Question

Radioactive lead ${ }_{82} Pb ^{201}$ has a half-life of $8$ hours. Starting from one milligram of this isotope, how much will remain after $24$ hours?

• A. $ \frac{1}{2}mg $
• B. $ \frac{1}{4}mg $
• C. $ \frac{1}{8}mg $
• D. $ \frac{1}{6}mg $

Answer 1

Answer: (C)

We know that mass left = initial mass $ \frac{1}{2}\times $ number of half lives
Here, initial mass $= 1 \,mg$,
number of half lives $ =\frac{24}{8}=3 $
$ \therefore $ mass left $ =1\times {{\left( \frac{1}{2} \right)}^{3}}=\frac{1}{8}mg $