The half-life of is . The time taken for the radioactivity of a sample of to decay to of its initial value is [2002]

Question

The half-life of ${}^{215}{At}$ is $100 μ s$ . The time taken for the radioactivity of a sample of ${}^{215}{At}$ to decay to ${\frac{1}{16}}^{th}$ of its initial value is [2002]

Smart Achievers · Accepted Answer

(1)

$A = A_{0} {(\frac{1}{2})}^{n};$ $n = number of half lives.$

$\frac{A_{0}}{16} = A_{0} {(\frac{1}{2})}^{n}$ $∴$ ${(\frac{1}{2})}^{4} = {(\frac{1}{2})}^{n}$

$∴$ $n = 4$

$Therefore, time taken to decay to$ $\frac{1}{16^{th}}$ $of its initial value.$

$∴$ $t = n \times t_{1 / 2} = (4 \times 100) μ s = 400 μ s$

Solution

Q.
The half-life of ${}^{215}{At}$ is $100 μ s$ . The time taken for the radioactivity of a sample of ${}^{215}{At}$ to decay to ${\frac{1}{16}}^{th}$ of its initial value is [2002]

1 $400 μ s$

2 $6.3 μ s$

3 $40 μ s$

4 $300 μ s$

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Solution

Q. The half-life of At215 is 100μs. The time taken for the radioactivity of a sample of At215 to decay to 116th of its initial value is [2002]

1 400 μs

2 6.3 μs

3 40 μs

4 300 μs