Q.16 Determine the correctness or otherwise of the following Assertion [a] and the
Reason [r].
Assertion [a]: The resolving power of a transmission electron microscope is
higher than that of the light microscope.
Reason [r]: The wavelength of electrons is shorter than that of visible light.
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) Both [a] and [r] are true but [r] is not the correct reason for [a]
(C) Both [a] and [r] are false
(D) [a] is true but [r] is false

Solution

Transmission electron microscopes (TEM) achieve higher resolving power than light microscopes due to the de Broglie wavelength of accelerated electrons being much shorter than visible light wavelengths. This directly explains the superior resolution in TEM. The correct answer is option (A).

Option Analysis

• (A) Both [a] and [r] are true and [r] is the correct reason for [a]: Correct. Resolving power d = 0.61λ/NA improves with shorter λ. Electrons accelerated to 100 keV have λ ≈ 0.0037 nm vs. visible light’s 400-700 nm, enabling atomic-scale imaging.
• (B) Both [a] and [r] are true but [r] is not the correct reason for [a]: Incorrect. Shorter electron wavelength is the fundamental reason per wave optics and de Broglie hypothesis.
• (C) Both [a] and [r] are false: Incorrect. TEM resolution reaches 0.1 nm, far better than light microscopy’s ~200 nm limit.
• (D) [a] is true but [r] is false: Incorrect. Electron wavelength is shorter, as λ = h/mv yields picometers for typical TEM voltages.

Wavelength Comparison

Visible light wavelengths range from 400-700 nm, limiting light microscope resolution to ~200 nm due to diffraction. In contrast, TEM uses electrons accelerated at high voltages (e.g., 100-300 kV), yielding wavelengths of 0.002-0.005 nm—over 100,000 times shorter.

de Broglie equation: λ = h/p (h = Planck’s constant, p = momentum).

Higher electron speed reduces λ, enhancing detail in biological samples like viruses or organelles.

Resolving Power Formula

Microscope resolving power is d = 0.61λ/NA, where NA is numerical aperture (~1.4 max). Shorter λ directly boosts resolution, making [r] the exact reason for [a].

Microscope Type	Typical Wavelength	Resolution Limit
Light	400-700 nm	200 nm
TEM	0.0037 nm	0.1 nm

CSIR NET Exam Relevance

This assertion-reason question tests wave-particle duality and microscopy principles, common in Unit 1 (Cell Biology). Option (A) is standard, as confirmed in multiple PYQs. For exams, recall: TEM for ultrastructure, light for live cells.