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(a) Use Bohr's model of the hydrogen atom to show that when the electron moves from the n state to the n – 1 state, the frequency of the emitted light is 2n – 1 e f = п?(п — 1)2 (b) Bohr's correspondence principle claims that quantum results should reduce to classical results in the limit of large quantum numbers. Show that as n→ 0, this expres- sion varies as 1/n³ and reduces to the classical frequency one expects the atom to emit. Suggestion: To calculate the classical frequency, note that the frequency of revolution is v/2Tr, where vis the speed of the electron and ris given by Equation 41.10. n²h? ke? n?h? n = 1, 2, 3, . .. (41.10) mr m,k_e? e"e

(a) Use Bohr's model of the hydrogen atom to show that when the electron moves from the n state to the n – 1 state, the frequency of the emitted light is 2n – 1 e f = п?(п — 1)2 (b) Bohr's correspondence principle claims that quantum results should reduce to classical results in the limit of large quantum numbers. Show that as n→ 0, this expres- sion varies as 1/n³ and reduces to the classical frequency one expects the atom to emit. Suggestion: To calculate the classical frequency, note that the frequency of revolution is v/2Tr, where vis the speed of the electron and ris given by Equation 41.10. n²h? ke? n?h? n = 1, 2, 3, . .. (41.10) mr m,k_e? e"e

Modern Physics
Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter4: The Particle Nature Of Matter
Section: Chapter Questions
Problem 37P
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(a) Use Bohr's model of the hydrogen atom to show that when the electron moves from the n state to the n – 1 state, the frequency of the emitted light is 2n – 1 e f = п?(п — 1)2 (b) Bohr's correspondence principle claims that quantum results should reduce to classical results in the limit of large quantum numbers. Show that as n→ 0, this expres- sion varies as 1/n³ and reduces to the classical frequency one expects the atom to emit. Suggestion: To calculate the classical frequency, note that the frequency of revolution is v/2Tr, where vis the speed of the electron and ris given by Equation 41.10.
Transcribed Image Text:(a) Use Bohr's model of the hydrogen atom to show that when the electron moves from the n state to the n – 1 state, the frequency of the emitted light is 2n – 1 e f = п?(п — 1)2 (b) Bohr's correspondence principle claims that quantum results should reduce to classical results in the limit of large quantum numbers. Show that as n→ 0, this expres- sion varies as 1/n³ and reduces to the classical frequency one expects the atom to emit. Suggestion: To calculate the classical frequency, note that the frequency of revolution is v/2Tr, where vis the speed of the electron and ris given by Equation 41.10.
n²h? ke? n?h? n = 1, 2, 3, . .. (41.10) mr m,k_e? e"e
Transcribed Image Text:n²h? ke? n?h? n = 1, 2, 3, . .. (41.10) mr m,k_e? e"e
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