Electron microscopes

Overview

The de Broglie wavelength of an accelerated electron, and the transmission and scanning tunnelling microscopes.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State the de Broglie wavelength equation relating an electron's wavelength to its momentum.

   Model answer

   λ = h/p, where λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the electron.

2. 2

   In the de Broglie equation λ = h/p, what does each symbol represent?

   Model answer

   λ is the de Broglie wavelength, h is the Planck constant, and p is the momentum of the particle.

3. 3

   When an electron is accelerated from rest through a potential difference V, how is its kinetic energy related to V?

   Model answer

   The kinetic energy gained equals eV, where e is the elementary charge.

4. 4

   Explain why an electron accelerated from rest through potential difference V gains kinetic energy equal to eV.

   Model answer

   Work is done on the electron by the electric field; the work done equals charge × potential difference = eV, which is converted entirely to kinetic energy.

5. 5

   State the formula for the momentum of an electron accelerated from rest through a potential difference V.

   Model answer

   p = √(2mₑeV), where mₑ is the electron mass, e is the elementary charge, and V is the potential difference.

6. 6

   How is the formula p = √(2mₑeV) derived for an accelerated electron?

   Model answer

   Kinetic energy Eₖ = eV and Eₖ = p²/(2mₑ); combining these gives p² = 2mₑeV, so p = √(2mₑeV).

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