Modern Physics
Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
bartleby

Concept explainers

Question
Chapter 4, Problem 1Q
To determine

The assumptions of Bohr’s model of atom, its significance and its contradiction with classical physics.

Expert Solution & Answer
Check Mark

Answer to Problem 1Q

The significance of Bohr’s model is that it predicts the allowed energy levels of the hydrogen atom. However, it contradicts with the fact that orbiting electron doesn’t radiate energy.

Explanation of Solution

The assumptions of Bohr’s model are given as follows:

  • Electrons in an atom orbit around the nucleus in circular orbits.
  • Not all but only certain orbits are stable. Electrons in stable orbits do not radiate energy. The allowed orbits are also called stationary orbits.
  • When an electron jumps from a higher to lower orbit, photon of energy same as the energy difference between the two levels is emitted.

The energy of the emitted photon is,

    hf=EiEf

Here, h is the Planck’s constant, f is the frequency, Ei is the energy of the initial orbit and Ef is the energy of the final orbit.

  • The angular momentum of the electron in a stationary orbit is an integral multiple of .

The electron’s orbital angular momentum is,

    mvr=n

Here, is the reduced Planck’s constant, m is the mass of the electron, v is the velocity of the electron, r is the radius of its orbit and n is the principal quantum number.

Using the above, assumptions, the allowed energy levels and hence the emission and absorption wavelengths of the hydrogen atom can be calculated.

Conclusion:

Even though the energy levels can be predicted, one of the limitations of the Bohr’s model is that it assumes that orbiting electrons don’t radiate energy. According to classical electromagnetism, any accelerated charge must radiate energy.

Therefore, Bohr’s atomic model contradicts with the classical physics.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Knowledge Booster
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Modern Physics
    Physics
    ISBN:9781111794378
    Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
    Publisher:Cengage Learning
    University Physics Volume 3
    Physics
    ISBN:9781938168185
    Author:William Moebs, Jeff Sanny
    Publisher:OpenStax
    An Introduction to Physical Science
    Physics
    ISBN:9781305079137
    Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
    Publisher:Cengage Learning
  • Glencoe Physics: Principles and Problems, Student...
    Physics
    ISBN:9780078807213
    Author:Paul W. Zitzewitz
    Publisher:Glencoe/McGraw-Hill
    The Solar System
    Physics
    ISBN:9781305804562
    Author:Seeds
    Publisher:Cengage
    Stars and Galaxies
    Physics
    ISBN:9781305120785
    Author:Michael A. Seeds, Dana Backman
    Publisher:Cengage Learning
  • Modern Physics
    Physics
    ISBN:9781111794378
    Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
    Publisher:Cengage Learning
    University Physics Volume 3
    Physics
    ISBN:9781938168185
    Author:William Moebs, Jeff Sanny
    Publisher:OpenStax
    An Introduction to Physical Science
    Physics
    ISBN:9781305079137
    Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres
    Publisher:Cengage Learning
    Glencoe Physics: Principles and Problems, Student...
    Physics
    ISBN:9780078807213
    Author:Paul W. Zitzewitz
    Publisher:Glencoe/McGraw-Hill
    The Solar System
    Physics
    ISBN:9781305804562
    Author:Seeds
    Publisher:Cengage
    Stars and Galaxies
    Physics
    ISBN:9781305120785
    Author:Michael A. Seeds, Dana Backman
    Publisher:Cengage Learning