Solving the Fermi Energy of Copper: Momentum, Wavelength, Velocity

[sanjeeb]

please help me solve this...
fermi energy of copper is 7eV.
what is the fermi momentum of an electron in copper?
what is the de Broglie wavelength of the electron?
what is the fermi velocity?///
please help/////

 

[hage567]

Show your work so far.

 

[m2003]

The Fermi energy of a material is a fundamental property that describes the highest energy level of the electrons in that material at absolute zero temperature. In the case of copper, the Fermi energy is 7eV. To determine the Fermi momentum of an electron in copper, we can use the formula p = √(2mE), where p is the momentum, m is the mass of the electron, and E is the Fermi energy. Plugging in the values for copper, we get p = √(2*9.11*10^-31 kg * 7 eV) = 2.61*10^-24 kg*m/s.

The de Broglie wavelength of an electron is given by λ = h/p, where h is Planck's constant and p is the momentum. Substituting the value of p that we calculated above, we get λ = 6.63*10^-34 J*s / 2.61*10^-24 kg*m/s = 2.54*10^-10 m.

Finally, the Fermi velocity can be calculated using the formula v = p/m, where v is the velocity and m is the mass of the electron. Substituting the values for copper, we get v = 2.61*10^-24 kg*m/s / 9.11*10^-31 kg = 2.87*10^6 m/s. This is a very high velocity, which is expected for a metal like copper, where the electrons are highly mobile.

I hope this helps you understand how to solve for the Fermi energy, momentum, wavelength, and velocity of an electron in copper. Remember to always use the appropriate formulas and units when solving for these properties.