The half-life of 215At is 100 μ s. The time taken for the radioactivity of sample of 215 At to decay to (1/16)th of its initial value is

Question

The half-life of 215At is 100 μ s. The time taken for the radioactivity of sample of 215 At to decay to (1/16)th of its initial value is (A) 100 μ s. (B) 200 μ s. (C) 300 μ s. (D) 400 μ s.

Tardigrade Admin · Accepted Answer

N = (N0/16) and T = 100 μs Using, (N/N0) = ( (1/2) )t/T we get (1/16) = ( (1/2) )t/T or ( (1/2) )4 = ( (1/2) )t/T or (t/T) = 4 or t = 4 T = 4 × 100 = 400 μs

Q. The half-life of $^{215} A t$ is $100 μ s$ . The time taken for the radioactivity of sample of $^{215} A t$ to decay to $\frac{1}{16}^{t h}$ of its initial value is

$100 μ s$ .

$200 μ s$ .

$300 μ s$ .

$400 μ s$ .

N = $\frac{N _{0}}{16}$ and T = 100 $μ$ s
Using, $\frac{N}{N _{0}} = (\frac{1}{2})^{t / T}$ we get $\frac{1}{16} = (\frac{1}{2})^{t / T}$
or $(\frac{1}{2})^{4} = (\frac{1}{2})^{t / T}$ or $\frac{t}{T}$ = 4 or $t$ = 4 T = 4 $\times$ 100 = 400 $μ$ s

Q. The half-life of 215At is 100μs. The time taken for the radioactivity of sample of 215At to decay to 161​th of its initial value is

100μs.

200μs.

300μs.

400μs.