Question

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

• A. 15 minutes
• B. 30 minutes
• C. 45 minutes
• D. 1 hour

Answer 1

Answer: (B)

30 minutes

Answer 2

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

$\Rightarrow T = 0.5\mspace{6mu} hour$ = 30 minutes.