Given below are two statements : one is labeled as Assertion A and the other is labelled as Reason R. Assertion A : An electron microscope can achieve better resolving power than an optical microscope. Reason R : The de Broglie's wavelength of the electrons emitted from an electron gun is much less than wavelength of visible light. In the light of the above statements, choose the correct answer from the options given below :

Both A and R are true and R is the correct explanation of A.

Both A and R are true but R is NOT the correct explanation of A.

Dual Nature of Radiation PYQ — JEE Main 2021 · 26 Feb · Shift 1 · Q58 with Solution

View written solutionFree

Correct answer: C

Assertion A: An electron microscope can achieve better resolving power than an optical microscope.

Resolving power depends on the wavelength used. A smaller wavelength gives a smaller diffraction limit, hence better resolution.

For a microscope, the minimum resolvable distance is roughly proportional to wavelength: $d \propto \lambda$

Since electron microscopes use electrons whose associated de Broglie wavelength can be extremely small, they can resolve much finer details than visible-light optical microscopes.

Therefore, Assertion A is true.
Reason R: The de Broglie wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light.

The de Broglie wavelength of an electron is $\lambda = \frac{h}{p}$

Electrons accelerated through a potential difference acquire large momentum, so their wavelength becomes very small, typically much smaller than visible light wavelengths (visible light is about $400\text{ nm}$ to $700\text{ nm}$ ).

Therefore, Reason R is true.
Check whether R explains A:

The reason an electron microscope has better resolving power is exactly that the wavelength of electrons is much smaller than that of visible light.

Since resolving power improves as wavelength decreases, R correctly explains A.
Option analysis:
- A: A is false but R is true. ❌
- B: Both A and R are true but R is NOT the correct explanation of A. ❌
- C: Both A and R are true and R is the correct explanation of A. ✅
- D: A is true but R is false. ❌

Hence, the correct answer is C.

More from Dual Nature of Radiation

View written solutionFree

Correct answer: C

Assertion A: An electron microscope can achieve better resolving power than an optical microscope.

Resolving power depends on the wavelength used. A smaller wavelength gives a smaller diffraction limit, hence better resolution.

For a microscope, the minimum resolvable distance is roughly proportional to wavelength: $d \propto \lambda$

Since electron microscopes use electrons whose associated de Broglie wavelength can be extremely small, they can resolve much finer details than visible-light optical microscopes.

Therefore, Assertion A is true.
Reason R: The de Broglie wavelength of the electrons emitted from an electron gun is much less than the wavelength of visible light.

The de Broglie wavelength of an electron is $\lambda = \frac{h}{p}$

Electrons accelerated through a potential difference acquire large momentum, so their wavelength becomes very small, typically much smaller than visible light wavelengths (visible light is about $400\text{ nm}$ to $700\text{ nm}$ ).

Therefore, Reason R is true.
Check whether R explains A:

The reason an electron microscope has better resolving power is exactly that the wavelength of electrons is much smaller than that of visible light.

Since resolving power improves as wavelength decreases, R correctly explains A.
Option analysis:
- A: A is false but R is true. ❌
- B: Both A and R are true but R is NOT the correct explanation of A. ❌
- C: Both A and R are true and R is the correct explanation of A. ✅
- D: A is true but R is false. ❌

Hence, the correct answer is C.

Dual Nature of Radiation question

Dual Nature of Radiation question

More from Dual Nature of Radiation

Dual Nature of Radiation question

Dual Nature of Radiation question

More from Dual Nature of Radiation