Question

A radioactive element 'X' converts into another stable element 'Y'. Half life of 'X' is 2 hrs. Initially only 'X' is present. After time 't', the ratio of atoms of 'X' and 'Y' is found to be 1:4, then 't' in hours is

• A. 2
• B. 4
• C. between 4 and 6
• D. 6

Answer 1

The correct option is C between 4 and 6

Let number of atom of element $X$ initially, $X_o=100$

After time $t,$ $\frac{X}{Y}=\frac{1}{4}$

$\therefore$ Number of atom of element $X$ and $Y$ after time $t$ is $20$ and $80$ respectively.

Thus using $\frac{0.693}{t_{1/2}}t=2.303lo{g}_{10}\frac{X_o}{X}$

$\therefore \frac{0.693}{2}t=2.303lo{g}_{10}\frac{100}{20}⟹t=4.65hours$