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Question

Two radioactive samples consist of equal number of atoms.The half lives are 2 hours and 4 hours respectively.The ratio of their activities then is

A
4:1
B
1:1
C
2:1
D
1:2
Solution
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Correct option is B. 1:2
let the $$N$$ no. of atoms in $$x$$ and $$y$$ both.
assume $$\Delta N$$ ho. af atoms decay in \Deltat time.
We knouthe rate of disintegration
$$\frac{\Delta N}{D t} \propto N$$
$$\frac{\Delta N}{\Delta t}=\lambda N$$
we know $$\lambda=\frac{0.693}{t / 2}$$
So $$\lambda_{1}=\frac{0.693}{2}, \lambda_{2}=\frac{0.693}{4}$$
$$\frac{y}{x}=\frac{\lambda N}{\lambda_{x} N}$$
$$\frac{y}{x}=\frac{0.693 \times 2}{4 \times 0.693}$$
$$\frac{y}{x}=\frac{1}{2}$$
$$[B] 1: 2$$

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