Chapter 11, Problem 20A

Interpretation Introduction

Interpretation:

The success and failure of Bohr’ theory is to be explained

Concept introduction:

Bohr’s theory is applicable only for one-electron atom like hydrogen atom but it does not give any explanation for the multi-electron atom.

Answer to Problem 20A

Success: The Bohr’s theory has been successful in various aspects but the main success is, it gives the valid frequency spectra for hydrogen-like atom.

Failure: This theory was discarded because it fails to explain the spectra for multi-electron atom.

Explanation of Solution

Bohr’s postulates are given as:

1. An electron can occupy only in allowed energy levels.
2. When electrons jump from lower to higher energy levels and from higher to lower energy levels, theenergy is absorbed or emitted in the form of electromagnetic radiation.
3. Electrons are revolving around the nucleus in a circular orbit.
4. An electron’s angular momentum in the orbit is quantized. And linear momentum is an integral multiple of $\frac{\text{h}}{\text{2π}}$ .

  $\begin{array}{c}L=mv{r}_n\\ =n\frac{h}{2\pi }\\ \text{where,}m=\text{mass of the electron}\\ v=\text{velocity of the electron}\\ h=\text{Planck's constant}\\ r_n=\text{radius of the }{n}^{\text{th}}\text{ orbit}\\ n=\text{1,2,3}\mathrm{......}\end{array}$

5. It also gives the valid spectra for one-electron atom such as hydrogen atom.

Failure: Bohr’s theory does not explainthe energy spectra for multiple electron atom.

Conclusion

Bohr’s theory is applicable only for one-electron atom not for multi-electron atom.