Explanation 1) Concept: By using the concept of momentum, we find the wave number in each region; after that, we use the wave function in each region to find out the reflection coefficient. With the help of reflection coefficient, we find the transmission coefficient, and from the transmission coefficient, we can find the current on the other side of the step boundary. 2) Formula: i) k = 2 π p h ii) R = B 2 A 2 iii) I t = T I 0 iv) T + R = 1 3) Given: i) v = 900 m / s ii) I = 5.00 m A iii) m = 9.1 × 10 - 31 k g iv) V = - 1.25 μ V 4) Calculations: The momentum is p = m v So that the wave vector is k = 2 π p h k = 2 π m v h By substituting the value, we get k = 2 π × 9.1 × 10 - 31 × 900 6.626 × 10 - 34 k = 7.77 × 10 6 m - 1 … … … … … … … … … … … … … … … … … … … … … … … … … … … … 1 Now the total energy in region 1 is given by the formula E = p 2 2 m + U U = 0 So the total energy is the kinetic energy K = E = 1 2 m v 2 K = 1 2 × 9.1 × 10 - 31 × 900 2 K = 3.69 × 10 - 25 J K = 3.69 × 10 - 25 × 1.6 × 10 - 19 K = 2.306 μ e V Now in region 2, V = - 1.25 μ V The kinetic energy of the electron is K b = E - U b K b = 2.306 - 1.25 K b = 1.056 μ e V So that the corresponding wave number is k b = 2 π p h k b = 2 π 2 m E - U b h k b = 2 π 2 m K b h By substituting the value, we can get k b = 2 π 2 × 9.1 × 10 - 31 × 1.056 × 10 - 6 × 1.6 × 10 - 19 6.626 × 10 - 34 k b = 5

Fundamentals of Physics, Volume 1, Chapter 1-20

10th Edition

ISBN: 9781118233764

Author: David Halliday

Publisher: WILEY

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Chapter 38, Problem 73P

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The current on the other side of the step boundary.

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Chapter 38, Problem 72P

Chapter 38, Problem 74P

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The current on the other side of the step boundary.

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Chapter 38 Solutions

To find:

The current on the other side of the step boundary.