Question

Devise a straightforward method that allows you to calculate (a) the speed and (b) the angular momentum of an electron in the nth Bohr orbit. Your expressions should contain the number of the orbit, n, and constants.

Using the formula that you devised, calculate the speed of an electron and the angular momentum of an electron in the tenth Bohr orbit. Units for answers are m/s for speed and J/s for angular momentum.

Answer 1

Angular Momentum Quantization

In the Bohr model, the wavelength associated with the electron is given by the DeBroglie relationship

and the standing wave condition that circumference = whole number of wavelengths. In the hydrogenic case, the number n is the principal quantum number.

These can be combined to get an expression for the angular momentum of the electron in orbit. (Note that this assumes a circular orbit, a generally unwarranted assumption.)

Thus L is not only :conserved, but constrained to discrete values by the quantum number n. This quantization of angular momentum is a crucial result and can be used in determining the Bohr orbit radii and Bohr energies.

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velocity

equate centripetal force with coulomb force between two point charges.
mv