Question 39.10: Mass Change in a Radioactive Decay The ^216Po nucleus is uns......
Mass Change in a Radioactive Decay
The { }^{216} \mathrm{Po} nucleus is unstable and exhibits radioactivity (Chapter 44). It decays to { }^{212} \mathrm{~Pb} by emitting an alpha particle, which is a helium nucleus, { }^{4} \mathrm{He}. The relevant masses are m_{i}=m\left({ }^{216} \mathrm{Po}\right)=216.001915 \mathrm{u} and m_{f}=m\left({ }^{212} \mathrm{~Pb}\right)+m\left({ }^{4} \mathrm{He}\right)= 211.991898 \mathrm{u}+4.002603 \mathrm{u}.
(A) Find the mass change of the system in this decay.
(B) Find the energy this mass change represents.
(A) Conceptualize The initial system is the { }^{216} Po nucleus. Imagine the mass of the system decreasing during the decay and transforming to kinetic energy of the alpha particle and the { }^{212} \mathrm{~Pb} nucleus after the decay.
Categorize We use concepts discussed in this section, so we categorize this example as a substitution problem.
Calculate the mass change:
\begin{aligned}\Delta m & =216.001915 \mathrm{u}-(211.991898 \mathrm{u}+4.002603 \mathrm{u}) \\& =0.007414 \mathrm{u}=1.23 \times 10^{-29} \mathrm{~kg}\end{aligned}
(B) Use Equation 39.24
E_{R} = m c^{2} (39.24)
to find the energy associated with this mass change:
\begin{aligned}E & =\Delta m c^{2}=\left(1.23 \times 10^{-29} \mathrm{~kg}\right)\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)^{2} \\& =1.11 \times 10^{-12} \mathrm{~J}=6.92 \mathrm{MeV}\end{aligned}