Question

If the number of electrons per unit volume for the sodium crystal is \(2.55\times10^{28}/\text{m}^3\), then the value of Hall coefficient is:

• A. \(2.45\times10^{31}\ \text{m}^3/\text{C}\)
• B. \(-2.45\times10^{-31}\ \text{m}^3/\text{C}\)
• C. \(-2.45\times10^{-10}\ \text{m}^3/\text{C}\)
• D. \(2.45\times10^{-12}\ \text{m}^3/\text{C}\)

Hint:

For electron conduction, Hall coefficient is negative: \(R_H=-\frac{1}{ne}\).

Answer 1

The Correct Option is C

Concept:
For electrons, Hall coefficient is: \[ R_H=-\frac{1}{ne} \] where, \[ n=\text{number of electrons per unit volume} \] and \[ e=1.6\times10^{-19}\ \text{C} \]

Step 1: Write the given value. \[ n=2.55\times10^{28}\ \text{m}^{-3} \]

Step 2: Apply the formula. \[ R_H=-\frac{1}{ne} \] \[ R_H=-\frac{1}{(2.55\times10^{28})(1.6\times10^{-19})} \] \[ R_H=-\frac{1}{4.08\times10^9} \] \[ R_H=-2.45\times10^{-10}\ \text{m}^3/\text{C} \] \[ \therefore \text{Correct Answer is (C)} \]