Question

The speed of electrons in a scanning electron microscope is \(1 \times 10^7\) 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:

• A. 1837
• B. \(\frac{1}{1837}\)
• C. \(\sqrt{1837}\)
• D. \(\frac{1}{\sqrt{1837}}\)

Hint:

Heavier particles have smaller de-Broglie wavelengths at the same speed, leading to much higher resolution.

Answer 1

The Correct Option is A

Step 1: Resolving power (\(RP\)) is inversely proportional to the wavelength \(\lambda\): \(RP \propto \frac{1}{\lambda}\).
Step 2: According to de-Broglie's hypothesis: \(\lambda = \frac{h}{p} = \frac{h}{mv}\).
Step 3: Therefore, \(RP \propto \frac{mv}{h}\). Since \(v\) and \(h\) are the same for both: \[RP \propto m\]
Step 4: The ratio of resolving powers is: \[\frac{RP_{proton}}{RP_{electron}} = \frac{m_p}{m_e} \approx 1837\]