Solutions Of Free Electron Theory Numericals

1. If a metal has 5.82 × 10^28 conduction electrons/m3, find the relaxation time in a metal of resistivity 1.543 × 10^−8 Ω-m.

2. A uniform silver wire has a resistivity of 1.54×10^−8 Ω-m at room temperature. For an
electric field of 1 V/cm, calculate (i) Relaxation time τ, (ii) Drift velocity Vd and (iii) mobility μ.

3. Calculate the energy difference between the ground state and first excited state in eV for an
electron in a one-dimensional rigid box of length 1 oA. Mass of the electron = 9.1×10^−31 kg
and h = 6.626×10−34 J-S.

4. Fermi velocity of electron in Cs metal is 0.73×106 m/s. Calculate its Fermi energy & Fermi

5. Find the temperature at which there is 1.0 % probability that a state with energy 0.5 eV above
Fermi energy will be occupied.

6. Find the probability with which an energy level 0.02 eV below the Fermi level will be occupied
at room temperature of 300 K and at 1000 K.

7. Calculate the probability of an electron occupying an energy level 0.02 eV above the Fermi
level at 200 K and 400 K in a material.

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