The binding energy of the k-shell electron in a Uranium atom (Z = 92, A = 238) will be modified due to (i) screening caused by other electrons and (ii) the finite extent of the nucleus as follows:
(a) increases due to (i), remains unchanged due to (ii).
(b) decreases due to (i), decreases due to (ii).
(c) increases due to (i), increases due to (ii)
(d) decreases due to (i), remains unchanged due
to (ii).?

Question

Answer

Binding Energy Modification in Uranium Atom
The binding energy of the k-shell electron in a Uranium atom is influenced by two main factors: screening by other electrons and the finite extent of the nucleus.
1. Screening Effect
- Screening occurs when inner electrons reduce the effective nuclear charge experienced by outer electrons.
- In Uranium (Z = 92), the presence of multiple electrons leads to significant electron-electron interactions.
- This results in a decrease in the binding energy of the k-shell electron due to the reduced effective nuclear charge felt by the electron.
2. Finite Nucleus Effect
- The finite size of the nucleus also impacts the binding energy.
- An electron in the k-shell interacts with a nucleus that is not a point charge but has a finite volume.
- However, the effect of the nucleus's finite extent does not significantly change the binding energy of the k-shell electron, as its primary influence is related to the average distance of the electron from the nucleus.
Conclusion
Based on the effects described:
- The binding energy decreases due to screening (i), as the effective nuclear charge is diminished.
- The binding energy remains unchanged due to the finite extent of the nucleus (ii), since this effect is relatively minor for k-shell electrons.
Therefore, the correct answer is: (d) decreases due to (i), remains unchanged due to (ii).

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