Question

Exercise 6:

A) How does the Heisenberg Uncertainty (with momentum and position) force us to abandon a deterministic universe?

B) In what important ways is the Bohr model of the atom incompatible with quantum theory? Include the concept of orbits and what is known about angular momentum.

Answer 1

Part A)

In a deterministic view of the universe, we can predict where a particle will be at any time in the future if we know the following: its initial position, its initial momentum, and the forces acting on it. This allows us to determine the future of the particle. If we have this information for all the particles in the universe, we can determine the future of the entire universe.

The Hisenberg uncertainty principle tells us that a particle can not have a well defined position and momentum at the same time. Thus, we can not know the position and momentum of any particle for the same instance in time. Indeed, a particle does not have a well defined position and momentum at the same time. This forces us to abandon a deterministic view of the universe.

Part B)

According to the Bohr model of an atom, electrons revolve around the nucleus on well defined orbits at perticular distances from the nucleus. Each orbit has an angular momentum associtated with it. Any electron in a perticular orbit will move with the perticular angular momentum associated with the orbit.

According to unertainty principle, a particle does not have a well defined angular position and angular momentum(different version of the generalized uncertainty principle, not the Hisenberg uncertainty principle between position and momentum). This is directly in oppostion to the Bohr model of an atom.

Thus, the Bohr model of an atom is incompatible with quantum theory, as it describes electrons having a perticular angular position and angular momentum at the same time, which is not allowed by quantum theory.