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20075EE2_1_problem_set3 - field of intensity = 10 v/cm is...

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EE2 (Winter 2007) Home-work: Problem Set 3 Due date: 10-22-2007 (Note in all problems assume T = 0K) 1. Consider a rectangular box of dimensions 15 x 20 x20 Angstrom units. Consider the state n x = 2, n y = 4 and n z = 3 for free electrons. What are the values of the x,y and z components of momentum and the kinetic energy. 2. For the electrons in problem 1, what are the normalization constants A x , A y and A z ? 3. Lithium is a monovalent element. Assuming T = 0 K, find the maximum speed of the electron given the density of Lithium to be 4.6 x 10 22 atoms per cm 3 . (In this problem each Lithium atom contributes one free electron to the density of free electrons.) 4. In problem 3, if it is assumed that the collision or scattering relaxation time is c to be 2 x 10 -12 second, a) what is the average k value in the absence of an electric field? and b) what is the value of k under steady state conditions when an electric
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Unformatted text preview: field of intensity = 10 v/cm is applied? 5. For the two conditions in problem 4, draw qualitatively the distribution of the electrons either in the momentum or k space. 6. Write down the expression for dNv x /dv x , the distribution of electrons as a function of v x , the x-component of velocity in a metallic conductor. 7. Write the expression for the number of electrons per unit volume that will escape into vacuum at temperature T given E B is the surface barrier energy. You can express your answer in terms of the work-function ( = E B- E F ). 8. Assume a solid has 10 22 electrons per cm 3 . What is the average speed of the electrons at T = 0K. 9. Suppose E varies as 0.5 (h/2 } 2 (k – k ) 2 /(2 m). What is the effective mass of an electron at the state with k = 0.35k ? Why does it not vary with k?...
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