what is the connection between the fact that the free electrons in a metal body obey fermi statistics law and that the photoelectric effect is virtually temperature independent?
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Photoelectric effect is temperature dependent, you would obtain different results if let's say you use tungsten and its photoelectric characteristics are different in different temperatures. The rate at which the electrons are emitted from a photo cathode is independent of its temperature. Fermi-Dirac statistics simply put has to do with the arrangement of energy states in an atom where the electrons follow Pauli's exclusion principle. – Spoilt Milk Dec 03 '16 at 05:18
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Why do you say that the photoelectric effect is independent of temperature? – garyp Dec 04 '16 at 15:28
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Temperature affects energy levels and bands levels in metal .
At higher temperatures a certain fraction, characterized by the Fermi function, will exist above the Fermi level. The Fermi level plays an important role in the band theory of solids.
Here is a particular study for a particular problem of the work function of silver:
The results for pure silver metal show an evolution of the work function with temperature; a decrease of this parameter of about 0.2 0.3 eV is observed when the cathode temperature reaches 700 K, independently of the nature of the material. The obtained results are rather approximate. This method is not very accurate at higher temperature, because above 700 K the thermionic current dominates and the measurements of the photoelectric current are falsified by large fluctuations.
The temperature variation of the EWF of metals with increasing temperature may be caused by a series of different combined factors like thermal expansion, the internal effect of atomic vibrations, the variation of the chemical potential, spontaneous volume magnetostriction (for ferromagnetic metals Ni, Fe, …) etc .
So it is not correct that the work function is independent of temperature.
There are too many factors entering , and one of them will be the energy changes in the the Fermi level of the particular material.
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are all the electrons above fermi level in an atom are in free (gaseous) state of a metal – Umamaheswara Reddy Dec 04 '16 at 11:05
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The fermi level does not exist at an atomic picture, it exists in a lattice of atoms, if you read the links, there are bands where electrons belong to the whole lattice and not to individual atoms. – anna v Dec 04 '16 at 11:13
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It does not start from zero, it starts from the fermi energy level, described by the fermi function, http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/Fermi.html – anna v Dec 04 '16 at 12:53
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please see the picture I posted . I this it is filled from energy 0 to ef – Umamaheswara Reddy Dec 04 '16 at 15:19
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please see the picture I posted, in it it is filled from energy 0 to ef – Umamaheswara Reddy Dec 04 '16 at 15:23
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else , please explain me the ef derivation. ef =fermi energy – Umamaheswara Reddy Dec 04 '16 at 15:24
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did you look at the links ? http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/Fermi.html . this video tries to do that https://www.youtube.com/watch?v=j1Z6mUYl8Bg – anna v Dec 04 '16 at 15:58