Question

Spectroscopy deals with interaction of electromagnetic radiation with matter. What is the speed of this radiation in vacuum in m/s?

• A. \( 6 \times 10^8 \)
• B. \( 5 \times 10^8 \)
• C. \( 4 \times 10^8 \)
• D. \( 3 \times 10^8 \)

Hint:

Remember that \( 3 \times 10^8 \text{ m/s} \) is approximately \( 300,000 \text{ km/s} \).
Light could circle the Earth's equator about \( 7.5 \) times in just one second!
This value is constant for the entire electromagnetic spectrum, from radio waves to gamma rays.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the fundamental physical constant representing the speed of electromagnetic radiation (light) as it travels through a vacuum.
This constant is central to the study of spectroscopy and physics.
Key Formula or Approach:
The speed of light in vacuum is denoted by the symbol \( c \).
The exact defined value of \( c \) is \( 299,792,458 \) meters per second.

Step 2: Detailed Explanation:

• Nature of Electromagnetic Radiation:
Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate through space.
This spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
In a vacuum, all these forms of radiation travel at exactly the same speed.

• Scientific Significance:
The value \( 3 \times 10^8 \text{ m/s} \) is the standard approximation used in scientific calculations.
According to Einstein's theory of relativity, this is the universal speed limit; no information or matter can travel faster than this.
It relates energy and mass through the equation \( E = mc^2 \).

• Effect of Medium:
While the speed is a constant in a vacuum, it slows down when passing through other media like air, water, or soil.
The ratio of the speed in vacuum to the speed in a medium is known as the refractive index (\( n = c/v \)).
In soil water or glass, light travels significantly slower than \( 3 \times 10^8 \text{ m/s} \).

• Relationship with Wavelength and Frequency:
The speed of radiation is the product of its wavelength (\( \lambda \)) and its frequency (\( \nu \)):
\[ c = \lambda \nu \]

Step 3: Final Answer:
The speed of electromagnetic radiation in a vacuum is approximately \( 3 \times 10^8 \text{ m/s} \).