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

By BYJU'S Exam Prep

Updated on: September 25th, 2023

(a) 1.724 x 104 cm-1 and 5.172 x 1012 s-1

(b) 1.724 x 104 cm-1 and 5.172 x 1014 s-1

(c) 1.724 x 1012 cm-1 and 5.172 x 104 s-1

(d) 1.724 x 1012 cm-1 and 5.172 x 102 s-1

The wavenumber and frequency of yellow radiation having wavelength 5800 Å are 1.724 x 104 cm-1 and 5.172 x 1014 s-1. Steps to Calculate wavenumber and frequency

Step 1:

v̂ = 1/λ and v = c/λ

Now, for the calculation of wave number (v̂)

λ = 5800 Å = 5800 x 10-8 cm

= 5800 x 10-10 m

Step 2:

v̂ = 1/λ = 1/ (5800 x 10-10m)

= 1.724 x 106 m-1

= 1.724 x 104 cm-1

Calculating the frequency(v)

Step 3:

v = c/λ = 3 x 108 ms-1/ 5800 x 10-10 m

= 5.172 x 1014 s-1

A wave’s spatial frequency, measured in cycles per unit distance or radians per unit distance, is how a wave number is defined. In multidimensional systems, the wave vector’s magnitude is measured by the wavenumber. It is a scalar quantity, wavenumber.

### Applications of a Wavenumber

1. The spatial frequency is calculated from a wavenumber.
2. In X-ray diffraction, neutron diffraction, electron diffraction, and basic particle physics, wavenumbers and wave vectors are essential.
3. Wavenumber can also be used to define other concepts, such as optics and wave scatterings in physics, in addition to spatial frequency.
4. A wavenumber can be used to define the canonical momentum of quantum mechanical waves, which is the wavenumber multiplied by the decreased Planck’s constant Group velocity.

Summary:

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

The wavenumber and frequency of yellow radiation having wavelength 5800 Å are 1.724 x 104 cm-1 and 5.172 x 1014 s-1. Wavenumber is the spatial frequency of a wave which is measured in radians per unit distance or cycles per unit distance.

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