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    Quantam phenomena is a topic I struggle with quite a lot, but one question that always seems to appear is why the kinetic energy of an emitted electron has a maximum value and can never seem to get the answer around my head. Could someone please explain why the KE of an emitted electron is a maximum value?

    Any replies would be appreciated,
    thanks!
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    Is this a question about the photoelectric effect?
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    (Original post by Darth_Narwhale)
    Is this a question about the photoelectric effect?
    Yeah, it is
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    (Original post by titfortat)
    Quantam phenomena is a topic I struggle with quite a lot, but one question that always seems to appear is why the kinetic energy of an emitted electron has a maximum value and can never seem to get the answer around my head. Could someone please explain why the KE of an emitted electron is a maximum value?

    Any replies would be appreciated,
    thanks!
    The energy of the electron is limited to that of the incoming photon that collides with it. From what I can remember, you explain this with the equation Ekmax = hf-Ø. Ø is the work function of the (metal) surface that the electron is escaping from. If the work function is greater than hf then electrons will not be emitted, regardless of the intensity of the incoming photons

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    Okay so einstein said that: hf = Φ + Ekmax, which means that some of the energy of the incoming photon is required to remove the electron from the surface of the metal (phi), and the rest of the energy of the photon goes into the kinetic energy of the electron. There is a certain energy 'cost' to remove the electron from the metal, so only photons of high enough energy (frequency) will produce a photoelectron. This is the 'fundamental frequency.' If we consider a photon that has enough energy (i.e. with a frequency above the fundamental frequency), then the equation describes what happens to the energy when the electron is knocked off the surface of the metal. However obviously not all electrons are on the surface, therefore for most electrons, some of the energy will be used to get that electron to the surface. This means that there is less energy remaining once the electron is moved to the surface and then knocked off, hence it has a lower KE. This KEmax is the maximum kinetic energy that the electron would have if it didn't have to be raised to the surface first, so only those electrons already at the surface of the metal will have this KE. Does that make sense?
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    (Original post by titfortat)
    Quantam phenomena is a topic I struggle with quite a lot, but one question that always seems to appear is why the kinetic energy of an emitted electron has a maximum value and can never seem to get the answer around my head. Could someone please explain why the KE of an emitted electron is a maximum value?

    Any replies would be appreciated,
    thanks!
    I must admit, this is actually a very complex topic to get your head around

    I think the main idea is that once a photon has collided with an electron, all of the energy from the photon will be transferred to the electron. And the energy of a photon is hf , therefore, the electron will gain energy equal to hf.
    In order for the electron to be emitted from the metal surface, the energy it has gained from the photon (hf) needs to be greater than the work function energy of the metal ( Φ ). So hf > Φ . The kinetic energy will be the energy that is left over once the energy of the work function has been lost to the metal.

    Therefore, the kinetic energy an electron will be carrying when it leaves the metal is hf - energy losses.
    The maximum amount of energy an electron can lose when it leaves the metal is the work function (because the electron has to do work to break the bonds holding it in the metal in order to escape)
    Therefore, the maximum kinetic energy of an electron would be given by hf - Φ.
    Another way you could look at it is the total energy, hf, = Φ + Ekmax (the kinetic energy here cannot be any higher because the work function of the metal is a constant value, therefore the kinetic energy is a maximum).
    Plank's constant is also a constant, and so is the frequency of the incident photons, and so it is not possible for the kinetic energy to vary and be higher than a certain value, which in this case is Ekmax.

    I hope this helps
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    If I recall, the maximum value is basically what the Ek would be if the electron just left the surface of the metal. However, some electrons may be deeper into the surface (weird) and so will need to use some kinetic energy escaping the surface of the metal (do work).Therefore the kinetic energy may vary so they call it a maximum value as not all electrons will have this value- some will be lower.

    Edit: This is for monochromatic light- if white light for example, the Ek may vary up to a maximum due to the different frequencies of light, which will produce a bigger energy and as the work function is the same the Ek of the emitted electrons will vary up to a maximum. However the answer I gave above is the one I have seen in mark schemes (not quite the same wording) and is what I use.
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    emduck LeCroissant Darth_Narwhale 98matt thank you all so much!!
 
 
 
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