Question

The Fermi energy of copper is 7.0eV. Verify that the corresponding Fermi speed is 1600 km/s.

Short answer

The corresponding Fermi speed for Fermi energy value 7.0 eV is 1600 km/s .

Step-by-step solution

The given data

Fermi energy of copper, $E_F=7.0eV$

Understanding the concept of energy and speed

The energy of a body due to its speed, is known as kinetic energy of the body. The total work done in moving from one place to another is stored in the bodyin the form of kinetic energy.

Formula:

The kinetic energy of a system,$E=\frac{1}{2}m{v}^2$ (i)

Calculation of the Fermi energy

Using the given data of Fermi energy of copper in equation (i), we can get the value of the corresponding Fermi speed as follows:

$$\begin{gathered} v_f=\sqrt{\frac{2E_F}{m}} \\ =c\sqrt{\frac{2E_F}{m{c}^2}} \\ =\left(3\times {10}^{5}km/s\right)\sqrt{\frac{2\left(7.0eV\right)}{\left(5.11\times {10}^{5}eV\right)}} \\ =1.6\times {10}^3\mathrm{km}/\mathrm{s} \end{gathered}$$

Hence, the value of the speed is $1.6\times {10}^3\mathrm{km}/\mathrm{s}$.