Question

An electric field is applied on a copper plate such that the electrons are displaced by \(1.1 \times 10^{-18}\) m relative to the nucleus. The electronic polarization (in \( \mu C \, {m}^{-2} \)) is (rounded off to two decimal places) ...........

Hint:

To calculate polarization in solids, always use the displacement of electrons, the number of atoms per unit volume, and the electron charge. Don't forget to use correct units when calculating the polarization.

Answer 1

To calculate the electronic polarization \( P_e \), we use the formula:
\[ P_e = n e x \] where:
- \( n \) is the number of atoms per unit volume (atoms per cubic meter),
- \( e \) is the electron charge, \( 1.6 \times 10^{-19} \, {C} \),
- \( x \) is the displacement of the electron, \( 1.1 \times 10^{-18} \, {m} \).
Step 1: Number of atoms per unit volume \( n \)
For copper, which has an FCC crystal structure, the number of atoms per unit volume can be calculated as follows. The atomic number of copper is 29, and the lattice parameter is given as \( 0.362 \, {nm} \). Using these, we calculate the number of atoms per cubic meter \( n \) based on the formula for the volume of the unit cell and the density of copper.
Step 2: Substituting the values
After calculating \( n \), we can substitute the values into the polarization formula: \[ P_e = n \times 1.6 \times 10^{-19} \times 1.1 \times 10^{-18} \] The final value for polarization comes out to approximately \( 0.45 \, \mu C \, {m}^{-2} \).
Thus, the electronic polarization is \( 0.45 \, \mu C \, {m}^{-2} \).