Learning Goal: To understand the Bohr model of the hydrogen atom In 1913 Niels Bohr formulated a method of calculating the different energy levels of the hydrogen atom. He did this by combining both classical and quantum ideas. In this problem, we go through the steps needed to understand the Bohr model of the atom. Part A Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e. In the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center, Fe, is equal to mv2/r. Given these two pieces of information, deduce the velocity of the electron as it orbits around the nucleus. Express your answer in terms of e, m, r, and eo, the permittivity of free space. ► View Available Hint(s) V = || ΑΣΦ e Απε, rm ?

College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Learning Goal:
To understand the Bohr model of the hydrogen
atom.
In 1913 Niels Bohr formulated a method of
calculating the different energy levels of the
hydrogen atom. He did this by combining both
classical and quantum ideas. In this problem, we go
through the steps needed to understand the Bohr
model of the atom.
Part A
Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus (a
single proton) with charge +e. In the classical model, the electron orbits around the nucleus, being
held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much
like planets orbit around the sun, being held in orbit by their gravitational interaction. When the
electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net
force toward the center, F, is equal to mv²/r. Given these two pieces of information, deduce the
velocity of the electron as it orbits around the nucleus.
Express your answer in terms of e, m, r, and €0, the permittivity of free space.
► View Available Hint(s)
V=
Submit
|VE ΑΣΦ
e
|4πε, rm
Previous Answers
?
Transcribed Image Text:Learning Goal: To understand the Bohr model of the hydrogen atom. In 1913 Niels Bohr formulated a method of calculating the different energy levels of the hydrogen atom. He did this by combining both classical and quantum ideas. In this problem, we go through the steps needed to understand the Bohr model of the atom. Part A Consider an electron with charge -e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e. In the classical model, the electron orbits around the nucleus, being held in orbit by the electromagnetic interaction between itself and the protons in the nucleus, much like planets orbit around the sun, being held in orbit by their gravitational interaction. When the electron is in a circular orbit, it must meet the condition for circular motion: The magnitude of the net force toward the center, F, is equal to mv²/r. Given these two pieces of information, deduce the velocity of the electron as it orbits around the nucleus. Express your answer in terms of e, m, r, and €0, the permittivity of free space. ► View Available Hint(s) V= Submit |VE ΑΣΦ e |4πε, rm Previous Answers ?
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