Half life of radioactive element is 12.5 Hour and its quantity is 256 gm . After how much time (in H

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Half life of radioactive element is $12.5\; Hour$ and its quantity is $256\; gm$. After how much time (in $Hours$) its quantity will remain $1 \;gm$

A

$50$

B

$100$

C

$150$

D

$200$

(AIPMT-2001)

Solution

$M=M_{0}\left(\frac{1}{2}\right)^{n}$

Here, $M=1 \;g, M_{0}=256 g, t_{1 / 2}=12.5 h$

$1=256\left(\frac{1}{2}\right)^{n}$

$\frac{1}{256}=\left(\frac{1}{2}\right)^{n}$

$\left(\frac{1}{2}\right)^{8}=\left(\frac{1}{2}\right)^{n}$

$n=8=\frac{t}{T_{1 / 2}}$

$t=8 T_{1 / 2}=8 \times 12.5=100 \;h$

Standard 12

Physics

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