Question

The half-life of a radioisotope is $5$ years. After $25$ years, the mass of the undecay isotope remaining in a sample is $60$g. What was the initial mass of the isotope in the sample?

• A. $960$g
• B. $1920$g
• C. $600$g
• D. $3000$g

Answer 1

The correct option is B $1920$g

$\begin{array}{c}n=\text{no. of half}\text{lifes}\\ N_0=\text{Initial mass}\end{array}$

$\begin{array}{c}\text{Half life}{t}_{1/2}=5\text{years}\\ \text{Total Time}T=25\text{years}\\ N=\text{left mass}=60g\\ T=n\times t_{1/2}\\ 25=n\times 5\\ n=5\\ N=N_0\times {\left(\frac{1}{2}\right)}^n\\ 60=N_0\times {\left(\frac{1}{2}\right)}^5\\ 60\times 32=N_0\\ 1920g=N_0\end{array}$