Question 43.6: Mass Change in a Radioactive Decay The ^216Po nucleus is uns...
Mass Change in a Radioactive Decay
The { }^{216} Po nucleus is unstable and exhibits radioactivity. It decays to { }^{212} Pb by emitting an alpha particle. The relevant masses, in atomic mass units, are m_i=m\left({ }^{216} Po\right)=216.001 914 u and m_f=m\left({ }^{212} Pb\right)+m\left({ }^4 He\right)=211.991 898 u+4.002 603 u.
(A) Find the mass change of the system in this decay.
(B) Find the Q value for this decay.
(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} Pb nucleus after the decay.
Categorize We use concepts discussed in this section, so we categorize this example as a substitution problem.
Calculate the change in mass using the mass values given in the problem statement.
\begin{aligned}\Delta m=m_f-m_i & =(211.991 898 u+4.002 603 u)-216.001 914 u\\& =-0.007 413 u=-1.23 \times 10^{-29} kg\end{aligned}(B) Use Equation 43.14 to evaluate the Q value:
Q=-\Delta E_R=\left(M_{X}-M_{Y}-M_\alpha\right) c^2 (43.14)
\begin{aligned}Q=-\Delta E_R & =-(\Delta m) c^2=-\left(-1.23 \times 10^{-29} kg\right)\left(3.00 \times 10^8 m/s\right)^2 \\& =1.11 \times 10^{-12} J=6.92 MeV\end{aligned}