Question

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 :

• 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.

Hint:

Resolving power of a microscope varies inversely with the wavelength used; electrons have a much smaller de Broglie wavelength than visible light.

Answer 1

The Correct Option is C

The limit of resolution of a microscope is \(d \approx \frac{1.22\lambda}{2\,\mathrm{NA}}\), so smaller wavelength gives better resolving power.
Electrons accelerated through a potential V have \(\lambda = \frac{h}{\sqrt{2meV}}\), of the order of \(10^{-11}\) m to \(10^{-10}\) m, far smaller than visible light (about \(5\times10^{-7}\) m). So R is true.
Because of this small wavelength, an electron microscope has much better resolving power. So A is true and R is the correct explanation of A.
Answer: (3) Both A and R are true and R is the correct explanation of A.