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)

0.75

Answer 2

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 $=3 / 4=0.75$