Question

What is the wavelength of violet light with a frequency of $750 \times {10^{12}}Hz$?

Answer 1

Hint: Wavelength and frequency are inversely proportional to each other. There relation is given be $\nu = \dfrac{c}{\lambda }$ where $\nu $ is the frequency of the light, $\lambda $ is the wavelength of the light, and $c$ is the speed of light whose value is given as$c = 3 \times {10^8}m{s^{ - 1}}$. Lower wavelength corresponds to maximum energy as well as maximum frequency.

Complete answer:
According to Planck’s theory light behaves as a particle. His theory says that different atoms and molecules can emit or absorb energy in discrete quantities only. The smallest amount of energy that can be emitted or absorbed in the form of electromagnetic radiation is known as quantum. The light particles are called photons. Planck explained the distribution of intensity of the radiation from the black body as a function of frequency or wavelength at different temperatures.
 The energy associated with each photon with frequency each photon with frequency $\nu $ is given by,
$E = h\nu = \dfrac{{hc}}{\lambda }$
Because $\nu = \dfrac{c}{\lambda }$
Where, E is the energy of a photon or quantum, $\nu $ is the frequency of emitted radiation.
In the question we are given the frequency of $750 \times {10^{12}}Hz$ and we have to find out the wavelength. We can use the equation of relation between frequency, wavelength and speed of light (In vacuum) c, given as:
$\nu = \dfrac{c}{\lambda }$
Where the value of speed of light is given as $c = 3 \times {10^8}m{s^{ - 1}}$
By rearranging the formula it becomes:
$\lambda = \dfrac{{3 \times {{10}^8}}}{{750 \times {{10}^{12}}}}$
$ \Rightarrow \lambda = \dfrac{{3 \times {{10}^8}}}{{750 \times {{10}^{12}}}}$
$ \Rightarrow \lambda = 4 \times {10^{ - 7}}m$
Therefore the wavelength of the violet light is $4 \times {10^{ - 7}}m$

Note:
Planck’s quantum theory was proposed by Max Planck. He gave this theory to explain emission and absorption of radiation. It also explains the photoelectric effect. An ideal body which can emit and absorb radiation of all frequencies is called a black body. The radiation emitted by such bodies is called black body radiation.