Chapter 7, Problem 7A.2E

Interpretation Introduction

Interpretation:

The wavenumber for emitted radiation during transition of hydrogen atom with respect to change in given energy has to be calculated.

Concept Introduction:

Wavenumber is the total number of wavelengths observed at a unit distance. Equation for wavenumber can be given as,

  $\text{Wavenumber, }\overline{\text{ν}}\text{ =}\frac{\text{1}}{\text{λ}}\text{ = }\frac{\text{ν}}{\text{c}}\boxed{\begin{array}{c}\text{here, }\\ \text{λ}\text{=}\text{wavelength}\\ \text{ν}=\text{frequency}\\ \text{c = speed of light}\end{array}}$

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

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