Two isotopes P and Q, radioactive in nature atomic weight of P and Q are 10 and 20, P and Q are mixed in equal amount (weight). After 20 days their weight ratio is found to be 1 : 4, `t_(1//2)(P)=10` day, find `t_(1//2)(Q)=?`

Options

A. zero
B. 5 day
C. 20 day
D. infinite

Answer

D

Explanation

Let initial amount of P and Q are x g.
Initial mode of P and Q are `(x)/(10) and (x)/(20)`.
After 20 min. i.e., `2xxt_(1//2)` time
No. of moles of P left `=((x)/(10))/((2)^(2))=(x)/(10)`
Weight of P left `=(x)/(4)`g.
`therefore` For Q after 20 min weight left `=(x)/(4)xx4=x`
`k=(2.303)/(20).log((x//20)/(x//20))=0`
`therefore" "((l_(1))/(2))_(2)=(0.693)/(0)=oo`