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6) An electron in a box Goal: Understanding Heisenberg's uncertainty principle Suppose an electron is confined to a box that is about 0.50 x 10-10 m on a side. If this distance is taken as the uncertainty in the position of the electron, (a) Calculate the corresponding minimum uncertainty in the momentum. 2.1 x1024 (b) Because the electron is confined to a stationary box, its average momentum is zero. The magnitude of the electron's momentum is nonzero, however. Assuming the magnitude of the electron's momentum is the same as its uncertainty in momentum, calculate the corresponding kinetic energy. 2.4×10-3 (1) a) 2.18 eV b) 1.16 x 10-27 kg m/s (2) a) 5.5 x 10 Hz b) 1.59 x 10-19 J (3) a) 6.55 x 10-10 b) 3.04 x 10-16 J c) 2 x 10-18 J (4) 2080 m/s (5) a) 6.64 x 10-5 m b) 1.72 x 10-34 m x 104 kg m/s b) 2.4 x 10-18J (6) a) 2.1

6) An electron in a box Goal: Understanding Heisenberg's uncertainty principle Suppose an electron is confined to a box that is about 0.50 x 10-10 m on a side. If this distance is taken as the uncertainty in the position of the electron, (a) Calculate the corresponding minimum uncertainty in the momentum. 2.1 x1024 (b) Because the electron is confined to a stationary box, its average momentum is zero. The magnitude of the electron's momentum is nonzero, however. Assuming the magnitude of the electron's momentum is the same as its uncertainty in momentum, calculate the corresponding kinetic energy. 2.4×10-3 (1) a) 2.18 eV b) 1.16 x 10-27 kg m/s (2) a) 5.5 x 10 Hz b) 1.59 x 10-19 J (3) a) 6.55 x 10-10 b) 3.04 x 10-16 J c) 2 x 10-18 J (4) 2080 m/s (5) a) 6.64 x 10-5 m b) 1.72 x 10-34 m x 104 kg m/s b) 2.4 x 10-18J (6) a) 2.1

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter28: Quantum Physics
Section: Chapter Questions
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11.6.2
6) An electron in a box Goal: Understanding Heisenberg's uncertainty principle Suppose an electron is confined to a box that is about 0.50 x 10-10 m on a side. If this distance is taken as the uncertainty in the position of the electron, (a) Calculate the corresponding minimum uncertainty in the momentum. 2.1 x1024 (b) Because the electron is confined to a stationary box, its average momentum is zero. The magnitude of the electron's momentum is nonzero, however. Assuming the magnitude of the electron's momentum is the same as its uncertainty in momentum, calculate the corresponding kinetic energy. 2.4×10-3 (1) a) 2.18 eV b) 1.16 x 10-27 kg m/s (2) a) 5.5 x 10 Hz b) 1.59 x 10-19 J (3) a) 6.55 x 10-10 b) 3.04 x 10-16 J c) 2 x 10-18 J (4) 2080 m/s (5) a) 6.64 x 10-5 m b) 1.72 x 10-34 m x 104 kg m/s b) 2.4 x 10-18J (6) a) 2.1
Transcribed Image Text:6) An electron in a box Goal: Understanding Heisenberg's uncertainty principle Suppose an electron is confined to a box that is about 0.50 x 10-10 m on a side. If this distance is taken as the uncertainty in the position of the electron, (a) Calculate the corresponding minimum uncertainty in the momentum. 2.1 x1024 (b) Because the electron is confined to a stationary box, its average momentum is zero. The magnitude of the electron's momentum is nonzero, however. Assuming the magnitude of the electron's momentum is the same as its uncertainty in momentum, calculate the corresponding kinetic energy. 2.4×10-3 (1) a) 2.18 eV b) 1.16 x 10-27 kg m/s (2) a) 5.5 x 10 Hz b) 1.59 x 10-19 J (3) a) 6.55 x 10-10 b) 3.04 x 10-16 J c) 2 x 10-18 J (4) 2080 m/s (5) a) 6.64 x 10-5 m b) 1.72 x 10-34 m x 104 kg m/s b) 2.4 x 10-18J (6) a) 2.1
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