Chapter 7, Problem 7.31QP

Interpretation Introduction

Interpretation:

The wavelength of emitted light when an electron from hydrogen atom transit from ${\text{n}}_{\text{i}}\text{=}5\text{to}{\text{n}}_{\text{f}}\text{=}3$ has to be calculated.

Concept introduction:

Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion.  By using this he derived a formula for energy levels of electron in H-atom.

$\begin{array}{l}\text{E}\text{=}\frac{{\text{-R}}_{\text{H}}}{{\text{n}}^{\text{2}}}\text{n}\text{=}\text{1,2,3,}\mathrm{......}\text{(For}\text{hydrogen}\text{atom)}\\ \\ {\text{R}}_{\text{H}}\text{is}\text{Rydberg}\text{constant}\text{(2}\text{.179}\text{×}{\text{10}}^{\text{-18}}\text{J)}\text{.}\\ \\ \text{Eis}\text{energy}\text{level}\text{.}\\ \\ \text{n}\text{is}\text{principal}\text{quantum}\text{number}\text{.}\end{array}$

Relation between frequency and wavelength is,

$\text{C}\text{=}\text{λν}$

Where,

C is the speed of light.

$\text{ν}$ is the frequency.

$\text{λ}$ is wavelength.