Variable oxidation numbers are possible for:

Correct — C, Iron. Iron is the only transition metal on the list, and variable oxidation number is the signature property of that block. The reason lies in the arrangement of iron's electrons: it is 3d⁶ 4s², and the 3d and 4s levels are so close in energy that both sets of electrons are available for bonding. Give up the two 4s electrons and you have iron(II); give up one 3d electron as well and you have iron(III). Both are stable and both are everyday — ferrous sulphate is the iron(II) salt used in anaemia treatment, while rust is hydrated iron(III) oxide, and the ferrate ion pushes iron as far as +6 in strongly oxidising conditions. Compare that with the alternatives. A group 1 metal has exactly one loosely held electron outside a noble-gas core; taking a second would mean breaking into that core, which costs far more energy than any chemical reaction returns. A group 2 metal has two, and the same argument stops it at +2. So sodium is always +1, lithium always +1, calcium always +2, and only iron has a real choice.

• (a)Sodium — Sodium is a group 1 metal with the configuration 2, 8, 1. Losing the single outer electron gives the neon core and the stable Na⁺ ion; removing a second would break into that filled shell, so sodium shows only +1.
• (b)Calcium — Calcium is a group 2 metal with two electrons in its outermost shell. It loses both to reach the argon configuration and is therefore invariably +2 — as in calcium oxide, calcium carbonate and calcium chloride alike.
• (d)Lithium — Lithium is the first member of group 1, with configuration 2, 1. Losing its one outer electron leaves the helium core, so lithium is +1 in every compound it forms; there is no lithium(II) chemistry.

Oxidation number is the charge an atom would carry if every bond it makes were treated as fully ionic. For most main-group metals it is fixed by the group: group 1 metals show +1, group 2 metals +2, because losing the outer electrons empties a shell and reaching further would break a noble-gas core. The transition metals behave differently. Their (n – 1)d and ns orbitals are almost equal in energy, so electrons from both are available for bonding, and a single element can appear in several states. Manganese runs from +2 to +7; iron's common states are +2 and +3. The same near-equality of energy levels also explains the coloured ions, the paramagnetism and the catalytic activity typical of the block.

This is a one-word question if you spot which option belongs to a different part of the periodic table. Sodium and lithium are group 1, calcium is group 2, and iron is the sole transition metal — so the property being asked about, variable oxidation number, points straight at it. A useful cross-check is to name a compound for each: sodium chloride and lithium chloride are both NaCl-type, single-charge salts, calcium is +2 in everything from limestone to bleaching powder, but iron gives two different chlorides, FeCl₂ and FeCl₃, and two different oxides in common use. If an element has two well-known chlorides, its oxidation number is variable — and that is a test you can run without recalling any theory at all.

• Iron's configuration is 3d⁶ 4s², and its common oxidation states are +2 and +3; it reaches +6 in the ferrate ion.
• The closeness in energy of the (n – 1)d and ns orbitals is what makes both sets of electrons available for bonding in transition metals.
• Group 1 metals such as sodium and lithium show only +1; group 2 metals such as calcium show only +2.
• Iron forms two chlorides, FeCl₂ and FeCl₃, and rust is hydrated iron(III) oxide, while ferrous sulphate is an iron(II) salt.
• Along with variable oxidation states, transition metals typically show paramagnetism, coloured ions, catalytic activity and complex formation.

• Assuming any metal can show more than one oxidation state; the main-group metals here are locked to a single value by their group.
• Confusing valency with oxidation number — related ideas, but oxidation number can be negative and is defined for every atom in a compound.
• Treating zinc as a typical transition metal on this point; its d subshell is full, so it shows only +2.

Either as a which-element-shows-variable-states item like this one, or by asking for the oxidation number of a named element in a given compound or ion.

• practice — not a real PYQ

  The oxidation number of iron in Fe₂O₃ is

  • (a)+1
  • (b)+2
  • (c)+3
  • (d)+6

  Answer(c) +3 — oxygen is −2, so three oxygens give −6, and two iron atoms must together supply +6, that is +3 each. Fe₂O₃ is the iron(III) oxide of rust.

• practice — not a real PYQ

  Variable oxidation states are characteristic of the transition elements chiefly because

  • (a)their atoms are larger than those of other metals
  • (b)the (n – 1)d and ns orbitals are close in energy, so electrons from both take part in bonding
  • (c)they always form covalent compounds
  • (d)their nuclei are unstable

  Answer(b) the (n – 1)d and ns orbitals are close in energy, so electrons from both take part in bonding — which is why manganese ranges from +2 to +7 while a group 1 metal is fixed at +1.