The atomic mass of uranium `._(92)^(238)U` is `23.058 u`, that of throium` ._(90)^(234)Th` is `234.0436 u` and that of an alpha particle `._2^4He` is `4.006 u`, Determine the energy released when `alpha-decay` converts`._(92)^(238)U` into `._(92)^(238) U`. int `._(90)^(234)Th`.

Explanation

Since energy is released during the decay, the combined mass of the `._(92)^(234)Th` daughter nucleus and the `alpha -` particle is less than the mass of the `._(92)^(238)U` parent nucleus. The difference in mass is equivalent to the energy released. We will determine the difference in mass in atomic mass units and then use the fact that `1 u` is equialent to `931.5 MeV`.
The decay and the masses are shown below:
`underset(238.0508 u)(._(90)^(238)U) rarr underset (ubrace(234.0436 u" "4.0026 u)_("238.0462 u")) (._(90)^(234)+._2^4He)`
The decrease in mass is `238.0508 u- 238.0462 u = 0.0046 u`. As usual, the masses are atomic and include the mass of the orbital electrons. But this causes no error here bacause the same total number of electrons is included for `._(92)^(234) Th` plus `._2^4He`, on the other. Since `1 u` is equivalent to `931.5 MeV`, the released energy is` 4.3 MeV`. When `alpha-decay ` occurs as discussed in Illustration `5.10`, the energy released appears as kinetic energy of the recoiling `._(90)^(234) Th` nucleus and the `alpha` - particle , except for a small portion carried away as ` gamma -ray`. Illustration `5.11` discusses how the `._(90)^(234)Th` nucleus and the `alpha` - particle share the released energy.