Q.9 Assuming independent non-interacting electrons, the first ionization energy of Helium atom is
(A) 13.6 eV
(B) 27.2 eV
(C) 54.4 eV
(D) 108.8 eV
Answer: 54.4 eV (Option C)
The first ionization energy of a helium atom, assuming
independent non-interacting electrons, is
54.4 eV.
In this approximation, each electron is treated as moving only in the
electrostatic field of the nucleus, and
electron–electron repulsion is ignored.
Energy Calculation
Helium has atomic number Z = 2.
Using the hydrogen-like atom model, the energy of an electron in the
ground state (n = 1) is given by:
En = −13.6 Z2 / n2 (in eV)
For helium:
- Z = 2
- n = 1
E = −13.6 × (2)2 = −54.4 eV
The first ionization energy is the energy required to remove
one electron from the atom:
He → He+ + e−
Thus, the ionization energy equals the magnitude of the orbital energy:
First ionization energy = 54.4 eV
Reality vs Approximation
In real helium atoms, electrons repel each other, reducing the effective
nuclear charge experienced by each electron.
Because of this screening effect, the
experimental first ionization energy of helium is much lower,
about 24.6 eV.
However, this problem explicitly assumes
independent, non-interacting electrons, so electron–electron
repulsion is neglected.
Option Analysis
- (A) 13.6 eV – Ionization energy of hydrogen (Z = 1)
- (B) 27.2 eV – Equals 2 × 13.6 eV; incorrect for helium
- (C) 54.4 eV – Correct under independent-electron model
- (D) 108.8 eV – Double of 54.4 eV; not the first ionization
✔️ Correct option: (C)
First Ionization Energy of Helium: Independent Electron Model
The independent non-interacting electron model is commonly used in
quantum chemistry to simplify multi-electron atoms.
In this model, each electron behaves like a hydrogen-like electron
with the full nuclear charge.
Core Formula
En = −13.6 Z2 / n2 eV
For helium (Z = 2, n = 1):
E = −54.4 eV
Exam Relevance (CSIR NET / GATE)
- Distinguish between independent-electron model and experimental values
- First ionization energy (model) ≠ observed value
- Second ionization energy of He+ is exactly 54.4 eV experimentally
- Frequently tested in atomic structure and quantum chemistry
Keywords: first ionization energy helium atom, independent non-interacting electrons,
helium ionization energy 54.4 eV, CSIR NET quantum chemistry
