An electron microscope has a high resolving power as it uses a stream of electrons compared to a traditional microscope that uses light. What is the main reason that the electron microscope has greater resolving power than a traditional light microscope?

Question

BlackTom AI · Accepted Answer

Resolution is limited by the probe wavelength: shorter wavelengths give higher resolving power. The electron microscope uses electrons whose de Broglie wavelength is many orders of magnitude smaller than visible light, so it can resolve much smaller features.

1. Relevant knowledge points and concepts
- Wave nature: both light and electrons exhibit wave behavior. The resolving power of any imaging system is fundamentally limited by diffraction and is approximately given by the Rayleigh criterion: resolution ≈ 0.61 λ / NA (λ = wavelength, NA = numerical aperture).
- de Broglie relation: moving particles have a wavelength λ = h / p (h = Planck’s constant, p = momentum). For an electron accelerated through a potential V, p ≈ sqrt(2 m e V) (non-relativistic), so λ ≈ h / sqrt(2 m e V).
- Smaller λ → smaller minimum resolvable distance → higher resolving power.

2. Step-by-step reasoning
- A light microscope uses visible light (λ ≈ 400–700 nm). Plugging λ into the Rayleigh formula gives minimum resolvable distances on the order of hundreds of nanometers.
- Electrons accelerated in an electron microscope have de Broglie wavelengths far below visible wavelengths; therefore the diffraction-limited spot size is much smaller and finer details can be resolved.

3. Example calculation (intermediate steps)
For electrons at V = 100,000 eV (100 keV):
- Convert energy: E = 100,000 eV × 1.602×10^(-19) J/eV = 1.602×10^(-14) J.
- Momentum p ≈ sqrt(2 m E) = sqrt(2 × 9.11×10^(-31) kg × 1.602×10^(-14) J) ≈ 1.71×10^(-22) kg·m/s.
- λ = h / p = 6.626×10^(-34) J·s / 1.71×10^(-22) ≈ 3.9×10^(-12) m = 0.0039 nm.
Compare: visible light ~500 nm vs electrons ~0.004 nm — a factor of ~10^5 smaller wavelength.

4. Why the correct answer is correct
Because resolution scales with wavelength, the much smaller de Broglie wavelength of electrons directly yields the greater resolving power of electron microscopes.

5. Why the other options are incorrect
- (a) Incorrect: light diffracts and produces interference patterns; electrons also diffract (wave nature). Diffraction occurs for both.
- (b) Incorrect: “size” of electrons vs photons is not the relevant factor; photons are quanta of light, and “smaller” is meaningless here. Wave wavelength matters.
- (c) Incorrect: manufacturing of lenses is not the main limiting factor; electron microscopes use electromagnetic lenses and the primary limit is diffraction-wavelength, not lens accuracy.

6. Conclusion
The correct answer is d. The de Broglie wavelength of the stream of electrons is smaller than the wavelength of light, which is why electron microscopes have greater resolving power. This matches the provided answer.

An electron microscope has a high resolving power as it uses a stream of electrons compared to a traditional microscope that uses light. What is the main reason that the electron microscope has greater resolving power than a traditional light microscope?单项选择题

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