Question

What are the draw backs of Bohrs atomic model? Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

Answer 1

1. Bohr treated electrons as particles where according to de Broglie's hypothesis, having a very low mass, electron also exhibits wave nature.

2. Bohr's model was acceptable only for nucleus having only one electron e.g. Hydrogen, $H{e}^{+1}$, $L{i}^{+2}$ etc. Bohr's model could not explain the spectra of multi-electronic atoms.

3. Bohr's model was two-dimensional where an atom is three-dimensional.

4. Bohr's model could not explain the effect electric field and magnetic field on spectra. (Stark effect and Zeeman effect)

5. Using a better spectrometer, the spectra showed very fine lines. Bohr's model could not explain the origin of those fine lines.

For angular momentum of an electron

$mvr=\frac{nh}{2\Pi }\to \left(1\right)$

then debroglie equation,

$\lambda =\frac{h}{mv}$

$mv=\frac{h}{v}\to \left(2\right)$

Putting the value of 1 and 2

$2\Pi r=n\left(\frac{h}{mv}\right)2\Pi r=n\lambda hence,2\Pi rrepresentshere,circumferenceoftheBohrorbit\left(r\right)$\\