Physics20785 marksNumerical: Fermi energy calculationeffective mass and holes
The density of aluminum is 2.70 text g/cm3 and its molecular weight is 26.98 g/mole. (a) Calculate the Fermi energy. (b) If the experimental value of EF is 12 eV, what is the electron effective mass in aluminum? [Aluminum is trivalent].
The density of aluminum is $2.70 \text{ g/cm}^3$ and its molecular weight is 26.98 g/mole. (a) Calculate the Fermi energy. (b) If the experimental value of $E_F$ is 12 eV, what is the electron effective mass in aluminum? [Aluminum is trivalent]. [5]
Quantity Value ------ Density, $\rho$ $2.70 \text{ g/cm}^3$ Molar mass, $M$ $26.98 \text{ g/mol}$ Valency, $Z$ 3 (trivalent) Experimental $EF$ $12 \text{ eV}$ $NA$ $6.022\times10^{23}\ \text{mol}^{-1}$ $$n = \frac{\rho NA Z}{M} = \frac{2.70 \times 6.022\times10^{23} \times 3}{26.98}$$ $$= \frac{4...