Nuclear Chemistry and RadioactivitymediumCOMPREHENSIVE

The nuclide , mass 49.9516 amu, is neutron rich. It decays to form , mass 49.94479 amu. If the emittNuclear Chemistry and Radioactivity Chemistry Question

Question

The nuclide $\text{Sc}^{50}$, mass 49.9516 amu, is neutron rich. It decays to form $\text{Ti}^{50}$, mass 49.94479 amu. If the emitted $\beta$-particle has a kinetic energy of 0.80 MeV, what is the kinetic energy of the antineutrino emitted simultaneously?

Answer: B

💡 Solution & Explanation

The mass defect is $\Delta m = 49.9516 \text{ amu} - 49.94479 \text{ amu} = 0.00681 \text{ amu}$. The total disintegration energy ($Q$-value) is $E = \Delta m \times 931.5 \text{ MeV/amu} = 0.00681 \times 931.5 \approx 6.34 \text{ MeV}$. By conservation of energy, $Q = \text{KE}_{\beta} + \text{KE}_{\bar{\nu}}$. Thus, $\text{KE}_{\bar{\nu}} = 6.34 \text{ MeV} - 0.80 \text{ MeV} = 5.54 \text{ MeV}$. Therefore, correct answer is B.

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