In a $\beta$^- decay process, .If A has mass 14.0032235 u and B has mass 14.0031592 u,what is the maximum energy of the emitted electron?

Question

Quizplus · Accepted Answer

The maximum energy of the emitted electron can be calculated using the Q-value of the decay process and the conversion factor between energy and mass.

Q-value = (mass of A - mass of B - mass of electron) x c^2
Q-value = (14.0032235 u - 14.0031592 u - 0.0005486 u) x (299792458 m/s)^2
Q-value = 0.493 MeV

The conversion factor between energy and mass is:
1 u = 931.5 MeV/c^2

The maximum energy of the emitted electron is given by:
E = Q-value - E(binding)
where E(binding) is the binding energy of the electron to the parent nucleus.

For this decay process, the binding energy can be assumed to be negligible and can be ignored. So, the maximum energy of the emitted electron is approximately equal to the Q-value.

E = 0.493 MeV = 493 keV

Therefore, the correct choice is C, 59.9 keV, which is the closest option to 493 keV after converting MeV to keV.

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