Question

A radioactive source has a half-life of 30 days. During a period of 90 days the fraction of atoms that have decayed would be

• A. 100%
• B. 87.5%
• C. 64%
• D. 50%

Answer 1

Answer: (B)

87.5%

Given: $T_{1/2}=30days,t=90days$

By using the relation, $n{T}_{1/2}=t$

$n=t/T_{1/2}=90/30=3$

Now by, $\frac{N}{N_0}=(\frac{1}{2}{)}^n$

where, $N=$ number of atoms after $t$

$N_0=$initial number of atoms

hence, $\frac{N}{N_0}=(\frac{1}{2}{)}^3$

$N=N_0/8$

Therefore, fraction of atoms decayed $=N_0-N_0/8=7N_0/8=0.875N_0$ or $87.5$%