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 `._(90)^(234)Th` daughter nucleus and the `alpha`- particle is less than the mass of the `._(90)^(238)U` parent nucleus. The difference in mass is equivalent to the energy released. We will determine the that 1 u is equivalent to 931.5 MeV. The decay and the masses are shown below:
`{:(._(92)^(238)Uto._(90)^(234)Th" + x"._(2)^(4)He),("238.0508 "ubrace("234.0436 4.0026 u")_("238.0462 u")):}`
The decrease in mass is 238.0508 u-238.0462 u=0.0046u. Since 1 u is equivalent to `931.5 MeV`, the released energy is 4.3 MeV. When `alpha` - decay occurs the energy released appears as kinetic energy of the recoiling `._(90)^(234)Th` nucleus and the `alpha` -particles, except for a small portion carried away as a `gamma`-ray.