How to Estimate the Fermi Energy for Potassium Metal?

AI Thread Summary
The discussion centers on estimating the Fermi energy for potassium metal, focusing on the contributions to heat capacity. The user has derived an expression for electronic heat capacity and recognizes that the heat capacity consists of both electron and phonon contributions. They seek guidance on estimating the Fermi energy, considering only the electron contribution due to potassium being a metal. A suggestion is made to equate the derived heat capacity expression to the linear term in the experimental heat capacity formula to find the Fermi temperature and subsequently the Fermi energy. This approach provides a pathway to solve the problem effectively.
Benlaww
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Homework Statement
(a) Conduction electrons in a metal can be modeled as an ideal Fermi gas. Using a simple
approximate argument, determine the electronic heat capacity Cv as a function of temperature T, for T<TF, where TF is the Fermi temperature.

How is your result different from that of a classical gas of electrons?

(b) The experimental heat capacity of potassium metal at low temperatures has the form
C=(aT + yT^3),
where a = 2.08 mJ mol-1 K-2 & y = 2.6 mJ mol-1 K-4

Briefly explain the physical origin of each of the two terms in the expression.

Estimate the Fermi energy for potassium metal.
Relevant Equations
C = (aT + yT^3)
I have completed part a, from which I got the expression: Cv = 3KTn/(T_f)

For part b, the first term is the electron contribution and the second term is the phonon contribution.

I'm stuck on how to estimate the fermi energy for the potassium metal. I'm thinking I only need to consider the electron contribution due to it being a metal but I don't know where to start?

Thank you
 
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Benlaww said:
Homework Statement:: (a) Conduction electrons in a metal can be modeled as an ideal Fermi gas. Using a simple
approximate argument, determine the electronic heat capacity Cv as a function of temperature T, for T<TF, where TF is the Fermi temperature.

How is your result different from that of a classical gas of electrons?

(b) The experimental heat capacity of potassium metal at low temperatures has the form
C=(aT + yT^3),
where a = 2.08 mJ mol-1 K-2 & y = 2.6 mJ mol-1 K-4

Briefly explain the physical origin of each of the two terms in the expression.

Estimate the Fermi energy for potassium metal.
Relevant Equations:: C = (aT + yT^3)

I have completed part a, from which I got the expression: Cv = 3KTn/(T_f)

For part b, the first term is the electron contribution and the second term is the phonon contribution.

I'm stuck on how to estimate the fermi energy for the potassium metal. I'm thinking I only need to consider the electron contribution due to it being a metal but I don't know where to start?

Thank you
Not a topic I'm familiar with, but since you haven' had any replies...

Assuming your answer to part a) is correct and taking n=1, could you not simply equate
3kTn/(T_f) to the aT term? That gives T_f, from which E_f is found.
 
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