UPSC Combined Geo-Scientist, Mains · 2016 · Mains Paper II
Q1(l). Ionization of helium ion
Question
Ionization removes the electron from n=1 to n=∞. Calculate the ionization energy of He⁺ in kJ mol⁻¹, given the hydrogen Rydberg energy 2.178×10⁻¹⁸ J. Compare it with hydrogen.
Answer in brief
I(He⁺)=5246 kJ mol⁻¹, four times the hydrogen value in the hydrogenic approximation.
Key points
- For a one-electron ion, Eₙ=-REZ²/n². The ionization limit has E_∞=0.
- With Z=2, the energy per ion is I=4RE=8.712×10⁻¹⁸ J.
- Multiplying by NA and dividing by 1000 gives 5246.4 kJ mol⁻¹. The Z² dependence reflects stronger electron–nucleus attraction; small reduced-mass corrections are neglected.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversIonization of helium ionAtomic structure
All parts of Question 1
- 1(a) Virial equation5 marks
- 1(b) Inclined capillary5 marks
- 1(c) Entropy and diffraction5 marks
- 1(d) Equipartition in hydrogen5 marks
- 1(e) Expansion cooling of helium5 marks
- 1(f) Temperature dependence of equilibrium5 marks
- 1(g) Ammonium chloride pH5 marks
- 1(h) Reverse osmosis5 marks
- 1(i) Rate-law determination5 marks
- 1(j) Monolayer surface area5 marks
- 1(k) Electrolysis of copper sulfate5 marks
- 1(l) Ionization of helium ion5 marks
- 1(m) Photochemical quantum yield5 marks
- 1(n) Momentum in a box5 marks
- 1(o) Formaldehyde electronic transitions5 marks
- 1(p) NMR distinction of ethers5 marks