JEE PYQ: Nuclear Physics Question 7
Question 7 - 2021 (25 Feb Shift 1)
Two radioactive substances $X$ and $Y$ originally have $N_1$ and $N_2$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{N_1}{N_2}$ will be equal to:
(1) $\frac{8}{1}$
(2) $\frac{1}{8}$
(3) $\frac{3}{1}$
(4) $\frac{1}{3}$
Show Answer
Answer: (1)
Solution
After $n$ half life, no. of nuclei undecayed $= \frac{N_0}{2^n}$ Given $T_{1/2,X} = \frac{T_{1/2,Y}}{2}$ So 3 half life of $Y$ = 6 half life of $X$ Given $N_X = N_Y$ (after 3 $T_{1/2,Y}$) $\frac{N_1}{2^6} = \frac{N_2}{2^3}$ $\frac{N_1}{N_2} = \frac{2^6}{2^3} = 2^3 = \frac{8}{1}$
BETA
