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# 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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/if-metal-has-582-10-conduction.html

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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/a-uniform-silver-wire-has-resistivity.html

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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/calculate-energy-difference-between.html

4. Fermi velocity of electron in Cs metal is 0.73×106 m/s. Calculate its Fermi energy & Fermi
temperature.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/fermi-velocity-of-electron-in-cs-metal.html

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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/find-temperature-at-which-there-is-10.html

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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/find-probability-with-which-energy.html

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.
Ans.https://engineeringsmartstudies.blogspot.com/2020/05/calculate-probability-of-electron.html
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