The atomic radius of hydrogen atom is

UPSC cancelled this question and credited no option, and the reason becomes visible the moment you ask what 'the atomic radius of hydrogen' is supposed to denote. An atom has no sharp edge, so its size is not measured but defined, and chemists use several incompatible definitions. The theoretical radius of the ground-state hydrogen atom — the Bohr radius — is about 53 picometres, and the calculated self-consistent-field value is quoted at the same 53 pm. Slater's empirical table of atomic radii in crystals assigns hydrogen 25 pm. The van der Waals radius, which governs how closely a non-bonded hydrogen can be approached, is about 120 pm. Half the internuclear distance in the H₂ molecule, whose bond length is roughly 74 pm, gives the covalent radius near 37 pm on the older convention, while modern tables that fit radii across the whole periodic table put it at 31 to 32 pm. Four conventions, four different numbers, and a stem that signals none of them — that is an item nobody can key, which is why the Commission withdrew it and awarded the marks to every candidate.

• (a)37 nanometer — This one fails on units alone and can be struck out in seconds. 37 nanometres is 37,000 picometres — a thousand times larger than any radius any convention assigns to any atom, and comparable to the size of a virus rather than of an atom.
• (b)37 picometer — 37 pm is half the H–H bond length, so it is a covalent radius rather than the radius of a free hydrogen atom, and the modern tabulations give 31 to 32 pm for that same quantity. It answers a different question from the one the stem appears to ask.
• (c)17 picometer — 17 pm corresponds to no published value of any hydrogen radius — not the empirical 25 pm, not the calculated 53 pm, not the covalent 31 to 37 pm, and not the van der Waals 120 pm.
• (d)57 picometer — This sits near the Bohr radius of about 53 pm without matching it. A value that is close to a real constant but not equal to it cannot be the intended answer, and this site served 57 picometer as the answer to this item until the paper was re-verified against the official key.

Atomic size is a defined quantity, not a directly measured one, because the electron cloud has no boundary. Chemists therefore quote covalent radii (half the distance between two bonded like atoms), metallic radii (half the distance between neighbours in the metal), van der Waals radii (half the closest approach of non-bonded atoms) and calculated radii from quantum mechanics. The four differ by a factor of four or more for hydrogen.

The school convention makes the ambiguity worse rather than better: NCERT tells students that for simplicity the term atomic radius will be used to mean the covalent radius for a non-metal and the metallic radius for a metal, and it illustrates this with chlorine, whose Cl–Cl distance of 198 pm gives an atomic radius of 99 pm. Applied to hydrogen the same recipe gives 37 pm, while the free-atom definitions give 25 pm or 53 pm. Nothing in the stem says which convention is in force. The honest lesson is not a number but a habit — when a physical quantity has several standard definitions, an examiner must pin one down before the item can have an answer, and when that does not happen the item gets withdrawn.

• Hydrogen's published radii: empirical 25 pm, calculated 53 pm, covalent 31 to 32 pm in modern tables, van der Waals 120 pm.
• The Bohr radius, the ground-state orbit radius of the hydrogen atom, is 52.9 pm and is a defined physical constant.
• The H–H bond length in the hydrogen molecule is about 74 pm, so half of it is about 37 pm.
• 1 nanometre = 1000 picometres, and no atom has a radius above about 300 pm — which is why the nanometre option fails on magnitude alone.
• Atomic radius decreases across a period as effective nuclear charge grows, and increases down a group as new shells are added.

• Assuming a physical quantity named in a stem has exactly one accepted value.
• Missing an option that is wrong by a factor of a thousand because the number looks familiar and only the unit has changed.
• Quoting the van der Waals radius of hydrogen, 120 pm, when the covalent or calculated radius is wanted.

Numerical periodicity items usually ask for an order rather than a value — arrange these atoms by size, or say which trend a property follows — because a bare value invites exactly the ambiguity that sank this question.

• practice — not a real PYQ

  Which one of the following statements about atomic radius is correct?

  • (a)It increases across a period from left to right
  • (b)It decreases down a group
  • (c)It decreases across a period from left to right
  • (d)It is constant within a period

  Answer(c) It decreases across a period from left to right — effective nuclear charge rises while the valence electrons stay in the same shell.

• practice — not a real PYQ

  The van der Waals radius of an atom is always

  • (a)smaller than its covalent radius
  • (b)larger than its covalent radius
  • (c)equal to its covalent radius
  • (d)equal to half its ionic radius

  Answer(b) larger than its covalent radius — bonded atoms are pulled closer together than non-bonded ones can approach.