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b) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable circular orbits. De Broglie explained what orbits could exist by postulating that electrons (and anything else) with momentum p have an associated wavelength X, given by \ = h/p where h is Planck's constant. Then the allowed orbits are those with an integer number n of wavelengths in the circumference of the orbit. For electrons as for planets, the total energy of an orbit is E = -mv2. i) Write down and explain the three key equations that enable the derivation of the Ryd- mee¹ berg constant (1Ry = 2 with n = 1 and Z = 1), defining all the symbols. Show by 8€²n²h² putting the values in that this gives -13.6 eV, -3.40 eV and -1.51 eV for the energies to three significant figures of the first three hydrogen energy levels. ii) Consider the helium ion, He¹+, with one electron orbiting the helium nucleus. Ex- plain what changes from the Bohr model for hydrogen, and find the energies to three significant figures of the first three energy levels of the He¹+ ion.

b) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable circular orbits. De Broglie explained what orbits could exist by postulating that electrons (and anything else) with momentum p have an associated wavelength X, given by \ = h/p where h is Planck's constant. Then the allowed orbits are those with an integer number n of wavelengths in the circumference of the orbit. For electrons as for planets, the total energy of an orbit is E = -mv2. i) Write down and explain the three key equations that enable the derivation of the Ryd- mee¹ berg constant (1Ry = 2 with n = 1 and Z = 1), defining all the symbols. Show by 8€²n²h² putting the values in that this gives -13.6 eV, -3.40 eV and -1.51 eV for the energies to three significant figures of the first three hydrogen energy levels. ii) Consider the helium ion, He¹+, with one electron orbiting the helium nucleus. Ex- plain what changes from the Bohr model for hydrogen, and find the energies to three significant figures of the first three energy levels of the He¹+ ion.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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b) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable circular orbits. De Broglie explained what orbits could exist by postulating that electrons (and anything else) with momentum p have an associated wavelength X, given by \ = h/p where h is Planck's constant. Then the allowed orbits are those with an integer number n of wavelengths in the circumference of the orbit. For electrons as for planets, the total energy of an orbit is E = -mv2. i) Write down and explain the three key equations that enable the derivation of the Ryd- mee¹ berg constant (1Ry = 2 with n = 1 and Z = 1), defining all the symbols. Show by 8€²n²h² putting the values in that this gives -13.6 eV, -3.40 eV and -1.51 eV for the energies to three significant figures of the first three hydrogen energy levels. ii) Consider the helium ion, He¹+, with one electron orbiting the helium nucleus. Ex- plain what changes from the Bohr model for hydrogen, and find the energies to three significant figures of the first three energy levels of the He¹+ ion.
Transcribed Image Text:b) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable circular orbits. De Broglie explained what orbits could exist by postulating that electrons (and anything else) with momentum p have an associated wavelength X, given by \ = h/p where h is Planck's constant. Then the allowed orbits are those with an integer number n of wavelengths in the circumference of the orbit. For electrons as for planets, the total energy of an orbit is E = -mv2. i) Write down and explain the three key equations that enable the derivation of the Ryd- mee¹ berg constant (1Ry = 2 with n = 1 and Z = 1), defining all the symbols. Show by 8€²n²h² putting the values in that this gives -13.6 eV, -3.40 eV and -1.51 eV for the energies to three significant figures of the first three hydrogen energy levels. ii) Consider the helium ion, He¹+, with one electron orbiting the helium nucleus. Ex- plain what changes from the Bohr model for hydrogen, and find the energies to three significant figures of the first three energy levels of the He¹+ ion.
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