First slide

Radio activity

Question

A radioactive sample undergoes decay as per the following graph. At time $t = 0$ , the number of undecayed nuclei is $N_{0}$ . Calculate the number of nuclei left after 10s. $[g i v e n \log_{e} (2) = 0.693]$

Easy

A

$N_{0} / e^{2}$
B

$N_{0} / e^{10}$
C

$N_{0} / e^{4}$
D

$N_{0} / e^{6.93}$

Solution

$t = 0, N = N_{0} t = 6.93, N = N_{0} / 4$
$N_{0} / 4$ is the sample left after two half-lives
$∴ 2 t_{1 / 2} = 6.93$
$\Rightarrow 2 \times \frac{0.693}{λ} = 6.93 \Rightarrow λ = 0.2 \sec^{- 1}$
$\Rightarrow t = 10 \sec$
$∴ N = N_{0} e^{- λ t} = N_{0} e^{- 0.2 \times 10} = \frac{N_{0}}{e^{2}}$

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