Which one among the following has largest energy per photon?

Correct — A, X-ray. The energy of one photon is E = hf = hc divided by the wavelength, so photon energy climbs as wavelength shortens. Order the four by wavelength and the answer falls out: infra-red runs from about 700 nanometres up to a millimetre, visible light spans roughly 400 to 700 nanometres, ultra-violet runs from about 10 to 400 nanometres, and X-rays occupy roughly 0.01 to 10 nanometres. X-rays are the shortest of the four by a wide margin, so each X-ray photon carries the most energy — of the order of kiloelectronvolts, against a few electronvolts for visible light.

• (b)Ultra-violet ray — Ultra-violet photons are more energetic than visible or infra-red ones, which is why they break chemical bonds and cause sunburn, but their wavelengths are still ten to a thousand times longer than an X-ray's.
• (c)Visible-ray — Visible light sits in the middle of the four. A green photon at 550 nanometres carries about 2.3 electronvolts, roughly a thousandth of a typical diagnostic X-ray photon.
• (d)Infra-red ray — Infra-red has the longest wavelength of the four and therefore the least energy per photon. It is felt as heat rather than seen, and it cannot ionise atoms.

Electromagnetic radiation carries energy in packets. For a single photon E = hf, where h is Planck's constant and f the frequency; since f = c divided by the wavelength, energy and wavelength move in opposite directions. Arranging the spectrum by increasing energy gives radio, microwave, infra-red, visible, ultra-violet, X-ray and gamma. Everything above ultra-violet is ionising, which is why the shielding rules for an X-ray room have no counterpart for a light bulb.

The item never mentions intensity, and that is the trap. A powerful infra-red lamp delivers far more total energy per second than a weak X-ray source, but energy per photon depends only on wavelength. Candidates who reach for brightness answer the wrong question. Memorising the spectrum in one direction is enough — put the four names in wavelength order and read off the shortest.

• Photon energy E = hc divided by wavelength, so short wavelength means high energy per photon.
• Approximate wavelength bands: X-ray 0.01-10 nm, ultra-violet 10-400 nm, visible 400-700 nm, infra-red 700 nm to 1 mm.
• A visible photon carries a few electronvolts; a diagnostic X-ray photon carries tens of kiloelectronvolts.
• X-rays and gamma rays are ionising because a single photon can strip an electron from an atom.
• Total energy delivered depends on intensity as well; energy per photon depends only on wavelength.

• Confusing intensity, which is energy per second, with energy per photon.
• Placing ultra-violet above X-ray because sunburn is the more familiar hazard.
• Reversing the relation and assuming long wavelength means high energy.

A one-line ordering item — the examiner wants to know whether the electromagnetic spectrum is memorised in the right direction.

• practice — not a real PYQ

  Which one of the following has the longest wavelength?

  • (a)Gamma rays
  • (b)X-rays
  • (c)Radio waves
  • (d)Ultra-violet rays

  Answer(c) Radio waves — they sit at the low-energy, long-wavelength end of the spectrum.

• practice — not a real PYQ

  The energy of a photon is directly proportional to which one of the following?

  • (a)Its wavelength
  • (b)Its frequency
  • (c)The speed of light in the medium
  • (d)The intensity of the beam

  Answer(b) Its frequency — E = hf, with h the Planck constant.