After two hours, one- sixteenth of the starting amount of a certain radioactive

Question

After two hours, one- sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is

Options:

A . 15 minutes

B . 30 minutes

C . 45 minutes

D . 1 hour

Answer: Option B
:
B

\frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{t}{T}} \Rightarrow (\frac{1}{16}) = {(\frac{1}{2})}^{\frac{2}{T}} \Rightarrow {(\frac{1}{2})}^{4} = {(\frac{1}{2})}^{\frac{2}{T}}

\Rightarrow

T = 0.5 hour = 30 minutes.

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