JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Modern Physics

Calculate the time interval between

33%

decay and

67%

decay if half-life of a substance is 20 minutes.

(A)13 minutes
(B)60 minutes
(C)40 minutes
(D)20 minutes✓ Correct

Answer: (D)

Solution

When

33%

has decayed, the fraction left is

\frac{2}{3}

; when

67%

has decayed, the fraction left is

\frac{1}{3}

. The second is half the first:

\frac{N _{2}}{N _{1}} = \frac{1/3}{2/3} = \frac{1}{2}

Radioactive decay is exponential, so the time taken for a sample to fall to half of whatever it held at the start of an interval is one half-life, independent of the starting amount. The interval between the two instants is therefore one half-life, that is

20

minutes.

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Single correct option

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