Consider an \(\alpha\) particle, which is the nucleus of \({ }_{2}^{4} \mathrm{He}\) atomic mass \(4.002603 \mathrm{u}\).

(a) Use the data in Table 10.1 to calculate the binding energy per nucleon.

(b) Release of an \(\alpha\) particle from a nucleus is a common mode of decay for many radioactive heavy nuclei. Explain why the \(\alpha\) decay of \({ }_{88}^{226} \mathrm{Ra}\) is more likely than decay by release of a \(p^{+}\). The atomic mass of \({ }_{87}^{225} \mathrm{Fr}\) is 225.025572 .

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Table 10.1 Some useful mass-energies Species Mass-energy (MeV) Mass unit 931.494 938.272 mpt me- 939.565 0.511