(d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?
(d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Part d

Transcribed Image Text:**Problem 1:**
(a) A non-relativistic, free particle of mass \( m \) is bouncing back and forth between two perfectly reflecting walls separated by a distance \( L \). Imagine that the two oppositely directed matter waves associated with this particle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of the ground state (first harmonic, \( n = 1 \)) and first excited state (second harmonic, \( n = 2 \)). Find the formula for the kinetic energy of the \( n \)-th harmonic.
(b) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger de Broglie wavelength?
(c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potential difference \( V \).
(d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron bound to a Bohr model hydrogen atom?
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