Which series goes from least energetic to most (with relation to electromagnetic waves)?

Question

BlackTom AI · Accepted Answer

Energy of electromagnetic radiation is proportional to its frequency (E = hf) and inversely proportional to wavelength (E = hc/λ), so higher frequency (shorter wavelength) means higher photon energy.

1) Relevant knowledge points and concepts
- E = hf (Planck’s relation) links photon energy E to frequency f; h is Planck’s constant.
- c = λf relates wavelength λ and frequency f; therefore E = hc/λ shows energy increases as wavelength decreases.
- The electromagnetic spectrum orders types of radiation by increasing frequency (and energy): radio → microwave → infrared → visible → ultraviolet → x-rays → gamma.

2) Step-by-step reasoning
- Identify relative positions on the spectrum: radio waves have the longest wavelengths (lowest frequency), infrared is shorter (higher frequency), ultraviolet is even shorter (higher frequency), and x-rays are much shorter (highest frequency among these four).
- Thus energy increases in the order: radio < infrared < ultraviolet < x-rays.

3) Example calculations (intermediate steps shown)
Use E = hc/λ with h = 6.626×10^−34 J·s and c = 3.00×10^8 m/s.
- Radio: take λ = 1.0 m → E = (6.626e-34)(3.00e8)/(1.0) = 1.99e-25 J ≈ 1.24e-6 eV.
- Infrared: take λ = 1.0×10^−6 m (1000 nm) → E = (6.626e-34)(3.00e8)/(1.0e-6) = 1.99e-19 J ≈ 1.24 eV.
- Ultraviolet: take λ = 1.0×10^−7 m (100 nm) → E = 1.99e-18 J ≈ 12.4 eV.
- X-ray: take λ = 1.0×10^−10 m (0.1 nm) → E = 1.99e-15 J ≈ 1.24×10^4 eV (12.4 keV).
These values clearly increase from radio to infrared to ultraviolet to x-ray.

4) Why the correct answer is correct
Because photon energy scales with frequency, and the listed sequence follows increasing frequency (decreasing wavelength), it correctly orders least energetic (radio) to most energetic (x-rays).

5) Why the other choices are incorrect (brief)
- "Microwave < ultraviolet < visible < radio": places radio as most energetic and misorders visible vs ultraviolet and microwaves; incorrect.
- "Gamma < infrared < visible < microwave": places gamma lowest (it’s actually highest) and misorders microwave after visible; incorrect.
- "X-rays < visible < ultraviolet < radio": places radio as highest and x-rays as lowest; reversed ordering; incorrect.

6) Conclusion
The correct ordering is Radio < infrared < ultraviolet < x-rays, which matches the provided answer.

Which series goes from least energetic to most (with relation to electromagnetic waves)?单项选择题

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