In the electromagnetic spectrum, the wavelengths corresponding to ultraviolet, visible and infrared radiations are represented by λ_uv, λ_vis and λ_ir respectively. Which of the following gives the correct increasing order (from shortest to longest) of these wavelengths?

Introduction / Context:

The electromagnetic spectrum is arranged according to wavelength or frequency and includes many familiar regions such as ultraviolet (UV), visible and infrared (IR) radiation. Competitive exams frequently test whether you know the relative positions of these regions. This question specifically asks you to identify the correct relationship between the wavelengths of ultraviolet, visible and infrared light, using the symbols λ_uv, λ_vis and λ_ir.

Given Data / Assumptions:

• λ_uv denotes wavelength of ultraviolet radiation.
• λ_vis denotes wavelength of visible light.
• λ_ir denotes wavelength of infrared radiation.
• We assume standard ordering of the electromagnetic spectrum in free space.

Concept / Approach:

In the electromagnetic spectrum, as we go from gamma rays to radio waves, wavelength increases and frequency decreases. Ultraviolet radiation lies just beyond the violet end of visible light and therefore has shorter wavelengths than visible light. Infrared radiation lies beyond the red end of visible light and therefore has longer wavelengths than visible light. Thus, the correct order of increasing wavelength must place ultraviolet first (shortest), then visible, then infrared (longest).

Step-by-Step Solution:

Verification / Alternative check:

Typical wavelength ranges confirm this ordering. Ultraviolet light has wavelengths roughly from 10 nm to 400 nm, visible light from about 400 nm to 700 nm, and infrared from about 700 nm to 1 mm. These numerical ranges clearly show that ultraviolet has the smallest wavelengths and infrared has the largest, with visible in between, matching λ_uv < λ_vis < λ_ir.

Why Other Options Are Wrong:

Option A: λ_uv < λ_ir < λ_vis incorrectly places infrared before visible, suggesting that visible has longer wavelength than infrared, which contradicts the spectrum.

Option B: λ_uv > λ_vis > λ_ir reverses the true order and claims ultraviolet has the longest wavelength.

Option C: λ_uv > λ_ir > λ_vis is also reversed and incorrect in every comparison.

Common Pitfalls:

A common mistake is to remember the order by frequency rather than wavelength and then forget that higher frequency means shorter wavelength. Another confusion is mixing infrared and ultraviolet simply because both are outside the visible range. To avoid errors, always remember the phrase ultraviolet on the short side, infrared on the long side of visible light.

Final Answer:

The correct relationship is λ_uv < λ_vis < λ_ir.