### Speed vs frequency

Posted:

**Mon Nov 19, 2018 1:35 pm**Can someone please explain, comment, and show that the speed, V, of the ejected electron and the frequency, v, of the incoming radiation are related by E=hv=l + 1/2mV^2.

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=16&t=36910

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Posted: **Mon Nov 19, 2018 1:35 pm**

Can someone please explain, comment, and show that the speed, V, of the ejected electron and the frequency, v, of the incoming radiation are related by E=hv=l + 1/2mV^2.

Posted: **Mon Nov 19, 2018 2:04 pm**

Because energy is conserved, the energy of an incoming photon (if an electron is ejected from the metal surface) is equal to the energy needed to eject the electron plus the kinetic energy of the electron. In the equation E=hv, h is a constant, meaning the energy of the photon is directly dependent on the photon's frequency. Similarly, the equation E=1/2mv^2 has two constants (1/2 and m), meaning kinetic energy of the electron depends on its velocity. Therefore, by the equation E= (work function) + (kinetic energy), the frequency of the incoming photon determines the ejected electron's velocity.

Posted: **Mon Nov 19, 2018 7:02 pm**

You could say that the speed of the ejected electron and the frequency of the incoming radiation are directly proportional, because if frequency increases, the energy of the incoming photon also increases. Thus, this will increase the kinetic energy of the electron due to the law of conservation of energy, and an increase in kinetic energy means an increase in the electron's speed.