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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
Table of content
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
- The spatial frequency is calculated from a wavenumber.
- In X-ray diffraction, neutron diffraction, electron diffraction, and basic particle physics, wavenumbers and wave vectors are essential.
- Wavenumber can also be used to define other concepts, such as optics and wave scatterings in physics, in addition to spatial frequency.
- 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.