# Planck's Equation

### What is Planck’s Equation?

Max Planck discovered a theory that energy is transferred in the form of chunks called as quanta, assigning as h. The variable h holds the constant value equal to 6.63 x 10-34 J.s based on International System of Units and the variable describes the frequency in s-1. The Planck’s law help us calculate the energy of photons when their frequency is known.

If the wavelength is known, you can calculate the energy by using the wave equation to calculate the frequency and then apply Planck’s equation to find the energy.

What is Planck’s Constant?

Put differently, Plank’s constant describes the relevancy between the energy per quantum (photon) of electromagnetic radiation to its frequency.

#### Solved Example:

A Green light has a wavelength of 525 nm. Determine the energy for the green light in joules.

#### Solution:

To find the Frequency;

As we know that, $c=\lambda \times v$,

$v=\frac{3 \times 10^{8}}{525}$

Hence, $v = 5.71 \times 10^{14}/s$

To find the Energy;

As we know that $E = h \times \nu$

= $(6.626 \times 10^{-34 })\times (5.71 \times 10^{14})$

= $3.78 \times 10^{-19} J/photon$

### Planck’s Law:

It states that electromagnetic radiation from heated bodies is not emitted as a continuous flow but is made up of discrete units or quanta of energy, the size of which involve a fundamental physical constant (Planck’s constant).

Mathematically,

$B_{\lambda }(T)=\frac{2hc^{2}}{\lambda ^{5}}\frac{1}{e^{\frac{hc}{kT\lambda }}-1}$

Where,

h = Planck’s Constant = $6.62\times 10^{-34}Js$

k = Boltzmann’s Constant = 1.381 × 10-23 J/K

Stay tuned to BYJU’S to know more about Planck’s law and Planck’s quantum theory along with worked problems and solutions.

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