JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Modern Physics

The speed of electrons in a scanning electron microscope is

1 \times 1 0^{7} m / s

. If 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✓ Correct
(B) $1837$
(C) $\frac{1}{1837}$
(D) $\frac{1}{1837}$

Answer: (A)

Solution

The resolving power of such an instrument varies inversely as the de Broglie wavelength of the particles it uses, and

λ = \frac{h}{m v}

. At a fixed speed the wavelength is inversely proportional to the mass, so

\frac{( resolving power ) _{proton}}{( resolving power ) _{electron}} = \frac{λ _{e}}{λ _{p}} = \frac{m _{p}}{m _{e}} = 1837

Replacing the electrons by protons of the same speed increases the resolving power by a factor of

1837

JEE Main · 2021 · 18 Mar 2021 · Shift 2 · Single correct option

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