First slide

Radio activity

Question

In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life?

Moderate

A

69.3%
B

63%
C

50%
D

37%

Solution

Number of atoms remains undecayed $N = N_{0} e^{- λt}$
Number of atoms decayed $= N_{0} (1 - e^{- λt})$
$= N_{0} (1 - e^{- λ x \frac{1}{λ}}) = N_{0} (1 - \frac{1}{e}) = 0.63 N_{0} = 63 % of N_{0} .$

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