Planck’s Equation

Planck’s Equation

Planck’s constant is a number, it describes the size of the energy packets that are contained within light. These packets of energy are called photons. Planck’s constant is given the symbol h and the value of h is equal to 6.63 x 10-34⁻³⁴ J\se.

What is Planck’s Equation?

While Planck’s constant can now be found in many equations, the equation that defines Planck’s constant is called the Planck-Einstein relation. Max Planck theorized that energy was transferred in chunks is known as quanta, equal to hυ. The variable h is a constant equal to 6.63 x 10-34⁻³⁴ J\sec based on International system of units and the variable υ represents the frequency in Hz. This equation allows us to calculate the energy of photons, given their frequency.

E = hυ

H = Plank’s Constant = 6.63 x 10-34⁻³⁴ J\sec = 4.136 x 10⁻¹⁵ eV.

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

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.

\({{B}_{\lambda }}(T)\,\,=\,\,\frac{2h{{c}^{2}}}{{{\lambda }^{5}}}\,\,-\,\,\frac{1}{{{e}^{\frac{hc}{kT\lambda }\,\,-\,\,1}}}\)

Problem: A Green light has a wavelength of 500nm. Determine the energy for the Green light in Joules?

Solution: Given,

Wavelength (λ) = 500 nm

Speed (c) = 3 x 10⁸ m/sec

We know that:

Speed (c) = Wavelength (λ) x Frequency (υ)

\(\Rightarrow \,\,Frequency(\upsilon )\,=\,\frac{Speed(c)}{Wavelength(\lambda )}\,=\,\frac{3\times {{10}^{8}}}{500\times {{10}^{9}}}=\,0.6\times {{10}^{-3}}/\sec \)

∴ Frequency (υ) = 0.6 x 10⁻³/ sec.

Now, to find the Energy:

E = h x υ

E = (6.626 x 10⁻³⁴) x (0.6 x 10⁻³)

∴ E = 3.98 x 10⁻³⁸ J/ Photon.