Radon undergoes decay by `alpha`- emission `""_(86)^(222) Rn overset(t_(1//2) = 3.8 "days") (to) ""_(84)^(218) Po + ""_(2)^(4) He`
Which of the following statements will be true for this decay process ?

Options

A. If the initial amount of radon was 1 mg , the amount of radon left after 11.4 days will 0.125 mg
B. Activity of radon after 7.6 days will be `N_(0) xx (5.3 xx 10^(-7)) s^-1` where `N_0` is the original number of atoms of the radon
C. The decay constant of radon is `2.1 xx 10^(-6) S^(-1)`
D. 60% of the radon will decay in 5 days approximately

Answer

A, B, C, D

Explanation

1 mg `overset(3.8 "days")(to) (1)/(2) overset(3.8 "days") (to) (1)/(4) overset(3.8 "days") (to) (1)/(8) , N_(0) 0.5 ((N_(0))/(2)) 0.25 ((N_(0))/(4)) 0.125`
(b) `A_(0) = ((0.693)/(3.8)) xx N_(0) , N_(0) = (( 1 xx 10^(-3))/(222) xx 6 xx 10^(23)) . A_(t) = ((0.693)/(3.8)) xx N_(t) darr` 76 days
`A_(t) = ((0.693)/(3.8)) xx ((N_(0))/(4)) , N_(t) = ((N_0)/(4)) = ((1 xx 10^(-3))/(222) xx 6 xx 10^(-23) xx (1)/(4))`
`A_(t) = ((0.693)/(3.8 xx 24 xx 60 xx 60) xx (N_0)/(4)) = (5.277 xx 10^(-7) xx N_(0)) sec^(-1)`
(c) `lambda = ((0.693)/(t_(1//2))) = ((0.693)/(3.8 xx 24 xx 60 xx 60)) = (((0.693)/(3.046)) xx 10^(-6) ) sec^(-1) = 2.1 xx 10^(-6) sec^(-1)`
(d) `((0.693)/(3.8)) xx t = 2.303 xx log ((600)/(400)) , t = ((0.4 xx 3.8)/(0.3040)) = 5`