NDA (II) 2018 General Ability Test · Question 108 of 146

Correct — A, 1 Å. One ångström is 10⁻¹⁰ metre, and that is the size of the X-ray region of the electromagnetic spectrum, which runs from roughly 0.01 to 10 nanometres. The number is easy to remember because it is also the scale of the atom: typical atomic radii and the spacing between planes of atoms in a crystal are about an ångström, which is precisely why X-rays and not light are used to work out crystal structures. The remaining options step upward by factors of ten thousand at a time and land in the infrared, the microwave and the radio-microwave regions instead.

• (b)1 μm — One micrometre is 10⁻⁶ metre, ten thousand times longer than an ångström. That is the infrared region, just beyond the red end of visible light — the radiation a warm body emits, not the radiation that passes through soft tissue.
• (c)1 mm — A millimetre is 10⁻³ metre and belongs to the microwave region, at the boundary with the far infrared. Radiation of that wavelength is used for radar and for heating food, and cannot resolve anything smaller than about a millimetre.
• (d)1 cm — A centimetre is longer still and sits firmly in the microwave band used for radar and satellite communication. It is about a hundred million times the wavelength of an X-ray.

The electromagnetic spectrum is one continuous family of waves, all travelling at the speed of light in vacuum and differing only in wavelength and therefore in frequency and photon energy. In order of increasing wavelength it runs gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves. Because energy is inversely proportional to wavelength, the short-wavelength end carries the most energetic photons and the greatest penetrating power.

You do not need to recall a table to answer this. Anchor the spectrum at visible light, which is about 400 to 700 nanometres, and then ask which side of it X-rays lie on. X-rays penetrate flesh and are far more energetic than light, so they must be at the short end — shorter than 400 nm and therefore far shorter than a micrometre. That leaves only the ångström. A related check worth keeping is that the NDA asked the same question in 2022 with the answer given as 1 nm, and both figures are correct because the X-ray band is about 0.01 to 10 nm wide; 1 Å is simply 0.1 nm, well inside it.

• 1 ångström equals 10⁻¹⁰ metre, or 0.1 nanometre.
• The X-ray band spans roughly 0.01 to 10 nanometres, so both 1 Å and 1 nm fall inside it.
• Visible light runs from about 400 nm at the violet end to about 700 nm at the red end.
• X-ray wavelengths match the spacing between atomic planes in a crystal, which is what makes X-ray diffraction possible.

• Assuming a shorter wavelength means a smaller number in whatever unit is printed; the unit is doing the work here, not the digit.
• Confusing the micrometre with the nanometre, which are a thousand apart.
• Placing X-rays beyond the red end of the visible spectrum because they are invisible; ultraviolet, X-rays and gamma rays all lie beyond the violet end.

Asked as a one-line order-of-magnitude recall in which all four options are lengths and the unit is the whole question.

• practice — not a real PYQ

  Which one of the following regions of the electromagnetic spectrum has the longest wavelength?

  • (a)Ultraviolet
  • (b)Infrared
  • (c)X-rays
  • (d)Gamma rays

  Answer(b) Infrared — it lies beyond the red end of visible light, while ultraviolet, X-rays and gamma rays all lie beyond the violet end with progressively shorter wavelengths.

• practice — not a real PYQ

  X-rays are used to determine the structure of crystals because their wavelength is comparable to

  • (a)the diameter of a human hair
  • (b)the spacing between atomic planes in the crystal
  • (c)the wavelength of visible light
  • (d)the thickness of a soap film

  Answer(b) the spacing between atomic planes in the crystal — both are of the order of an ångström, so the crystal acts as a diffraction grating for X-rays.