De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation

A uniform magnetic field B exist in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule for angular momentum, calculate (a) the smallest possible radius of the electron (b) the radius of the nth orbit and (c) the minimum possible speed of the electron.

The simple Bohr model is not applicable to He 4 atom because ______.

1. He⁴ is an inert gas.
2. He⁴ has neutrons in the nucleus.
3. He⁴ has one more electron.
4. electrons are not subject to central forces.

Using Bohr’s second postulate of quantization of orbital angular momentum show that the circumference of the electron in the n^th orbital state in hydrogen atom is n times the de Broglie wavelength associated with it.

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level n to level (n − 1). For large n, show that this frequency equals the classical frequency of revolution of the electron in the orbit.

Plot a graph showing the variation of de Broglie wavelength (X) associated with a charged a particle of mass m, versus  `1/sqrtV` where V is the potential difference through which the particle is accelerated. How does this graph give us information regarding the magnitude of the charge of the particle? 

Answer the following question.
State Bohr's quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum it belongs. 

Show that the radius of the orbit in hydrogen atom varies as n², where n is the principal quantum number of the atom.

Calculate the shortest wavelength of the spectral lines emitted in Balmer series.

[Given Rydberg constant, R = 10⁷ m^–1]