Hydrogenic (one-electron) ions provide a convenient way to compare the strength of…
PHYSICS · Multi-part · CBSE · Physics · Electric Charges and Fields · Electric Charges and Fields
Problem
Hydrogenic (one-electron) ions provide a convenient way to compare the strength of electrostatic attraction between a nucleus and an electron across different nuclear charges. Consider the following two species:
• H (atom): Z = 1, average electron–nucleus distance 5.29×10⁻¹¹ m
• Li²⁺ (ion): Z = 3, average electron–nucleus distance 3.04×10⁻¹¹ m
Assume each nucleus is a point charge of magnitude +Ze and that each species contains exactly one electron.
(a) Calculate the magnitude of the electrostatic force acting on the electron in the hydrogen atom.
(b) Calculate the magnitude of the electrostatic force acting on the electron in the Li²⁺ ion.
(c) Compute the ratio of the Li²⁺ force to the H force and comment on the numerical result.
(d) Use your finding from part (c) to predict which species has the larger first ionization energy and justify your prediction in terms of electrostatic considerations.
(e) Discuss how your analysis illustrates the combined influence of nuclear charge and electron–nucleus separation on periodic trends in ionization energy.