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 :

Solution

Physics sir · 3 steps

Resolution is set by wavelength, and fast electrons have a far shorter wavelength than visible light.

1. What limits resolution. A microscope cannot separate two points that are closer than about one wavelength of the wave it uses. The smallest resolvable distance is proportional to λ, so a shorter wavelength gives a higher resolving power.

   dₘᵢₙ = (1.22 λ)/(2n sin θ) ⇒ resolving power ∝ 1/λ

2. Electron wavelength. An electron accelerated through a potential V has λ = h/√2meV ≈ 1.227/√V nm. For V = 10 kV this is about 0.012 nm, while visible light is 400 to 700 nm. So R is true: the electron wavelength is tens of thousands of times smaller.
3. So. The electron's de Broglie wavelength is much shorter, so the electron microscope resolves much finer detail. A is true, R is true, and R is exactly the reason for A, so the answer is (c).

The idea to keep. Resolving power goes as 1/λ. Whenever a question compares microscopes, compare the wavelengths of the waves they use, and for electrons use λ = h/√2meV.

Answer from the NTA final answer key. Solution by PrepWiser.