In artificial radioactivity, 1.414 `times 10^(6)` nuclei are disintegrated into `10^(6)` nuclei in 10 min. The half-life in minutes must be :

Options

A. 5
B. 20
C. 15
D. 30

Answer

A

Explanation

From Rutherford-Soddy law
`" "N=N_(0)(1/2)^(n)`
`" "n=t/T`
`therefore" "10^(6)=1.414 times 10^(6) (1/2)^(t//T)`
`rArr" "(1000)/((1414)=(1/2)^(t//T)`
`rArr" "(1/2)^(2)=(10/12)^(2)" (Approximately)"`
`rArr" "n=2`
`rArr" "n=t/T=2`
`rArr" "T=10/2=5"min"`