evaluate the fermi function for an energy KT above the fermi energy. find the temperature at which there is a 1% probability that a state,

Complete Question

Evaluate the Fermi function for an energy kT above the Fermi energy. Find the temperature at which there is a 1% probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron.

a

The Fermi function for the energy KT is  

b

The temperature is  

Step-by-step explanation:

From the question we are told that

   The energy considered is  

Generally the Fermi  function is mathematically represented as

    Here K is the Boltzmann constant with value

             is the Fermi energy

             is the initial energy level which is mathematically represented as

So

=>  

=>  

=>  

Generally the probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron is mathematically represented by the  Fermi  function as

Here is that energy level that is  0.5 ev above the Fermi energy  

=>  

=>  

=>  

=>  

=>  

Taking natural  log of both sides

=>  

=>    

Note eV is electron volt and the equivalence in Joule is    

So

=>  

x = 23.78

step-by-step explanation:

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step-by-step explanation: