Chapter 28, Problem 2Q

To determine

ToDetermine:

Reasons why Bohr’s theory of atom is not compatible with quantum mechanics, particularly uncertainty principle.

Answer to Problem 2Q

Solution:

In a Bohr atom, the location and momentum of an electron is precisely known, without any error. However, quantum mechanics is based on the Heisenberg Uncertainty Principle, which states that any measurement of momentum or location will always have some error. Hence, these two contradict each other.

Explanation of Solution

The Bohr Atom is a concept that predates Heisenberg Uncertainty Principle.

$△x△p\ge \frac{h}{4\pi }$

It was derived using macroscopic (classical)mechanics, using the laws of circular motion and Coulomb’s Law of electrostatic attraction.

$\begin{array}{l}\frac{m{v}^2}{r}=\frac{1}{4\pi \xi }\frac{Z{e}^2}{r^2}\\ v=u+at\end{array}$

Both equations allow us to know simultaneously the position and momentum of the electron; something ruled out experimentally and by quantum principles.