Question 25.5: Calculating the Energy of a Nuclear Reaction with the Mass-E...

Calculating the Energy of a Nuclear Reaction with the Mass-Energy Relationship

What is the energy, in joules and in megaelectronvolts, associated with the ∝ decay of _{}^{238}\text{U}?

_{92}^{238}\text{U} \longrightarrow _{90}^{234}\text{Th} + _{2}^{4}\text{He}

The nuclidic (atomic) masses in atomic mass units (u) are from Table D.5 in Appendix D:

_{92}^{238}\text{U} = 238.0508  u   \quad _{90}^{234}\text{Th} = 234.0437  u   \quad _{2}^{4}\text{He} = 4.0026  u

Analyze
The key concept here is the fact that, during a nuclear reaction, a loss or gain of mass is balanced by a gain or loss of energy. We need to determine the loss or gain of mass and then use the conversion factors (25.21) and (25.22) to convert the loss or gain of mass to the corresponding amount of energy.

1 \text { atomic mass unit }(u)=1.4924 \times 10^{-10}  J                                                                            (25.21)

1 \text { atomic mass unit (u)} = 1.4924 \times 10^{-10}  J \times \frac{1  MeV }{1.6022  \times  10^{-13}  J }=931.5  MeV                  (25.22)