First slide

Radio activity

Question

After one average life, what will be the ratio of number of undecayed nuclei to the number of decayed nuclei of a radioactive sample? [Take e = 2.7]

Moderate

A

7:9
B

12:19
C

10:17
D

11:17

Solution

Mean life $= t_{m} = \frac{1}{λ}$
Required ratio $= \frac{N_{0} e^{- {λt}_{m}}}{N_{0} (1 - e^{- {λt}_{m}})} = \frac{e^{- 1}}{1 - e^{- 1}}$
$= \frac{1}{e - 1} = \frac{1}{2.7 - 1} = \frac{10}{17}$

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