Question

Calculate the frequency and wave number of radiation with wavelength 480 nm.

Answer 1

Hint: We can calculate all the three quantities that are frequency, wavelength, wave number if any one of them is given. This can be done using the following formula:
Frequency $=\nu ~=~\dfrac{c}{\lambda }$
Wave number $=\dfrac{1}{\lambda }$

Complete step by step answer:
Frequency is defined as the number of occurrences of a repeating event per unit of time. For a wave it is the number of waves occurring per unit of time. It is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event or wave per second.
Wavelength is the distance between identical points (adjacent crests or troughs) in the adjacent cycles of a wave signal propagated in space.
The wave number can be defined as the spatial frequency of a wave, measured in cycles per unit distance or radians per unit distance. Whereas frequency is defined as the number of waves per unit time, wavenumber is the number of waves per unit distance.
$\lambda =480\text{ nm}~=~480\times {{10}^{-9}}\text{m}$ as $1\text{ nm }\!\!~\!\!\text{ }=~{{10}^{-9}}\text{ nm}$
$c~=~3\times {{10}^{8}}m/s$
Frequency, $\nu ~=~\dfrac{c}{\lambda }~=~\dfrac{3\times {{10}^{8}}m/s}{~480\times {{10}^{-9}}m}$
$\nu ~=~6.25\times {{10}^{14}}~Hz$
Wave number, $\dfrac{1}{\lambda }=\dfrac{1}{480\times {{10}^{-9}}}=2.083\times {{10}^{6}}{{m}^{-1}}$

Note:
The energy carried by a single photon is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Energy is given by $E=\dfrac{hc}{\lambda }$where,
E = Energy
H = Planck’s constant
$\lambda $ = wavelength of light