Chapter 11, Problem 15A

Interpretation Introduction

Interpretation:

The experiment which tells about the quantization of energy levels of hydrogen atom need to be explained.

Concept introduction:

Niels Bohr was the first scientist who proves that the orbits of electrons in atom are quantized.

He proposed that the linear momentum of the electron in its orbit is quantized. It has only discrete energy levels.

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

Answer to Problem 15A

Niels Bohr proposed a model of the atom in which he tells that the orbits in which electrons are revolves are quantized. The energy carried apart from an atom by a photon comes from the electron releasing from one allowed orbit to another and is thus quantized.

Explanation of Solution

Bohr proposed that the circular orbits of electrons are quantized. The amount of emitted energy and absorb energy is also quantized due to quantization of orbit and produced discrete spectra. Each orbit has distinct amount of energy.

When electrons are jump from higher to lower energy level or lower to higher energy level then they emits or absorb the photon respectively. So, the energy of photons is also quantized.

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 revolve around the nucleus in circular orbit.
4. An electron’s angular momentum in the orbit is quantized. And linear momentum is integral multiple of $\frac{\text{h}}{\text{2π}}$

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

Conclusion

Niels Bohr’s model of one electron atom like hydrogen atom is the experiment which gives the concept of quantized energy levels.