First slide

Radio activity

Question

The half-life of a radioactive substance against $α$ -decay is $1.2 x 10^{7} s$ . What is the decay rate for $4 x 10^{15}$ atoms of the substance?

Moderate

A

$4.6 x 10^{12} atoms / s$
B

$2.3 x 10^{11} atoms / s$
C

$4.6 x 10^{10} atoms / s$
D

$2.3 x 10^{8} atoms / s$

Solution

$\frac{dN}{dt} = λN \Rightarrow |\frac{dN}{dt}| = \frac{0.693}{T_{1 / 2}} x N \frac{0.693}{1.2 x 10^{7}} x 4 x 10^{15} = 2.3 x 10^{8} atoms / \sec$

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