Question

If the frequency of an electromagnetic radiation is 9 *
1018 Hz, then the wavenumber of the radiation will be

Answer 1

Given:

Frequency of electromagnetic radiation = 9 × 10¹⁸ Hz

To find:

Wavenumber of the electromagnetic radiation

Solution:

Relation between wavenumber and wavelength is used to calculate wavenumber. As wavenumber is reciprocal of wavelength which is represented as follows,

             $\bar{\nu} = \frac{1}{\lambda}$

Firstly, to calculate wavelength, relation between wavelength and frequency of electromagnetic radiation is used,

                $\nu = \frac{c}{\lambda}$

here, ν = frequency of electromagnetic radiation

         c = speed of light

        λ = wavelength of electromagnetic radiation

Values are given as,

      ν = 9 × 10¹⁸ Hz

      c = 3 × 10⁸ ms⁻¹

so, by putting all the values wavelength can be calculated as,

         $\lambda = \frac{3 \times 10^8 ms^-^1}{9 \times 10^1^8 s^-^1}$

         λ = 0.33 × 10⁻¹⁰ m

        λ = 0.33 × 10⁻¹² cm

Now, wavenumber can be calculated as,

         $\bar{\nu} = \frac{1}{0.33 \times 10^-^1^2 cm}$

         $\bar{\nu}$ = 3.03 × 10¹² cm⁻¹

Therefore, wavenumber of given electromagnetic radiation is 3.03 × 10¹² cm⁻¹.