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The atomic mass of thorium .(90)^(234)Th...

The atomic mass of thorium `._(90)^(234)Th` is `234.04359 u`, while that of protactinium `._(91)^(234)Pa` is `234.04330 u`. Find the energy released when `beta` decay changes `overset(234)(90)Th` into

Text Solution

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To find the energy released, we follows the usual procedure of determining how much the mass has decreased because of the decay and then calculating the equivalent energy. The decay and the masses are shown below:
`underset(234.04359 u) (._(90)^(234)Th) rarrubrace(._(91)^(234)Pa+._(1)^(0)e)_("234.04330 u")`
When the `._(90)^(234)Th` nucleus of a thorioum atom is converted into a `._(91)^(234)Pa ` nucleus, the number of orbital electrons remains the same, so the resulting protactinium atom is missing one orbital electron. However, the given mass includes all `91` electrons of a neutral protactinium atom. In effect, then, the value of `234.04330 u` for `._(91)^(234)Pa` already includes the mass of the `beta` particle. Tha mass decrease that accompanies the `beta^(-)` decay is `234.04359 u -234.04330u = 0.00029 u`. The equivalent energy `(1 u=931.5MeV)` is` 0.27 MeV`. This is the maximum kinetic energy that the emittted electron can have.
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