Which one of the following is the size of hydrogen atom ?
- (a)10^-10 m
- (b)10 μm
- (c)10 mm
- (d)1000 Å
Answer
Why
Correct — A, (a) 10^-10 m. The hydrogen atom is the smallest and simplest atom there is — one proton with one electron around it — and its diameter is of the order of 10^-10 metre, which is one angstrom. The standard number behind this is the Bohr radius, the radius of the electron's ground-state orbit in the Bohr model, equal to about 0.53 x 10^-10 m; doubling it gives a diameter of roughly 1.06 x 10^-10 m, so 10^-10 m is the right order of magnitude. That figure is worth memorising because it is not special to hydrogen: atoms in general are one to a few angstroms across, which is why the angstrom exists as a unit at all and why it is the natural yardstick for bond lengths and crystal spacings. Keep the companion number beside it — the nucleus is about 10^-15 m across, so the atom is roughly a hundred thousand times wider than the nucleus at its centre, and is overwhelmingly empty space.
Why the others are wrong
- (b)10 μm — Ten micrometres is 10^-5 metre — a hundred thousand times larger than an atom. That is the scale of a CELL, not of an atom: a human red blood cell is about 7 micrometres across and a typical animal cell of the order of tens of micrometres, which is why cells are visible under an ordinary light microscope while atoms are not. The option is offered because the micro prefix reads as 'very small' and the Greek mu looks appropriately scientific; but there are three more prefixes to go — nano, then pico, then femto — before atomic and nuclear sizes are reached.
- (c)10 mm — Ten millimetres is one centimetre — a length you can see and measure with a school ruler, and about 10^8 times the size of a hydrogen atom. Nothing in atomic physics is measured in millimetres. This option exists as an obvious anchor at the wrong end of the scale, and its real function is to reward a candidate who works in orders of magnitude: converting every option to metres in scientific notation gives 10^-10, 10^-5, 10^-2 and 10^-7, and the answer is then simply the smallest.
- (d)1000 Å — This is the most carefully built of the three wrong options, because it uses the right UNIT with the wrong number. One angstrom equals 10^-10 metre, so 1000 angstrom is 10^-7 metre, or 100 nanometres — a thousand times too large for an atom. That is the scale of a virus or of a colloidal particle, not of an atom. A candidate who has learnt only the phrase 'atomic sizes are measured in angstrom' and not the value that goes with it will find this option convincing. The figure to hold is that an atom is of the order of ONE angstrom, a few at most, so a thousand of them is a different world.
Concept
Order-of-magnitude estimation is a skill the general ability paper tests directly, and the way to hold it is a ladder of standard lengths in metres: the nucleus at about 10^-15 m, an atom at about 10^-10 m, a small molecule at a few times 10^-10 m, a virus at about 10^-7 m, a bacterium at about 10^-6 m, an animal cell at about 10^-5 m, and a grain of sand at about 10^-3 m. Each rung is a factor of ten or more from its neighbours, so a wrong answer on this ladder is not slightly wrong but wildly wrong. The units that go with those rungs matter as much as the numbers: 1 angstrom = 10^-10 m, 1 nanometre = 10^-9 m, 1 micrometre = 10^-6 m, 1 millimetre = 10^-3 m, and 1 fermi or femtometre = 10^-15 m, the unit used for nuclear sizes. For the hydrogen atom in particular, the Bohr model puts the ground-state electron at the Bohr radius, about 0.53 angstrom, from the proton; the modern quantum-mechanical picture replaces the orbit by a probability cloud but gives the same characteristic size, since the Bohr radius is the distance at which the electron is most likely to be found. The comparison between atom and nucleus is the point Rutherford's gold-foil experiment established: almost all the mass of an atom is concentrated in a nucleus a hundred thousand times smaller than the atom, and the rest is the electron cloud.
Questions of this shape reward a candidate who converts before comparing. The four options are printed in four different units — a power of ten in metres, micrometres, millimetres and angstrom — and the mixture is the difficulty. Put them all into metres and the item becomes trivial. It is also worth noticing that the paper prints the exponent as a true superscript on the page; in this transcription it is written with a caret, so 10^-10 m means ten to the power minus ten metres. The unit conversions here are exactly the ones a general ability paper expects a graduate to carry without a reference table.
Key facts
- The diameter of a hydrogen atom is of the order of 10^-10 metre, that is about one angstrom.
- The Bohr radius, the ground-state electron orbit radius in the Bohr model of hydrogen, is about 0.53 x 10^-10 metre.
- 1 angstrom = 10^-10 m; 1 nanometre = 10^-9 m; 1 micrometre = 10^-6 m; 1 fermi (femtometre) = 10^-15 m.
- An atomic nucleus is about 10^-15 metre across, so an atom is roughly 100,000 times wider than its nucleus.
- Atoms generally measure one to a few angstrom, which is why the angstrom is the working unit for bond lengths and crystal spacings.
- 1000 angstrom is 10^-7 metre, the scale of a virus or a colloidal particle, not of an atom.
- 10 micrometres is the scale of a biological cell; a human red blood cell is about 7 micrometres across.
- Hydrogen is the simplest atom, with one proton and one electron and, in its commonest isotope, no neutron.
Study next
Common traps
- Comparing options that are printed in different units without converting them all to metres first.
- Treating 'micro' as small enough for atomic scale. It is five orders of magnitude too large.
- Knowing that atomic sizes are quoted in angstrom but not that an atom is about ONE angstrom, which makes 1000 angstrom look right.
- Confusing the size of the atom, about 10^-10 m, with the size of the nucleus, about 10^-15 m.
- Reading 10^-10 as ten to the power ten, or losing the minus sign when the superscript is written inline.
Order-of-magnitude items appear in the physics and chemistry blocks of EPFO EO/AO papers as sizes, and elsewhere as unit conversions. The usual shapes are 'which one of the following is the size or order of X', 'arrange these in increasing order of size', and 'one angstrom equals how many metres'. The distractor built on the right unit with a wrong multiplier, as here, is the standard trap in this family.
Related PYQs
EPFO_EOAO_2020_Q54Open & attempt →Who among the following discovered Proton ?
- (a) J.J. Thomson
- (b) E. Goldstein
- (c) E. Rutherford
- (d) J. Chadwick
Answer(b) E. Goldstein
The chemistry block's item on who discovered the proton. It belongs to the same story as this one: the experiments that established what is inside an atom are also the experiments that established how small the nucleus is compared with the atom around it.
Practice
- practice — not a real PYQ
One angstrom is equal to
- (a)10^-6 m
- (b)10^-8 m
- (c)10^-10 m
- (d)10^-15 m
Answer(c) 10^-10 m
- practice — not a real PYQ
The diameter of an atomic nucleus is of the order of
- (a)10^-10 m
- (b)10^-12 m
- (c)10^-15 m
- (d)10^-20 m
Answer(c) 10^-15 m