Question

Bohr versus Schrodinger.Compare and contrast the Bohr model and the Schrodinger model for hydrogen. What are the ways that they are the same and the ways that there aredifferent? Be complete in your answer.

Answer 1

Bohr model

Bohr assumed, that electron as a particle moves in an orbit around the nucleus under the influence of the electrostatic attraction of the nucleus; circular or elliptical orbits are allowed. For simplicity, Bohr considered only circular orbits, and introduced several assumptions
1)Instead of a continuum of orbits, which are possible in classical mechanics, only a dis-
crete set of circular stable orbits, called stationary states, are allowed. Atoms can exist
only in certain stable states with definite energies: E1, E2, E3, etc.
2)The allowed (stationary) orbits correspond to those for which the orbital angular momentum of the electron is an integer multiple of h.
This is known as the Bohr quantization rule of the angular momentum.
3)As long as an electron remains in a stationary orbit, it does not radiate electromagnetic
energy. Emission or absorption of radiation can take place only when an electron jumps
from one allowed orbit to another. The radiation corresponding to the electron’s transition from an orbit of energy En to another Em is carried out by a photon of energy
hv = En - Em.

Schrodinger model(comparison with Bohr model)

A major problem with Bohr's model was that it treated electrons as particles that existed in precisely-defined orbits. Based on de Broglie's idea that particles could exhibit wavelike behavior, Schrödinger theorized that the behavior of electrons within atoms could be explained by treating them mathematically as matter waves.

The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by “n” the principle quantum number.

Schrodinger's model allowed the electron to occupy three-dimensional space. It therefore required three quantum numbers, to describe the distribution of electrons in the atom.

Although both agreed that In a hydrogen atom the electron’s motion is restricted by the inverse-square electric field of the nucleus. Electron radiates only during the transition from one state to another.

Bohr had assumed the angular momentum quantisation rule but in Schrodinger model it was naturally derived. Discrete set of energy states are naturally derived in later case.

In Bohr’s model of the hydrogen atom the electron is visualized as revolving around
the nucleus in a circular path. It implies that if a suitable experiment were performed, the electron would always be found a distance of r=a(n^2) (where n is the quantum number of the orbit and a is the radius of the innermost orbit) from the nucleus and in the equatorial plane , while its azimuth angle changes with time.

The Schrodinger model of the hydrogen atom modifies the Bohr model in two ways:

1 No definite values for r, , or can be given, but only the relative probabilities for finding the electron at various locations. This imprecision is, of course, a consequence of the wave nature of the electron.

2 We cannot even think of the electron as moving around the nucleus in any conventional sense since the probability density is independent of time and varies from place to place.