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

The correct option is B 30 minutes

$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{t}{T}}\Rightarrow \left(\frac{1}{16}\right)={\left(\frac{1}{2}\right)}^{\frac{2}{T}}\Rightarrow {\left(\frac{1}{2}\right)}^4={\left(\frac{1}{2}\right)}^{\frac{2}{T}}$
$\Rightarrow$ T = 0.5 hour = 30 minutes.