JEE Main · 2011 · 10 Apr 2011 · Offline · Modern Physics

The half life of a radioactive substance is 20 minutes. The approximate time interval

(t_{2} - t_{1})

between the time

t_{2}

when

\frac{2}{3}

of it has decayed and time

t_{1}

and

\frac{1}{3}

of it had decayed is :

(A)14 min
(B)20 min✓ Correct
(C)28 min
(D)7 min

Answer: (B)

Solution

Decay follows

N = N_{0} e^{- λ t}

. When one-third has decayed, two-thirds remain, so

λ t_{1} = ln \frac{3}{2}

; when two-thirds has decayed, one-third remains, so

λ t_{2} = ln 3

. The interval is

t_{2} - t_{1} = \frac{1}{λ} (ln 3 - ln \frac{3}{2}) = \frac{ln 2}{λ}

, which is exactly one half-life. Since the half-life is

20 min

t_{2} - t_{1} = 20 min

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option

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