# How does thermionic emission work?

I’ve been curious about understanding the mechanism behind themionic emission from what I have read I found that themionic emission happen when the energy from added temperature excess the work function of the material. I also readed when temperature excesses 1000k themionic emission happens but when I calculate the energy in Ev from that temperature I get a number no where close to the work function of tungsten a material commonly used as filament for electron guns so what gives?
Wien Law
~~~~~~~~~~~2.89e-3
Wavelength =————-
~~~~~~~~~~~~1000k
Wavelength = 289e-8m

Conversation of wavelength to Joules
~~(6.626e-27)(3e10)
E=—————————
~~~~~~289e-8m
E=0.06878e-18
Joules to Electron volts
E = 0.06878e-18 * 6.242e18

E = 0.4293ev
Tungsten Workfunction = 4.5ev
I not sure if I’m just calculating the temperature with the wrong equation but those numbers don’t seem anywhere closes , when I used the work function of tungsten to calculate the temperature I get a number that is insanely high

Ev to wavelength
~~~~~~~~~~~(6.626e-34)(3e10)
Wavelength= —————————-
~~~~~~~~~~~~(4.5ev)/(6.242e18)

Wavelength = 2.757e-7
Wavelength = 275.7nm

Wien law
~~~~~~2.89e-3
T(k) = ————
~~~~~~2.757e-7
T(k) = 10482.408k

10482 KELVIN!!! that way excess the melting temperature of tungsten and that far exceeds the temperature in any electron gun if I am calculating the temperature wrong how do I do it properly and can anyone confirm that thermionic emission happens from temperature exceeding work function?

I read that thermionic emission happens from exceeding the work function of material from it Wikipedia page(I know it’s not the most credible site)

I also read that the temperature for thermionic emission of t > 1000k from Wikipedia also.
Sorry for any grammar mistakes I’m not a very good at spotting them

Homework Helper
Gold Member
In the Wien's law calculation for the peak wavelength of the Planck blackbody emission spectrum, ## 4.96=\frac{E_{\lambda \, max}}{k_B T} ##, so that ## E_{\lambda \, max}=4.96 \, k_B T ## gets you a better number than if you just use ## k_B T ##, which is ## 1.38 \cdot 10^{-20}/1.602 \cdot 10^{-19} =.086 \, eV ## for ## T=1000 ##, and compare it to the work function ## W ##. Part of the answer would seem to be in the ## T^2 ## factor in the Richardson-Dushman equation. See http://simion.com/definition/richardson_dushman.html

sophiecentaur
sophiecentaur