Number of electrons present in the species H2+, He, H2 and O2+ respectively are:

Correct — A, 1, 2, 2, 15. There is one rule to apply and it applies four times: the number of electrons equals the total number of protons, which is the sum of the atomic numbers of the atoms present, minus the overall charge. Take them in order. H₂⁺ is two hydrogen nuclei, so two protons, carrying a single positive charge — two minus one gives one electron. That single electron sits in a bonding orbital shared between the two nuclei, giving a bond order of one half, and H₂⁺ is the simplest molecular ion there is, which is why quantum chemistry uses it as its first worked example. Helium is a neutral atom of atomic number two, so two electrons. H₂ is a neutral molecule of two hydrogen atoms, so one plus one, again two electrons — which makes H₂ and He isoelectronic, the same electron count on two completely different species. O₂⁺ is two oxygen atoms, eight protons each, sixteen in all, less one for the positive charge: fifteen. The sequence is therefore 1, 2, 2, 15. A detail worth knowing about that last species: the electron removed from O₂ to make O₂⁺ comes out of an antibonding orbital, so the bond actually gets stronger and shorter, and the bond order rises from two to two and a half.

• (b)1, 2, 1, 14 — Right about H₂⁺ and helium, then wrong twice. It gives H₂ one electron, which is really H₂⁺ counted again, and O₂⁺ fourteen, which would be O₂²⁺.
• (c)2, 2, 2, 16 — Ignores the charges altogether. Two, two, two and sixteen are the counts for neutral H₂, He, H₂ and O₂ — the answer of a candidate who read the formulae but not the plus signs.
• (d)0, 2, 1, 14 — Strips too much. It leaves H₂⁺ with no electrons at all, gives neutral H₂ a single electron, and takes two away from O₂ instead of one.

Electrons are counted from protons and charge, never from mass. For any species, add the atomic numbers of all the atoms in the formula to get the proton count, then subtract the charge — subtracting a positive charge because electrons have been removed, adding for a negative one because electrons have been gained. The mass number plays no part in this, which is what separates the calculation from questions about isotopes. Two species with the same electron count are called isoelectronic, and they often share shape and bonding even when they are made of different elements.

This is a four-part calculation dressed up as a recall question, and the marks are lost in reading rather than in arithmetic. Three of the four species carry a subscript, a superscript or both, and the subscript multiplies the atoms while the superscript changes the electron count — mixing them up produces precisely the wrong options offered here. The safe habit is to write out each species as protons first and only then apply the charge. It is also useful to notice what the question has quietly put side by side: H₂ and He both have two electrons, so the paper is testing whether a candidate can hold apart a neutral molecule and a neutral atom that happen to be isoelectronic.

• Number of electrons = sum of the atomic numbers of the atoms present − the overall charge.
• H₂⁺ has one electron and a bond order of one half; it is the simplest molecular ion and the standard test case of quantum chemistry.
• H₂ and He each have two electrons, which makes them isoelectronic despite being a molecule and an atom.
• O₂ has sixteen electrons, so O₂⁺ has fifteen.
• The electron lost in forming O₂⁺ comes from an antibonding orbital, so the bond order rises from 2 to 2·5 and the bond becomes shorter and stronger than in O₂.
• Neil Bartlett's dioxygenyl salt O₂⁺[PtF₆]⁻, made in 1962, is what led him to try the same reaction with xenon and produce the first noble-gas compound.

• Reading the subscript and the superscript as the same kind of number.
• Forgetting to subtract for a positive charge, which turns every species into its neutral parent.
• Bringing mass number into an electron count; only atomic number and charge matter.

As a multi-species count like this one, as an isoelectronic-pair question, or through bond order, where the electron count of O₂⁺, O₂ and O₂⁻ has to be turned into a strength comparison.

• practice — not a real PYQ

  Which one of the following has the same number of electrons as the neon atom?

  • (a)Na⁺
  • (b)Cl⁻
  • (c)Ca²⁺
  • (d)Ar

  Answer(a) Na⁺ — sodium has 11 protons and the ion has lost one electron, leaving 10, the same as neon.

• practice — not a real PYQ

  The bond order of the H₂⁺ ion is

  • (a)0
  • (b)0·5
  • (c)1
  • (d)2

  Answer(b) 0·5 — one electron in a bonding orbital and none in the antibonding orbital gives a bond order of one half.