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Nuclei

Question

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The half-life of radio isotope is 4 h. If initial mass of the isotope was 200 g, then mass remaining after 24 h will be

1.042 g

2.084 g

3.125 g

4.167 g

Solution

C.

3.125 g

half-life of radio isotope = 4 h

Initial mass M_o = 200 g

M = M_o ${(\frac{1}{2})}^{\frac{t}{t_{1 / 2}}}$

∴ M = 200 ${(\frac{1}{2})}^{\frac{24}{2}}$

= $200 {(\frac{1}{2})}^{6}$

= $\frac{200}{64}$

M = 3.125 g

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