Question

Calculate (a) wavenumber and (b) frequency of yellow radiation having wavelength 5800 Å.

NCERT Class XII
Chemistry - Main Course Book I

Chapter 2. Structure of Atom

Answer 1

Wavenumber of the yellow radiation is $\bold{1.72 \times 10^{6}\ \mathrm{m}^{-1}}$

Frequency of the yellow radiation is $\bold{5.17 \times 10^{14}\ \mathrm{sec}^{-1}}$

Given:  

Wavelength $=5800 \dot{\mathrm{A}}=5800 \times 10^{-10} \mathrm{m}$

Wavenumber $=\frac{1}{\text {wavelength}}$

Hence plug the given values:

Wavenumber $=\frac{1}{5800 \times 10^{-10} m}=1.72 \times 10^{6} m^{-1}$

Frequency $=\frac{C}{\text {wavelength}}$

Here,

C = Speed of light $=3 \times 10^{8}\ \mathrm{m} / \mathrm{sec}$

Plug the given values:

Frequency $=\frac{3 \times 10^{8}\ \mathrm{m} / \mathrm{sec}}{5800 \times 10^{-10}\ \mathrm{m}}$

Frequency $=5.17 \times 10^{14}\ \mathrm{sec}^{-1}$

Answer 2

Answer:

The frequency is $0.05\times10^{16}$ Hz and the Wave Number is $0.017\times10^{8} m^{-1}$.

Explanation:

Wavelength of radiation = $5800\AA$

                                         = $5800\times10^{-10} m$

Frequency =  $\frac{Speed\hspace{0.1cm}of\hspace{0.1cm} light}{Wavelength}$

                   = $\frac{3\times10^{-8}}{ 5800\times10^{-10}}$

                  = $0.05\times10^{16}$ Hz

Wave Number = $\frac{1}{Wavelength}$

                        =  $\frac{1}{5800\times10^{-10} }$

                        = $0.017\times10^{8} m^{-1}$

Hence, the frequency is $0.05\times10^{16}$ Hz and the Wave Number is $0.017\times10^{8} m^{-1}$.

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