7. 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

Resolving Power of Transmission Electron Microscope vs Light Microscope

Understanding the Assertion and Reason

The question asks us to determine whether the given assertion and reason are individually correct and whether the reason correctly explains the assertion.

The Assertion [a] states that the resolving power of a transmission electron microscope is higher than that of a light microscope. This statement is true.

The Reason [r] states that the wavelength of electrons is shorter than that of visible light. This statement is also true.

More importantly, the shorter wavelength of electrons is the fundamental reason why a transmission electron microscope can achieve much higher resolving power than a conventional light microscope. Therefore, both the assertion and reason are true, and the reason correctly explains the assertion.

Hence, the correct answer is Option (A).

What Is Resolving Power in Microscopy?

Resolving power is the ability of a microscope to distinguish two closely spaced points as separate objects. A microscope with high resolving power can reveal smaller and finer structural details that cannot be distinguished by a microscope with lower resolving power.

Resolution is usually expressed as the minimum distance between two points that can still be seen as separate. A smaller value of minimum resolvable distance means better resolution and therefore greater resolving power.

This distinction is important because resolution and resolving power are inversely related. If a microscope can resolve a very small distance, it has high resolving power.

Why Is the Assertion True?

Transmission Electron Microscopes Have Much Higher Resolving Power

The assertion states:

“The resolving power of a transmission electron microscope is higher than that of the light microscope.”

This statement is correct.

A conventional light microscope uses visible light to form an image. Visible light has wavelengths approximately in the range of 400–700 nm. Because of the diffraction limit, an ordinary light microscope generally has a maximum practical resolution of approximately 200 nm.

A transmission electron microscope, commonly called a TEM, does not use visible light. Instead, it uses a beam of accelerated electrons that passes through an extremely thin specimen. These electrons have wavelengths much shorter than visible light.

Because the electron wavelength is extremely small, a TEM can distinguish structures that are far smaller than those visible under a conventional light microscope. Therefore, the resolving power of a TEM is much higher.

The assertion is therefore true.

Why Is the Reason True?

Electrons Have a Much Shorter Wavelength Than Visible Light

The reason states:

“The wavelength of electrons is shorter than that of visible light.”

This statement is also correct.

According to the wave-particle duality of matter, electrons behave not only as particles but also possess wave-like properties. The wavelength associated with a moving electron is called the de Broglie wavelength.

It is expressed by the equation:

λ = h / p

where:

λ = wavelength of the electron

h = Planck’s constant

p = momentum of the electron

When electrons are accelerated through a high voltage in an electron microscope, their momentum increases significantly. As the momentum increases, their de Broglie wavelength decreases.

Therefore, the wavelength of accelerated electrons used in transmission electron microscopy is much shorter than the wavelength of visible light.

The reason is therefore true.

How Does Wavelength Control Microscope Resolution?

The resolving ability of a microscope is fundamentally limited by the wavelength of the radiation used for imaging. This relationship can be understood through the Abbe resolution equation:

d = λ / (2NA)

where:

d = minimum resolvable distance

λ = wavelength of the radiation used for imaging

NA = numerical aperture of the imaging system

According to this relationship, resolution improves when the wavelength becomes shorter. A shorter wavelength produces a smaller value of d, meaning that two points separated by a smaller distance can still be distinguished.

Visible light has a relatively long wavelength compared with accelerated electrons. Therefore, the diffraction limit restricts the ability of a light microscope to resolve extremely small structures.

Electrons, in contrast, have extremely short wavelengths. This greatly reduces the theoretical resolution limit and allows an electron microscope to reveal much finer structural details.

This directly proves that the reason correctly explains the assertion.

Relationship Between Electron Wavelength and TEM Resolving Power

The central scientific principle behind this question is straightforward: shorter wavelength produces better resolution.

A light microscope uses photons of visible light. Since visible light has wavelengths of several hundred nanometres, structures much smaller than approximately 200 nm cannot normally be distinguished by a conventional light microscope.

