Chapter 11, Problem 17A

Interpretation Introduction

Interpretation:

The Bohr’s theory of hydrogen atom is to be explained.

Concept introduction:

Hydrogen atom is one electron atom.

Answer to Problem 17A

Bohr’s postulates are given as:

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

Explanation of Solution

Bohr’s postulates are given as:

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

Which is given as,

  $\begin{array}{l}{\text{L= mvr}}_{\text{n}}\text{= n}\frac{\text{h}}{\text{2π}}\\ \text{where,}\text{m=}\text{mass}\text{of}\text{the}\text{electron}\\ \text{v=}\text{velocity}\text{of}\text{the}\text{electron}\\ \text{h=}\text{Plank's}\text{constant}\\ {\text{r}}_{\text{n}}\text{=}\text{radius}\text{of}\text{the}{\text{n}}^{\text{th}}\text{orbit}\\ \text{n=}\text{1,2,3}\mathrm{......}\end{array}$

Conclusion

Bohr including the some assumptions of Rutherford’s model and is proposed that the electrons are revolved around the nucleus in discrete energy level and the energy of the orbit is equal to the integral multiple of $\frac{\text{h}}{\text{2π}}$