Chapter 6.3, Problem 4CP

Interpretation Introduction

Interpretation:

The wavelength corresponding to the transition from $n=2\text{ to }n=1$ of an electron in a hydrogen atom is to be calculated.

Concept Introduction:

The wavelength of the radiation emitted is given by the expression as follows:

$\frac{1}{\lambda }=\frac{2.18\times {10}^{-18}\text{ J}}{hc}\left(\frac{1}{n_f{}^2}-\frac{1}{n_i{}^2}\right)$

Here, $\lambda$ is the wavelength, $n_f$ is the final energy level of the electron, $n_i$ is the initial energy level of the electron, $h$ is Planck’s constant, and $c$ is the speed of light.

The relation between meters (m) and nanometers (nm) is expressed as:

$1{\text{nm = 10}}^{-9}\text{m}$.

So, the conversion factor for converting m to nm is $\frac{1\text{ nm}}{{10}^{-9}\text{m}}$