NDA (II) 2017 General Ability Test · Question 114 of 150

Correct — A, X-rays. The energy of a single photon is Planck's constant multiplied by the frequency of the radiation, so the photon energy rises with frequency and falls with wavelength. Of the four choices, X-rays have by far the highest frequency: their wavelengths are of the order of one angstrom, that is about 0.1 nanometre, against roughly 400 to 700 nanometres for visible light, millimetres to centimetres for microwaves and metres or more for radio waves. Shortest wavelength therefore means highest frequency and the largest energy per photon, which is exactly why X-rays are ionising and the other three are not.

• (b)Radio waves — Radio waves lie at the long-wavelength end of the spectrum, with the lowest frequency of the four and therefore the smallest photon energy. A powerful transmitter delivers a lot of total energy, but only by sending an enormous number of very weak photons.
• (c)Light waves — Visible light sits between the infrared and the ultraviolet, with photon energies of a few electronvolts. That is enough to trigger vision and photosynthesis but thousands of times less than an X-ray photon.
• (d)Microwaves — Microwaves have wavelengths of the order of centimetres, so their photons are weaker than those of light. A microwave oven heats food not by energetic photons but by making water molecules rotate and rub against one another.

All electromagnetic radiation travels at the same speed in vacuum, so frequency and wavelength are inversely related, and the whole spectrum can be laid out in one order. From the lowest frequency upward it runs radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Photon energy climbs steadily along that sequence. Beyond the ultraviolet the photons become energetic enough to knock electrons out of atoms, which is what ionising radiation means.

The distinction that trips candidates is between the energy of one photon and the total energy of a beam. A radio station radiates kilowatts, far more total power than a dental X-ray unit, yet no radio wave can ionise an atom because each individual photon is far too feeble. This is the same lesson as the photoelectric effect, where increasing the brightness of red light never ejects an electron while a faint beam of ultraviolet does. It also explains the practical facts around X-rays — they pass through soft tissue, are absorbed by bone and by heavy elements like barium, and are used both for imaging and for treating some cancers, while calling for shielding of the operator.

• Photon energy equals Planck's constant times the frequency, so it rises with frequency and falls with wavelength.
• Order of increasing photon energy: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
• X-ray wavelengths are of the order of one angstrom, or about 0.1 nanometre; visible light runs from about 400 to 700 nanometres.
• X-rays are produced by bombarding a metal target with high-energy electrons, and are used in radiography and in radiotherapy.
• Gamma rays, which lie beyond X-rays, have shorter wavelengths and still higher photon energies.

• Confusing the total energy of a powerful beam with the energy of a single photon.
• Placing gamma rays and X-rays the wrong way round; gamma rays are the more energetic of the two.
• Assuming microwaves must be energetic because they cook food; they heat by molecular rotation, not by energetic photons.

NDA asks which listed radiation has the longest or shortest wavelength, or which has the greatest photon energy, or states two or three claims comparing bands.

• practice — not a real PYQ

  Which one of the following electromagnetic radiations has the longest wavelength ?

  • (a)X-rays
  • (b)Ultraviolet
  • (c)Radio waves
  • (d)Visible light

  Answer(c) Radio waves — the longest wavelength and hence the lowest frequency and photon energy of the group.

• practice — not a real PYQ

  The photon energy of an electromagnetic wave is

  • (a)directly proportional to its wavelength
  • (b)directly proportional to its frequency
  • (c)independent of frequency
  • (d)proportional to the square of the amplitude

  Answer(b) directly proportional to its frequency — energy equals Planck's constant times frequency.