**Question**

Show that the uncertainty relation forces us to reject the semi classical Bohr model for the hydrogen atom

**Solution**

In Bohr atom model we deal with the electron as a classical particle. The allowed orbits are defined by the quantization rules:

The radius r of a circular orbit and the momentum of the rotating electron must satisfy . To consider an electron’s model in classical terms , the uncertainties in its position and momentum must be negligible when compared to and . In other words and

This implies

(1)

On the other hand , the uncertainty relation imposes

(2)

So, equation 1 is incompatible with 2 , unless