Question

If a radioactive element with a half-life of $100$ years is found to have transmuted so that only $25\%$ of the original sample remains, what is the age of the sample, in years?

• A. $25$
• B. $50$
• C. $100$
• D. $200$
• E. $400$

Answer 1

The correct option is D $200$

The half life period $t_{1/2}=100years$
The decay constant $k=\frac{0.693}{t_{1/2}}=\frac{0.693}{100}=0.00693/year$
The age of the sample $t=\frac{2.303}{k}log\frac{a}{a-x}=\frac{2.303}{0.00693}log\frac{100}{25}=200year$