We are given the following atomic masses: 92238U=238.05079 u 24He=4.00260 u 90234Th=234.04363 u 11H=1.00783 u 91237Pa=237.05121 u. Take 1 u≡931.5 MeVHere the symbol Pa is for the element protactinium (Z = 91). Mark the CORRECT statement(s)
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a
The energy released during the α -decay of 92238U is 4.75 MeV rounded to two places after decimal.
b
The energy released during the α-decay of 92238U is 4.25 MeV rounded to two places after decimal.
c
The emission of proton from 92238U can be spontaneous.
d
The emission of proton from 92238U cannot be spontaneous.
answer is B.
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Detailed Solution
The energy released in α-decay is given by Q=(Mu−MTh−MHe)c2Substituting the atomic masses as given in the data, we findQ=(238.05079−234.04363−4.00260)u×c2=(0.00456 u)c2=(0.00456 u)c2 =(0.00456 u)(931.5 MeV/u)=4.25 MeV .If 92238U spontaneously emits a proton, the decay process would be 92238U→ 91237Pa+ 11HThe Q for this process to happen is =(MU−MPa−MH)c2=(238.05079−237.05121−1.00783)u×c2=(−0.00825 u)c2 =−(0.00825 u)(931.5 MeV/u) =−7.68 MeVThus, the Q of the process is negative and therefore it cannot proceed spontaneously. We will have to supply energy of 7.68 MeV to a 92238U nucleus to make it emit a proton.