10 N_(0)`
Family `10N _(0) 90N_0`
Now `10 N_(0) = 90 N_(0) e^(-lambda t) ` ltbgrgt `rArr (1)/(9) = e^(-0.693/(0.2)) xx 1) `
`[:. t_(1/2) = 20.3 min]`
rArr in (1)/(2) = (-0.693)/(20.3)t `
`rArr t = (21972 xx203)//0.693) `
` = 64.36 = 64 min `.