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(a) Calculate the frequency of revolution and the orbit radius of the electron in the Bohr model of hydrogen for n = 100 (b) Calculate the photon frequency for transitions from the n to n − 1 states for the same value of n as in part (a) and compare with the revolution frequencies found in part (a). (c) Explain how your results verify the correspondence principle.

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Tauseef Shaikh
Tauseef ShaikhLv10
20 Nov 2020

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

An electron is in the nth Bohr orbit of the hydrogen atom.

(a) Show that the period of the electron is

 

and determine the numerical value of to.

(b) On average, an electron remains in the n=2 orbit for approximately 10 microseconds before jump down to n= 1 orbit. How many revolutions does the electron make in the excited state?

(c) Define the period of one revolution as a one-electron year, analogous to an earth year is the period of the earth's motion around the sun. Explain whether we should think of the electron in n=2 orbit "as living for a long time"

(a) Find the frequency of the electron's orbital motion, fe, around a fixed nucleus of charge +Ze by using Equation 4.24 and  

(b) Show that the frequency of the photon emitted when an electron jumps from an outer to an inner orbit can be written 

 

for electronic configuration of adjacent orbitals nf - ni =1

examine the factor 

and use nf is greater than ni

(c) What do you conclude about the frequency of emitted radiation compared with the frequencies of orbital revolution in the initial and final states? What happens as ni ? 

 

Suppose two different hydrogen atoms, labeled A and B, have their electrons in state n = 4. Atom A emits light when its electron transitions directly from the n = 4 state to the n = 2 state. Atom B emits light twice, as its electron first transitions from the n = 4 state to the n = 3 state, then transitions from the n = 3 state to the n = 2 state. (a) Are the three wavelengths of light the same or different? (b) How does the energy of the photon from atom A compare to the total energy of the two photons from atom B?

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