The speed of electrons in a scanning electron microscope is 1 × 10⁷ ms⁻¹. If the protons having the same speed are used instead of electrons, then the resolving power of scanning proton microscope will be changed by a factor of :

Solution

Physics sir · 3 steps

Same speed means wavelength goes as 1/m, and a shorter wavelength resolves finer detail.

1. Resolving power. A microscope can separate two points only if they are farther apart than about one wavelength. So the resolving power is proportional to 1/λ.
2. de Broglie wavelength. For a particle of mass m moving with speed v, the wavelength is λ = h/mv. Here v is the same for both particles, so λ depends only on the mass.

   RPₚ/RPₑ = λₑ/λₚ = (h/mₑ v)/(h/mₚ v) = mₚ/mₑ = 1837

3. So. The proton is 1837 times heavier, so its wavelength is 1837 times shorter. The resolving power becomes 1837 times larger, which is option (b).

The idea to keep. Resolving power goes as 1/λ. At equal speed λ ∝ 1/m. At equal kinetic energy or equal accelerating voltage λ ∝ 1/√m. Check which quantity is held fixed.

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