A gamma ray has frequency f = 3 × 10²⁰ Hz. What is its wavelength in vacuum?
A1 × 10¹² m
B9 × 10²⁸ m
C1 × 10⁻¹² m
D3 × 10¹² m
Using c = fλ → λ = c/f = (3 × 10⁸ m/s) / (3 × 10²⁰ Hz) = 1 × 10⁻¹² m = 1 picometer. This places it in the gamma-ray region of the spectrum. The inverse relationship — higher frequency means shorter wavelength — is a direct consequence of c being constant for all EM waves in vacuum.
Question 2 True / False
X-rays travel faster than radio waves in vacuum because X-rays carry more energy.
TTrue
FFalse
Answer: False
All electromagnetic waves travel at exactly c = 3 × 10⁸ m/s in vacuum, regardless of frequency or energy. X-rays do carry more energy than radio waves (E = hf, and X-ray frequencies are vastly higher), but energy and speed are independent properties. Speed differences between EM wave types only appear in material media, where the index of refraction can vary with frequency.
Question 3 Short Answer
Why does the electromagnetic spectrum span such an enormous range of frequencies, yet all EM waves obey the same relationship c = fλ?
Think about your answer, then reveal below.
Model answer: The speed c is fixed for all EM waves in vacuum, so c = fλ is a constraint between frequency and wavelength — not a limit on what frequencies can exist. Any frequency is physically possible; the spectrum is wide because different physical processes (antenna oscillations, molecular vibrations, atomic transitions, nuclear decays) produce EM radiation at vastly different energy scales.
Radio waves arise from oscillating currents in antennas at MHz–GHz frequencies; infrared from molecular vibrations; visible light from atomic electron transitions; X-rays from inner-shell electron transitions and bremsstrahlung; gamma rays from nuclear transitions. Each process spans a different energy scale. c = fλ holds throughout — it's a consequence of Maxwell's equations — but it does not constrain f to any particular range.