Question

what is the fermi temperature if the fermi energy is 1.4e.v?

Answer 1

22400 k is the answer

Answer 2

The answer to the question is $\ 1.62521\times 10^{4}\ K$

CALCULATION:

Before going to answer this question, first we have to understand fermi energy and fermi temperature.

In quantum statistical mechanics, the fermi energy is defined as the maximum energy that can be occupied by the electrons at 0 K.On other hand it corresponds to the last filled level at absolute zero and the corresponding temperature is called fermi temperature.

As per the question, we are asked to calculate the fermi temperature.

The fermi energy is given as $E_{f}=\ 1.4\ ev$

The relation between fermi energy and fermi temperature is that -

                                      $E_{f}=\ kT_{f}$

Here, k is the Boltzmann's constant.

We know that 1 ev = $1.602\times 10^{-19}\ J$

                      1.4 ev = $1.4\times 1.602\times 10^{-19}\ J$

The fermi temperature is calculated as - $T_{f} =\frac{E_{f}} {k}$

                                                                   $=\ \frac{1.4\times 1.602\times 10^{-19}} {1.38\times 10^{-23}}\ K$

                                                                   $=\ 1.62521\times 10^{4}\ K$

                                                                         

                                                                                                             [ANS]