Question

The half - life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is :

• A. 1.042 g
• B. 2.084 g
• C. 3.125 g
• D. 4.167 g.

Answer 1

Answer: (C)

3.125 g

Answer 2

$t_{1/2} = 4hoursn = \frac{T}{t_{1/2}} = \frac{24}{4} = 6;N = N_{0}\left( \frac{1}{2} \right)^{N}$

or,$N = 200 \times \left( \frac{1}{2} \right)^{6} = 200 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = 3.125g.$