NDA (II) 2018 General Ability Test · Question 70 of 146

Correct — B, 1 nm = 10 Å. Take both units back to metres. One nanometre is 10⁻⁹ m, since 'nano' means a thousand-millionth. One ångström is 10⁻¹⁰ m by definition. Dividing one by the other, 10⁻⁹ ÷ 10⁻¹⁰ = 10, so a nanometre is ten ångströms — the nanometre is the larger of the two. The ångström survives in physics and chemistry because it is the natural size for atoms and bonds: an atom is roughly 1 to 3 Å across and the wavelength of an X-ray is of the order of 1 Å, so lengths at that scale come out as convenient small numbers.

• (a)1 nm = 10⁻¹ Å — This inverts the relation, making the nanometre one-tenth of an ångström. It is the correct statement written the wrong way round — the true inverse relation is 1 Å = 10⁻¹ nm.
• (c)1 nm = 1 Å — Treats the two units as identical. They differ by exactly a factor of ten, which matters: quoting an atomic radius of 1 Å as 1 nm overstates it tenfold.
• (d)1 nm = 10⁻² Å — Wrong in direction and in size — it would make the nanometre a hundredth of an ångström, out by a factor of a thousand from the true value.

Scientific work uses a ladder of sub-multiples of the metre, each a fixed power of ten below the last. A millimetre is 10⁻³ m, a micrometre 10⁻⁶ m, a nanometre 10⁻⁹ m and a picometre 10⁻¹² m. The ångström, written Å and named after the Swedish physicist Anders Jonas Ångström, is not an SI unit but is retained by convention at 10⁻¹⁰ m, which places it neatly between the nanometre and the picometre. The fermi or femtometre, 10⁻¹⁵ m, is the corresponding unit for nuclear dimensions.

Conversions between units of this kind are answered by writing both in metres and dividing, never by trying to recall the relation directly — recall is where the sign of the exponent gets flipped, and three of the four options here are exactly that mistake. It is worth fixing a few anchors at these scales so that an answer can be sanity-checked: an atom is about 1 Å across, visible light runs from roughly 400 to 700 nm, and X-rays have wavelengths near 1 Å, which is why they diffract from the planes of a crystal while visible light does not.

• 1 Å = 10⁻¹⁰ m and 1 nm = 10⁻⁹ m, so 1 nm = 10 Å.
• 1 micrometre = 10⁻⁶ m = 10⁴ Å; 1 picometre = 10⁻¹² m = 10⁻² Å.
• The fermi or femtometre, 10⁻¹⁵ m, is the scale of an atomic nucleus.
• X-ray wavelengths are of the order of 1 Å, comparable with the spacing of atoms in a crystal.
• Visible light spans roughly 400 to 700 nm, that is 4000 to 7000 Å.

• Flipping the exponent and making the ångström the larger unit.
• Confusing the nanometre with the micrometre, which is a thousand times larger.
• Assuming the ångström is an SI unit; it is a conventional unit retained for convenience.

Unit questions are quick marks that are lost to careless exponents — NDA asks for a conversion, or gives a physical quantity and asks which unit is the appropriate order of magnitude for it.

• practice — not a real PYQ

  The wavelength of visible light lies roughly between

  • (a)4 and 7 Å
  • (b)40 and 70 Å
  • (c)4000 and 7000 Å
  • (d)4 and 7 micrometres

  Answer(c) 4000 and 7000 Å — visible light runs from about 400 to 700 nm, and each nanometre is ten ångströms.

• practice — not a real PYQ

  One micrometre is equal to how many nanometres?

  • (a)10
  • (b)100
  • (c)1000
  • (d)10 000

  Answer(c) 1000 — a micrometre is 10⁻⁶ m and a nanometre 10⁻⁹ m, so the ratio is 10³.