I was trying to find the probability that an electron occupies the Fermi level at 0K.
Fermi function: {exp[(E-Ef)/kT] + 1}-1; (k = 8.314 J/mol/K)
According to my calculations, the answer would be 0.5.
Is that answer correct?
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that's not the Fermi-Dirac distribution, and I think that's what you mean when you say "Fermi function". – Marcus Müller Jan 04 '22 at 13:40
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I’m voting to close this question because off topic – Davide Andrea Jan 14 '22 at 16:43
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Your definition of the Fermi function is incorrect. Also, the derivation in your answer comes to the right result, 0.5, but from something wrong. I don't know how that happens. However,
I was trying to find the probability that an electron occupies the Fermi level at 0K.
That's not really something you can "figure out". It's the definition of the Fermi level that it's exactly the energy level with a 50% population probability – at any temperature, including 0 K.
Marcus Müller
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The probability that an electron occupies the Fermi level at 0K is 0.5.
At 0K, when E = Ef the probability becomes equal to 0.5.
Fermi function: f(E) = {exp[(E-Ef)/kT] + 1}-1; (k = 8.314 J/mol/K)
Moreover, At 0K,
when, E < Ef ====> f(E) = 1
when, Ef < E ====> f(E) = 0
Kavindu Nilshan
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it's not celar how you arrive at the 0.5. I mean, according to your formula, you have \$\lim_{T\to 0+} f(E(t)) \to e^{0/0}+1-1\$, and it's absolutely unclear how that would be 0.5, ever. – Marcus Müller Jan 04 '22 at 13:41