Thermionic Emission (AQA A Level Physics): Revision Note

Figure 1 shows a thin filament placed near an anode with a hole in it. Passing current through the filament generates a beam of electrons.

Figure 1

Explain why passing a current through the filament causes the emission of electrons.

Answer:

Step 1: Recall that thermionic emission requires a heated cathode (filament)

• The current heats the wire

Step 2: Explain why this higher temperature is needed

• The electrons in the filament gain enough kinetic energy to escape the filament and accelerate towards the anode

Remember that current passing through a wire causes it to heat up - it is the higher temperature, not the current, that gives the electrons enough energy to be easily attracted from the cathode towards the anode. 

An electron is accelerated through a vacuum by an electric field with a potential difference of 500 V. It exits through a small hole in a positive plate. 

Calculate its speed upon leaving the electric field. 

Answer:

Step 1: List the known quantities:

• Electron mass, m_e = 9.11 × 10⁻³¹ kg

• Magnitude of the charge of an electron, e =  1.60 × 10⁻¹⁹ C

• Potential difference, V = 500 V

Step 2: Recall the equation relating work done on an electron and kinetic energy

• To determine electron speed, v:

$eV=\frac{1}{2}{m}_e{v}^2$

Step 3: Rearrange this equation to make velocity the subject

• Multiply both sides by 2, divide both by mass and square root both sides to get:

$v=\sqrt{\frac{2eV}{m_e}}$

Step 4: Substitute the known quantities

• For the final answer:

$v=\sqrt{\frac{2\times \left(1.60\times {10}^{-19}\right)\times 500}{9.11\times {10}^{-31}}}=1.33\times {10}^7\mathrm{m}{\mathrm{s}}^{-1}$

This same concept of work done = kinetic energy is referred to again in Bertozzi's Experiment at the end of the Special Relativity section, so make sure you are familiar with this idea before moving on.