JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Modern Physics

Two radioactive substances

X

and

Y

originally have

N_{1}

and

N_{2}

nuclei respectively. Half life of

X

is half of the 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 :

(A) $\frac{3}{1}$
(B) $\frac{8}{1}$ ✓ Correct
(C) $\frac{1}{3}$
(D) $\frac{1}{8}$

Answer: (B)

Solution

Let the half life of

Y

T

; that of

X

is then

\frac{T}{2}

. Over a stretch of time

3 T

Y

passes through three half lives while

X

passes through six:

N_{Y} = \frac{N _{2}}{2 ^{3}} = \frac{N _{2}}{8}, N_{X} = \frac{N _{1}}{2 ^{6}} = \frac{N _{1}}{64}

The surviving numbers are equal, so

\frac{N _{1}}{64} = \frac{N _{2}}{8}

and

\frac{N _{1}}{N _{2}} = \frac{64}{8} = \frac{8}{1}

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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