Question

Yellow light emitted from a sodium lamp has a wavelength(a) of 580nm. Calculate the frequency(v) and wave number(V) of yellow light.

Answer 1

Hint: Yellow light lies in the visible range of the hydrogen spectrum. Write down the information provided in the question. After that apply the formula given below:
$v\text{ = }\dfrac{c}{\lambda }$
$V=\dfrac{1}{\lambda }$
Where,
v is frequency of yellow light
c is speed of light in vacuum
$\lambda $ is wavelength of light emitted
V is wave number for yellow light

Complete step-by-step answer:
We will define the terms wavelength, frequency and wave number and their relation for our understanding and then calculate their values by the values given in question.
Wavelength is the distance between identical points i.e. adjacent crests or troughs in the cycle of a waveform signal propagated along a wire or line in space. The common unit of wavelength used at atomic level is nanometre(nm).
Frequency is the number of occurrences of a repeating event in a unit time interval. It is commonly referred to as temporal frequency as well. The SI unit of frequency of hertz (Hz).
Wavenumber, in physical sciences, is defined as the spatial frequency of the wave. It is commonly measured in cycles per unit distance or radians per unit distance. In simple words wavenumber denotes the number of waves in unit distance.
The relation between frequency, wavelength and wavenumber has already been mentioned in the hint.
$v\text{ = }\dfrac{c}{\lambda }$
$V=\dfrac{1}{\lambda }$
It is given to us that,
$\lambda $ = 580 nm
c = $3\text{ x 1}{{\text{0}}^{8}}\text{ m}{{\text{s}}^{-1}}$
Substituting the values in the equations above,
$v\text{ = }\dfrac{\text{3 x 1}{{\text{0}}^{8}}}{\text{580 x 1}{{\text{0}}^{-9}}}$ = $\text{5}\text{.17 x 1}{{\text{0}}^{14}}\text{ }{{\text{s}}^{-1}}$
$V=\dfrac{1}{580\text{ x 1}{{\text{0}}^{-9}}}$ = $1.72\text{ x 1}{{\text{0}}^{6}}\text{ }{{\text{m}}^{-1}}$

Note: Keep in mind the units while substituting the values in an equation. It is advised to convert the units to their respective standard or SI units to avoid errors and wrong calculations.