Question

A radio-active elements has half-life of $15$ years. What is the fraction that will decay in $30$ years?

• A. 0.25
• B. 0.5
• C. 0.75
• D. 0.85

Answer 1

Answer: (C)

Fraction un decayed is given as,
$N/N_0=(1/2{)}^{(t/T)}$
Here, $t=30$ years and $T=15$ years
So,
$N/N_0=(1/2{)}^{((30\text{ years })/(15\text{ years }))}$
or, $N/N_0=(1/2{)}^2$
or, $N/N_0=1/4$
Therefore,
Fraction un decayed $=1-N/N_0$
or, Fraction un decayed $=1-(1/4)$
or, Fraction un decayed $=3/4=0.75$