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.