Work function and energy of X ray photon emitted by anode

[SecretSnow]

Hi guys, I'm constantly bothered by one assumption in my textbook..it says that the photon emitted by the accelerating electron boiled off from the cathode colliding into the anode, has E=hf neglecting the work function, since its negligible. I'm curious whether it's E=hf plus or minus the work function, and I'm really confused by this. Firstly, if I work backwards, like imagining it's a photon liberating the electron through the photoelectric effect instead, then the energy released should be E=hf + work function right? Since it emits the work function energy of the electron together with the photon right? However, how do we know they are separate values, since the work function energy can itself be incorporated into the hf value of the photon? Wouldn't it be the same then?

Next, I think it's E=hf - the work function since if the accelerated electron has an initiall KE of E=eV=hf-work function then wouldn't the emitted photon have energy E=hf -phi too? Hmm but I think this whole second paragraph is invalid since the electron is initially boiled off by heating right? I'm not sure...I hope you guys can help me clear my confusion! Although the reason is not really needed, I'm curious to find out, thanks a lot!

 

[mfb]

The initial electron cannot have a negative energy at the cathode - it starts with at least zero (and the required energy to exit the material is thermal energy), and has at least eV at the time it hits the anode. If the electron directly gets captured in the anode, hf=E=eV+work function might be possible as photon energy.

 

[SecretSnow]

Actually I don't get why the textbook even mentions work function in the first place. if the electron is boiled off,then initially if should have low or zero KE, which means by the time it reaches the anode, it should have E=eV. The thing is, does the work function applies in the anode? If yes, then I'm assuming after it reaches the anode it goes into the ground state right? (Since it's been decelerated to the lowest energy state possible) during this acceleration, the photon should have E=hf, now, I think, without work function, or it is inside the E=hf equation already. Where then does the work function even apply? Thanks a lot!

 

[SecretSnow]

I'm thinking if it could be the work function of anode it's saying, and that there might be electrons of the anode absorbing the photon produced by the colliding electrons? Is this possible? But if the energy of the photon emitted is high enough, then it should be able to liberate the electrons on the anode with kinetic energy supplied too, so it isn't insignificant is it? It's more like assuming the pathway of the photon doesn't collide with the anode...

 

[Nickie]

Hello! Thank you for reaching out with your question. I can understand your confusion regarding the work function and energy of the X-ray photon emitted by the anode. Let me try to explain it in a simple way.

The work function is the minimum amount of energy required to free an electron from the surface of a material. In the case of X-ray production, this work function is negligible compared to the energy of the accelerated electrons. This is why it is often neglected when calculating the energy of the emitted X-ray photon.

Now, let's consider the process of X-ray production in more detail. First, the electrons are accelerated from the cathode to the anode, gaining kinetic energy. When these high-speed electrons collide with the anode, they lose some of their kinetic energy, which is converted into X-ray photons. These photons have an energy equal to the energy lost by the electrons, which is given by the equation E=hf.

In this process, the work function is not involved because the electrons are not being freed from the surface of the anode. They are simply losing some of their kinetic energy, which is then converted into photons. Therefore, the equation for the energy of the X-ray photon is simply E=hf, without any additional terms.

To address your point about the photoelectric effect, you are correct in saying that if the electron was freed from the surface of the anode through the photoelectric effect, then the energy of the emitted photon would be E=hf + work function. This is because in this case, the work function is involved in the process of freeing the electron.

In summary, the work function is not included in the equation for the energy of the X-ray photon because it is not involved in the process of X-ray production. I hope this helps to clear up your confusion. If you have any further questions, please feel free to ask. Keep up the curiosity and happy learning!