Question

50V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of 1.00 kg of 50V is 1.75 Bq. What is the half-life in years?

Answer 1

Answer on Question #49454-Physics-Nuclear Physics

50V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of $1.00\mathrm{kg}$ of 50V is 1.75 Bq. What is the half-life in years?

Solution

The activity $R$ of a source is related to $N$ and $t_{\frac{1}{2}}$ by

$$R = \frac{0.693N}{t_{\frac{1}{2}}}.$$ $$N = \frac{m}{m_0} = \frac{1.00\ \mathrm{kg}}{\left(50 \cdot 1.66 \cdot 10^{-27} \frac{\mathrm{kg}}{\mathrm{nucleos}}\right)} = 0.012 \cdot 10^{27}\ \mathrm{nucleos}.$$

The half-life is

$$t_{\frac{1}{2}} = \frac{0.693N}{R} = \frac{0.693 \cdot 0.012 \cdot 10^{27}}{1.75\ \mathrm{s}^{-1}} = 4.752 \cdot 10^{24}\ \mathrm{s} = \frac{4.752 \cdot 10^{24}}{31557600}\ \mathrm{years} = 1.48 \cdot 10^{17}\ \mathrm{years}.$$

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