Arrange the following in the ascending order of wavelength :

(A) Gamma rays (λ₁)

(B) x-ray (λ₂)

(C) Infrared waves (λ₃)

(D) Microwaves (λ₄)

Choose the most appropriate answer from the options given below :

The correct answer is Option 3: λ₁ < λ₂ < λ₃ < λ₄

This means, in ascending order of wavelength: Gamma rays < X-rays < Infrared waves < Microwaves.

To solve this, we need to recall the electromagnetic spectrum. All the waves listed — gamma rays, X-rays, infrared waves, and microwaves — are forms of electromagnetic radiation. They differ only in their wavelengths (and frequencies). The electromagnetic spectrum arranges these waves in order of increasing wavelength (or decreasing frequency).

Step 1: Recall the approximate wavelength ranges for each type of wave.

(A) Gamma rays (λ₁): These have the shortest wavelengths in the entire electromagnetic spectrum.
Typical range: less than {10}^{-11} m (i.e., < 0.01 nm)

(B) X-rays (λ₂): X-rays have slightly longer wavelengths than gamma rays.
Typical range: approximately {10}^{-11} m to {10}^{-8} m (0.01 nm to 10 nm)

(C) Infrared waves (λ₃): These have much longer wavelengths, just beyond visible red light.
Typical range: approximately {10}^{-6} m to {10}^{-3} m (1 µm to 1 mm)

(D) Microwaves (λ₄): These have even longer wavelengths than infrared waves.
Typical range: approximately {10}^{-3} m to {10}^{-1} m (1 mm to 10 cm)

Step 2: Arrange them in ascending order of wavelength (shortest to longest).

Comparing the wavelength ranges:

Gamma rays (λ₁) < X-rays (λ₂) < Infrared waves (λ₃) < Microwaves (λ₄)

In terms of the given symbols, this is written as:

{\lambda }_1<{\lambda }_2<{\lambda }_3<{\lambda }_4

Step 3: Understand why this order makes sense.

In the electromagnetic spectrum, as we move from gamma rays toward radio waves, the wavelength increases progressively. A useful mnemonic to remember the order from short to long wavelength is:

Gamma → X-ray → Ultraviolet → Visible → Infrared → Microwave → Radio waves

From this sequence, it is clear that among the four given options, gamma rays have the shortest wavelength and microwaves have the longest wavelength, confirming our answer.

Conclusion: The correct ascending order of wavelength is λ₁ < λ₂ < λ₃ < λ₄, i.e., Gamma rays < X-rays < Infrared waves < Microwaves.