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Half life of radioactive element is 12.5 Hour and its quantity is 256 gm. After how much time its quantity will remain 1 gm : -
A
50 Hrs
B
100 Hrs
C
150 Hrs
D
200 Hrs
Detailed Solution
$N = N_0\left(\dfrac{1}{2}\right)^n \Rightarrow 1 = 256\left(\dfrac{1}{2}\right)^n$
$2^n = 256 = 2^8 \Rightarrow n = 8$ half lives
Time $= n \times T_{1/2} = 8 \times 12.5 = 100$ hours
(256 $\rightarrow$ 128 $\rightarrow$ 64 $\rightarrow$ 32 $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4 $\rightarrow$ 2 $\rightarrow$ 1 g)
$2^n = 256 = 2^8 \Rightarrow n = 8$ half lives
Time $= n \times T_{1/2} = 8 \times 12.5 = 100$ hours
(256 $\rightarrow$ 128 $\rightarrow$ 64 $\rightarrow$ 32 $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4 $\rightarrow$ 2 $\rightarrow$ 1 g)