Question

A metal has one free electron per atom, density $\rho = 0.97 \text{ g/cm}^3$ and molar mass $M = 39 \text{ g/mol}$. Calculate the Fermi energy $E_F$ of the metal:}

• A. \(4.5 \text{ eV}\)
• B. \(7.0 \text{ eV}\)
• C. \(5.5 \text{ eV}\)
• D. \(1.78 \text{ eV}\)

Hint:

To perform quick checks during competitive exams, remember that alkali metals with lower densities (like $K$ or $Na$) always have a small Fermi energy falling in the range of $1.5\text{ eV} - 2.5\text{ eV}$. Dense transition metals (like Copper) have higher Fermi energies around $7.0\text{ eV}$. This helps eliminate options (A), (B), and (C) immediately.

Answer 1

The Correct Option is D