09Spring-PS3-Solns

# 09Spring-PS3-Solns - EE2 Problem Set#3 Solutions Question...

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EE2 Problem Set#3 Solutions Question 1 (5 points): (a) If I have 5 electrons all at a potential of 1V, what is the total energy of the electrons (in eV)? (b) What is the voltage change for an electron if temperature is increased by 100K? (a) E one electron = q * V = 1.6 × 10 19 ( ) × 1 {C*V=J) 1.6 × 10 19 J = 1 eV E total = 5 *1 = 5 eV (b) E electron = 3 2 kT Δ E electron = 3 2 k Δ T = 3 2 k Δ T = 3 2 8.617 × 10 5 × 100 = 0.013 {eV} Δ V = Δ E q = 0.013 V { } Question 2 (10 points): Suppose the energy of an electron is given by E ( k ) = 2.74 × 10 -37 k 2 Joules where k is given in units of meter -1 . Find the effective mass, and give the ratio of the effective mass to the ordinary mass of the electron. E k ( ) = 2.74 × 10 37 k 2 Effective mass, m * = 2 d 2 E 2 dE dk = 2 × 2.74 × 10 37 k = 5.48 × 10 37 k d 2 E dk 2 = 5.48 × 10 37 m * = 2 d 2 E 2 = 6.625 × 10 34 2 π × 1 5.48 × 10 37 = 2.025 × 10 32 kg Ratio of effective mass to ordinary mass of electron = m * m 0 = 2.025 × 10 32 9.1 × 10 31 = 0.022

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Question 3 (10 points):
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09Spring-PS3-Solns - EE2 Problem Set#3 Solutions Question...

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