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Question:

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10⁻¹² m, the minimum electron energy required is close to:

25 keV

500 keV

1 keV

100 keV

Solution:

λ = h/p
λ = 7.5 × 10⁻¹² m
P = h/λ
KE = P²/2m = (h/λ)²/2m = (6.6 × 10⁻³⁴ J s / 7.5 × 10⁻¹² m)² / (2 × 9.1 × 10⁻³¹ kg)
KE = 25 keV