Question

If \( v_g, v_X \) and \( v_v \) are the speeds of gamma rays, X-rays and visible light respectively in vacuum, then

• A. \( v_g>v_v>v_X \)
• B. \( v_g<v_v<v_X \)
• C. \( v_g = v_v = v_X \)
• D. \( v_g>v_v<v_X \)
• E. \( v_X<v_g<v_v \)

Hint:

All electromagnetic waves have the same speed in vacuum irrespective of wavelength or frequency.

Answer 1

The Correct Option is C

Step 1: Understanding the Electromagnetic Spectrum:
Gamma rays, X-rays, and visible light are all different types of electromagnetic (EM) radiation. They form a part of the electromagnetic spectrum, which includes all forms of EM waves, from radio waves to gamma rays. These waves differ from each other in terms of their frequency and wavelength.
Step 2: A Fundamental Postulate of Physics:
A cornerstone of modern physics, established by Maxwell's equations and a key postulate of Einstein's theory of special relativity, is that all electromagnetic waves travel at the same constant speed in a vacuum. This speed is a universal constant known as the speed of light, denoted by \(c\).
\[ c \approx 3 \times 10^8 \, \text{m/s} \] This speed is independent of the frequency of the wave or the motion of the source.
Step 3: Detailed Explanation:
Since gamma rays (with speed \(v_g\)), X-rays (with speed \(v_x\)), and visible light (with speed \(v_v\)) are all forms of electromagnetic waves, their speeds in a vacuum must all be identical and equal to \(c\).
While their other properties differ greatly:
Frequency: \(f_{gamma}>f_{X-ray}>f_{visible}\)
Wavelength: \(\lambda_{gamma}<\lambda_{X-ray}<\lambda_{visible}\)
Energy per photon: \(E_{gamma}>E_{X-ray}>E_{visible}\)
Their speed in a vacuum remains the same.
\[ v_g = v_x = v_v = c \] Step 4: Final Answer:
The speeds of gamma rays, X-rays, and visible light are all equal in a vacuum.