A transmission electron microscope uses accelerated electrons with wavelengths much shorter than visible light. As a result, structures at the nanometre and even sub-nanometre scale can be studied under suitable conditions.

Therefore, the high resolving power of a TEM is directly related to the very short wavelength of the electrons used to produce the image.

The reason is not merely an additional true statement. It provides the correct scientific explanation for the assertion.

Light Microscope vs Transmission Electron Microscope

A light microscope and a transmission electron microscope differ mainly in the type of radiation used to form the image.

A light microscope uses visible light and glass lenses. Its resolving power is limited by the relatively long wavelength of visible light. Although it is extremely useful for studying cells, tissues, microorganisms, and many cellular structures, it cannot reveal the finest details of cellular ultrastructure.

A transmission electron microscope uses a beam of accelerated electrons and electromagnetic lenses. The electron beam passes through an ultrathin specimen, and differences in electron transmission generate a highly detailed image.

Because electrons have a much shorter wavelength, TEM can reveal extremely small structures such as cell membranes, ribosomes, viral particles, mitochondrial internal organization, and other components of cellular ultrastructure.

This difference in wavelength is the main physical basis for the difference in resolving power between the two microscopes.

Detailed Explanation of Option (A)

Both [a] and [r] Are True and [r] Is the Correct Reason for [a]

Option (A) is the correct answer.

The assertion is true because a transmission electron microscope has a much higher resolving power than a conventional light microscope.

The reason is also true because accelerated electrons have a much shorter wavelength than visible light.

The reason correctly explains the assertion because microscope resolution depends strongly on the wavelength used for imaging. The shorter wavelength of electrons allows a TEM to distinguish much smaller structures than a light microscope.

Therefore, Option (A) is correct.

Why Option (B) Is Incorrect

Both [a] and [r] Are True but [r] Is Not the Correct Reason for [a]

Option (B) correctly recognizes that both statements are individually true, but it incorrectly claims that the reason does not explain the assertion.

The shorter wavelength of electrons is directly responsible for the higher theoretical resolving power of the transmission electron microscope. Therefore, there is a clear cause-and-effect relationship between the reason and the assertion.

Since the reason correctly explains why TEM has higher resolving power, Option (B) is incorrect.

Why Option (C) Is Incorrect

Both [a] and [r] Are False

Option (C) is incorrect because neither statement is false.

The transmission electron microscope does have greater resolving power than the light microscope. In addition, accelerated electrons do have much shorter wavelengths than visible light.

Since both the assertion and the reason are scientifically correct, Option (C) cannot be the answer.

Why Option (D) Is Incorrect

[a] Is True but [r] Is False

Option (D) accepts the assertion as true but considers the reason false.

Although the first part is correct, the second part is scientifically incorrect. The wavelength associated with accelerated electrons is indeed much shorter than the wavelength of visible light.

This short electron wavelength is precisely what gives electron microscopy its potential for exceptionally high resolution.

Therefore, Option (D) is incorrect.

Why TEM Can Reveal Cellular Ultrastructure

The term ultrastructure refers to extremely fine structural details that cannot be adequately resolved with a conventional light microscope.

A light microscope can reveal the general organization of cells and tissues, but many smaller cellular components lie below its resolution limit. A transmission electron microscope can reveal much finer internal details because of its superior resolving power.

TEM is therefore widely used to study the internal organization of organelles, membrane architecture, ribosomes, viruses, cytoskeletal structures, and other nanoscale biological features.

The ability to visualize such fine structures ultimately depends on the much shorter wavelength of electrons compared with visible light.

Final Answer

The Assertion [a] is true because the resolving power of a transmission electron microscope is higher than that of a light microscope.

The Reason [r] is also true because accelerated electrons have a much shorter wavelength than visible light.

The reason correctly explains the assertion because a shorter wavelength allows a microscope to distinguish smaller structural details and therefore provides greater resolving power.

Correct Answer: (A) Both [a] and [r] are true and [r] is the correct reason for [a].