Consider the Bohr model of the doubly ionized lithium ion (3 protons) with a single electron. The ground state energy is -122.4 ev What is the kinetic energy for the electron in orbit? eV Write down the relationship between the kinetic energy K, the momentum p and the mass m K= write your answer as a formula, e.g. z=x^4/3y Use these to find the de Broglie wavelength of the electron in this orbit: The de Broglie wavelength is nm If the electron is actually a standing wave, what radius does this suggest for the electron's orbit? ro = nm Assuming classical uniform circular motion for the electron in the Coulomb potential at the radius computed above, what is the total energy of the atom? The potential energy is Oze?/(4Tte ro) O-ze?/(4ne ro) O-ze?/(8te ro) OZe?/(8Tte ro) The kinetic energy is Οze2/ (4πε r ) Ο Ze2/ (4πε r ) Ο-Ze2/(8πε r ) ΟZe2/ (8πε r) The total energy is Οze2/ (4πε r0) Ο-Ze2/ (4πε ro) O-Ze2/(8nɛ r0) Οze2/ (8πε r0) Hence the total energy is ev
Consider the Bohr model of the doubly ionized lithium ion (3 protons) with a single electron. The ground state energy is -122.4 ev What is the kinetic energy for the electron in orbit? eV Write down the relationship between the kinetic energy K, the momentum p and the mass m K= write your answer as a formula, e.g. z=x^4/3y Use these to find the de Broglie wavelength of the electron in this orbit: The de Broglie wavelength is nm If the electron is actually a standing wave, what radius does this suggest for the electron's orbit? ro = nm Assuming classical uniform circular motion for the electron in the Coulomb potential at the radius computed above, what is the total energy of the atom? The potential energy is Oze?/(4Tte ro) O-ze?/(4ne ro) O-ze?/(8te ro) OZe?/(8Tte ro) The kinetic energy is Οze2/ (4πε r ) Ο Ze2/ (4πε r ) Ο-Ze2/(8πε r ) ΟZe2/ (8πε r) The total energy is Οze2/ (4πε r0) Ο-Ze2/ (4πε ro) O-Ze2/(8nɛ r0) Οze2/ (8πε r0) Hence the total energy is ev
University Physics Volume 3
17th Edition
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:William Moebs, Jeff Sanny
Chapter7: Quantum Mechanics
Section: Chapter Questions
Problem 38P: Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen...
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