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Thermionic emission is the process of electrons being “boiled off”
a hot metal electrode due to their thermal energy overcoming the potential energy of the work function. Let us make a quick-and-dirty model of the rate of thermionic emission by modeling electrons in metals as particles trapped in a potential well.
a) Show that at room temperature (300 K) kBT is negligible compared to the work functions given in problem 1, i.e. the thermal energy of electrons is very small compared to the depth of the potential well.
problem 1 What is the minimum frequency of light needed to eject electrons from the following metals
in the photoelectric effect? The work functions given are in “electron-volts (eV),” which are a unit of energy equal to 1.602×10−19J.
•Silver (4.6 eV)
•Platinum (5.6 eV)
•Potassium (2.3 eV)
b) Consider electron states A at the bottom of the potential well and B having just escaped the potential well (i.e. the potential energy difference between states A and B is the work function). What is the ratio of probabilities of finding electrons in states A and B for platinum at 300 K, 1000 K, 2000 K? Is there a significant difference?
 
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