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# A radioactive sample decays by $$63$$% of its initial value in $$10s$$. It would have decayed by $$50$$% of its initial value in

A
$$7s$$
B
$$14s$$
C
$$1.4s$$
D
$$0.7s$$
Solution
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#### Correct option is A. $$7s$$A radioactive sample decays by $$63$$% in $$t=\dfrac{1}{\lambda}$$Hence $$\lambda=1/10$$$$N=N_0e^{-\lambda t}$$$$\dfrac{N_0}2=N_0e^{-0.1t}$$$$0.1t=ln2$$$$t=6.93s\approx7s$$

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