# How does thermionic emission work?

• Helloworld75344
In summary, thermionic emission occurs when the energy from added temperature exceeds the work function of the material. It typically happens at temperatures above 1000 Kelvin, but the actual temperature needed depends on the material being used. The peak wavelength of the Planck blackbody emission spectrum can be calculated using Wien's law and the Richardson-Dushman equation, which takes into account the temperature and the work function of the material. It is important to note that Tungsten is not commonly used as a source of electrons in thermionic cathodes, and the operating temperature for these cathodes is usually less than 600°C.

#### Helloworld75344

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

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
Thermionic cathodes do not use Tungsten as a source of electrons. They are coated with a range of materials. See this wiki link about hot cathodes. The operating temperature of many valve cathodes is less than 600°C (also mentioned in the link).
Edit: What have you read up about thermionic emission? Electrons do not totally escape from a hot cathode if there is no handy positive electrode nearby. Without an external field, they hang around the surface and return to the cathode which has become positively charged. Electrons do not need 'escape velocity'.

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• ## 1. What is thermionic emission?

Thermionic emission is a phenomenon where electrons are emitted from the surface of a heated material. This occurs due to the thermal energy of the material causing the electrons to gain enough energy to overcome the material's surface potential barrier.

## 2. How does temperature affect thermionic emission?

The rate of thermionic emission is directly proportional to the temperature of the material. As the temperature increases, the average kinetic energy of the electrons also increases, allowing more electrons to overcome the potential barrier and be emitted.

## 3. What is the role of the potential barrier in thermionic emission?

The potential barrier is a property of the material's surface that prevents electrons from escaping. In thermionic emission, the thermal energy of the material is enough to overcome this potential barrier, allowing electrons to be emitted.

## 4. What are some real-world applications of thermionic emission?

Thermionic emission has been used in devices such as vacuum tubes, X-ray tubes, and cathode ray tubes. It is also used in thermionic converters, which convert heat energy into electrical energy.

## 5. How does thermionic emission differ from other types of electron emission?

Thermionic emission differs from other types of electron emission, such as field emission, in that it is caused by thermal energy rather than an external electric field. It also typically occurs at higher temperatures compared to other types of emission.