Chapter 7, Problem 7C.3E

Interpretation Introduction

Interpretation:

The length of $\text{1D}$ box in which an electron takes wavelength of $\text{1}\text{.10}\text{μm}$ in order to excite from lowest level to first excited level has to be calculated.

Concept Introduction:

The energy equation for $1D$ is as follows,

$E_n=\frac{n^2{h}^2}{8m{L}^2}\boxed{\begin{array}{l}here,h=Planck\text{'}s\text{constant}\\ m=mass\\ L=\text{length}\\ n=1,2,3,\mathrm{..}\end{array}}$

The Planck’s equation says that radiant energy can exist only in form of discrete quanta and hence it is proportional to the frequency.

$\text{E}\text{=}\text{hν}\boxed{\begin{array}{c}\text{here,}\text{h = Planck’s constant }\left(\text{6}\text{.626}\times {\text{10}}^{\text{-34}}\text{J}\text{.s}\right)\text{which relates energy and frequency}\text{.}\\ \text{ν}\text{= the frequency}\\ \text{E = energy of light particle}\text{.}\end{array}}$