Question

The half life of radioactive Radon is `3.8 days` . The time at the end of which `(1)/(20) th` of the radon sample will remain undecayed is `(given log e = 0.4343 ) `
A. `3.8 days`
B. `16.5 days`
C. `33 days`
D. `76 days`

Answer 1

Correct Answer - b
`T_(1//2)=3.8 day`
`:. lambda =(0.693)/(t_(1//2))=(0.693)/(3.8)=0.182`
If the initial number of atoms is a =`A_(0)`, then after time t the number of atoms is `a//20`=A. We have to find `t`.
` t=(2.303)/(lambda) log.(A_(0))/(A)=(2.303)/(0.182) log.(a)/(a//20)=(2.303)/(0.182) log.20`
`=16.46 day`.