---
title: "Two helium atoms: bonding and antibonding orbitals"
subject: "Electrical Engineering Material"
chapter: 1
key: "semester_3/electrical_engineering_material:helium-atoms-bonding-orbitals"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/helium-atoms-bonding-orbitals
site: BCT Engineering
---

# Two helium atoms: bonding and antibonding orbitals

Electrical Engineering Material · Chapter 1: Theory of Metals

- Asked in: 2074 Asoj, 6 marks
- Video: [Valence Bond Theory, Hybrid Orbitals, and Molecular Orbital Theory](https://www.youtube.com/watch?v=nTujP4jCbsg) — Professor Dave Explains
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/helium-atoms-bonding-orbitals
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-1

## Question

What happen when inter-atomic separation between two helium atoms is very less? Describe on the basis of formation of bonding and antibonding molecular orbital.

## Answer

When two helium atoms are brought very close, their 1s orbitals overlap, but **no stable He₂ molecule forms**; the atoms repel each other. Molecular orbital (LCAO) theory explains why.

#### Molecular orbitals formed
Each He atom has the configuration $1s^2$ (two electrons). Overlap of the two 1s orbitals gives:

$$
\psi_\sigma = \psi_{1s}(A) + \psi_{1s}(B) \qquad \text{(bonding, lower energy)}
$$

$$
\psi_{\sigma^*} = \psi_{1s}(A) - \psi_{1s}(B) \qquad \text{(antibonding, higher energy)}
$$

#### Filling the orbitals
There are 4 electrons in total. Each MO can hold only 2 electrons with opposite spins (Pauli exclusion principle):
- 2 electrons go into the bonding orbital $\sigma$;
- the other 2 are **forced into the antibonding orbital** $\sigma^*$.

```text
 Energy
   |           sigma*   _^v_   (2 e, raises E)
   |                   /    \
   |  1s  _^v_  ------        ------  _^v_  1s
   |   He(A)           \    /          He(B)
   |           sigma    _^v_   (2 e, lowers E)
```

#### Result
- The rise in energy of the antibonding orbital is **larger** than the fall of the bonding orbital (the antibonding level is pushed up more than the bonding level is pulled down).
- So with both orbitals full, the total energy of He–He is **higher** than that of two separate He atoms.
- Bond order $= \frac{1}{2}(N_b - N_a) = \frac{1}{2}(2 - 2) = 0$: no bond.

```text
 E (He-He)
  ^
  |\
  | \     total energy: purely repulsive,
  |  \    no minimum
  |   '.
  |     '-.__
 0+-----------'--------------------> R
```

As the separation decreases further, the electron clouds overlap more, the antibonding electrons put charge outside the internuclear region, and the nuclei repel strongly. Hence the two He atoms push each other apart.

#### Conclusion
Helium does not form He₂; it exists as a **monatomic gas**. Only very weak Van der Waals forces act between He atoms, which is why helium liquefies only at about 4.2 K. In contrast, H₂ is stable because its 2 electrons fill only the bonding orbital.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How many electrons must the He-He molecular orbitals hold?
   A. 2
   B. 3
   C. 4
   D. 8
   Answer: C. Each He has 2 electrons, 4 in total. (Key point: Electron count)

2. How are they placed?
   A. All four in sigma
   B. Two in sigma and two forced into sigma*
   C. Two in sigma* and two unpaired
   D. One in each orbital
   Answer: B. Each MO takes only two, so two go into the antibonding orbital. (Key point: Filling)

3. Bond order of He2 is:
   A. 1
   B. 2
   C. 0.5
   D. 0
   Answer: D. (2 - 2)/2 = 0. (Key point: Bond order)

4. Why is He2 not stable?
   A. Antibonding energy rise exceeds bonding fall, so total energy is higher than separated atoms
   B. Bonding orbital rises in energy
   C. Helium atoms attract too strongly
   D. 1s orbitals do not overlap
   Answer: A. With both orbitals full, net energy is raised and the atoms repel; He stays monatomic. (Key point: Energy effect)

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