Consider the following statements about visible light, UV light and X-rays : 1. The wavelength of visible light is more than that of X-rays. 2. The energy of X-ray photons is higher than that of UV light photons. 3. The energy of UV light photons is less than that of visible light photons. Which of the statements given above is/are correct?
- (a)1, 2 and 3
- (b)1 and 2 only
- (c)2 and 3 only
- (d)1 only
Correct — B, statements 1 and 2 only. Every claim here follows from one relation, E = hc/λ, which says that photon energy rises as wavelength falls. Order the three radiations by wavelength — X-rays are shortest, then ultraviolet, then visible light — and the energies run the other way. Statement 1 is therefore true, because visible light does have a longer wavelength than X-rays: visible light spans roughly 400 to 700 nanometres while X-rays are of the order of 0·01 to 10 nanometres. Statement 2 is true for the same reason, since X-rays sit at much shorter wavelengths than ultraviolet and so carry far more energy per photon. Statement 3 is the false one, and it is false by inversion: ultraviolet lies at shorter wavelengths than visible light, so its photons are more energetic, not less.
- (a)1, 2 and 3 — This accepts statement 3, which reverses the ultraviolet-visible relation. If ultraviolet photons carried less energy than visible light, sunburn and ozone-layer damage would be caused by ordinary daylight rather than by the ultraviolet component of it.
- (c)2 and 3 only — It keeps the false statement 3 and drops the true statement 1. Statement 1 is the least controversial claim in the whole item — X-rays penetrate the body precisely because their wavelength is thousands of times shorter than that of visible light.
- (d)1 only — Too cautious. It rejects statement 2, but statement 2 sits on the same rule that made statement 1 true — shorter wavelength, higher photon energy — and X-rays are far shorter than ultraviolet. The energy of an X-ray photon is measured in thousands of electronvolts against a few electronvolts for ultraviolet.
The electromagnetic spectrum, arranged from long wavelength to short, runs radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. All of them travel at the same speed in vacuum, so wavelength and frequency are inversely related through c = fλ, and the energy carried by a single photon is E = hf, which is the same as hc/λ. That single chain explains why the biological effect of radiation changes so sharply along the spectrum: microwaves can only heat, ultraviolet can break chemical bonds and damage DNA, and X-rays and gamma rays ionise atoms outright.
Statement-based items like this one reward ordering rather than recall. Write the three radiations along a line by wavelength, longest first — visible, ultraviolet, X-ray — and then simply read each statement against the line. Statement 3 fails the moment you notice that ultraviolet sits on the short side of visible, which is also why it is the component of sunlight that burns skin. A second useful check is that the visible band is the one your eye responds to, and its neighbours are named for lying just outside it: infra-red below the red end, ultra-violet above the violet end.
- Photon energy is E = hf = hc/λ, so shorter wavelength always means a more energetic photon.
- Visible light spans roughly 400–700 nm; ultraviolet lies just below 400 nm; X-rays are of the order of 0·01–10 nm.
- The spectrum from long to short wavelength runs radio, microwave, infrared, visible, ultraviolet, X-ray, gamma ray.
- All electromagnetic radiations travel at the same speed in vacuum, about 3 × 10⁸ metres per second.
Two statements survive the ordering and one does not, which gives option (b).
- Mixing up the direction of the relation between wavelength and energy — they move opposite ways, always.
- Assuming ultraviolet is weaker than visible light because it is invisible.
- Confusing intensity with photon energy. A very bright red lamp still delivers low-energy photons; a faint ultraviolet source delivers high-energy ones.
NDA asks which radiation has the greatest or least wavelength or photon energy, or sets two or three such statements and asks which are correct.
Assertion (A): In the visible spectrum of light, red light is more energetic than green light. Reason (R): The wavelength of red light is more than that of green light.
- (a) Both A and R are individually true and R is the correct explanation of A
- (b) Both A and R are individually true but R is not the correct explanation of A
- (c) A is true but R is false
- (d) A is false but R is true
Answer(d) A is false but R is true
The same inversion trap inside the visible band — longer wavelength means less energy, so red is the weaker photon, exactly as ultraviolet is the stronger one here.
Which one among the following waves carries the maximum energy per photon ?
- (a) X-rays
- (b) Radio waves
- (c) Light waves
- (d) Microwaves
Answer(a) X-rays
Statement 2 of this card asked as a standalone question, over a wider slice of the spectrum.
Which one of the following types of radiations has the smallest wavelength?
- (a) Microwaves
- (b) Infra-red
- (c) Visible light
- (d) X-rays
Answer(d) X-rays
Statement 1 of this card from the other end — fixing where X-rays sit on the wavelength ladder relative to visible light.
- practice — not a real PYQ
Arrange the following in order of increasing photon energy: infrared, visible light, ultraviolet, X-rays.
- (a)X-rays, ultraviolet, visible light, infrared
- (b)Infrared, visible light, ultraviolet, X-rays
- (c)Visible light, infrared, ultraviolet, X-rays
- (d)Ultraviolet, X-rays, visible light, infrared
Answer(b) Infrared, visible light, ultraviolet, X-rays — energy rises as wavelength falls.
- practice — not a real PYQ
Two electromagnetic radiations travel through vacuum. Compared with the one of longer wavelength, the other has
- (a)a lower frequency and a lower photon energy
- (b)a higher frequency and a higher photon energy
- (c)a higher frequency but the same photon energy
- (d)a greater speed
Answer(b) a higher frequency and a higher photon energy — the speed in vacuum is the same for both, so only frequency and energy change.