Planck's constant Definition and Symbol

The energy emitted in the form of packets in an irregular way is referred to as photons. The energy of every photon is proportional to the frequency, i.e. E depends on f.

E ∝ f
E = k x h x u….(1)
(k = number of photons, also ‘k’ is an integer)

'h' is referred to as Planck's constant in this context.

What exactly is Planck's Quantum Theory?

Dr. Max Planck, a German physicist, proposed Planck's quantum theory. According to this idea, the energy emitted is not eternal but exists in the form of packets known as quanta. This energy is referred to as the "Quantum of energy." We call a single packet quanta, where it is an integer number, as opposed to the continuous supply of energy, which has different values.

Packets are energy units that are referred to as Quanta, but photons are used for packets for the visible light.

Consider the following equation:
E = h x c/λ….(2)
h = 6.626 x 10⁻³⁴

c = 3 x 10⁸ m/s

Place this value in equation 2

(6.626 x 10⁻³⁴) x (3 x 10⁸)/λ

(19.878 x 10⁻²⁶)/λ ∽ (2 x 10²⁵)/λ

We get,

M = (2 x 10²⁵)/λ

This presents the value for a single photon's energy, and for 'k' photons, it is:

E = (k x 2 x 10²⁵)/λ

Only when the wavelength, is supplied in meters, is the value of E computed. It is supplied in another unit, say Angstrom, we can easily convert 1 Angstrom to meters (1 Angstrom = 10⁻¹⁰m).

Where

h = Planck's constant

h = h = Energy of quantum of an electromagnetic radiation divided by frequency

In the SI system, Planck's constant 'h' is measured in Joule-seconds.

h = 6.626 x 10⁻³⁴

In the M.K.S system, Electronvolt or (eV): 1 eV = 1.6 x 10⁻¹⁹ Joule

E = (12400/λ) eV for λ in Å

E = (1240/λ) eV for λ in nm

Value for λ when E = 4.13 V

E = 12400/λ

4.13 = 12400/λ

λ = 12400/4.13 = 3000 Å

What's the Big Deal About Planck's Constant?

A black body is a perfect physical body that absorbs all electromagnetic radiation. When heated, light is reflected that falls on it, but with different quantities of wavelengths.

In the above graph, it can be seen that the shorter the wavelength, the less wave emission there is, and then there comes a point when we obtain the maximum wavelength, Vmax, which signifies maximum emission. The visible light is represented by the Vmax, which is seen as a peak in the above graph.

What occurs here is that as we travel farther, the wavelength increases while the emission of waves decreases. As we go further, we observe that the emission of waves is minimal but not zero. (All wavelengths, regardless of quantity or frequency, are radiated. But, based on the theoretical reasoning, you must have seen in the curve that the graph is symmetric from the beginning to the point where the wavelength is highest, but what happens beyond that? Even when the wavelength is small, the emission of waves is maximal. When the wavelength is reduced, there is a significant change. Dr. Max Planck, a prominent German physicist, proposed the adjustment to the above principle. Where he saw light as a 'k' number of pieces or packets called photons by the relation.

E = k x h x f
k = number of photons
After his experiments, the theoretical and practical curves that were not symmetrical to each other became symmetrical, implying that Dr. Planck's hypothesis was true.

When an iron rod gets heated up, photons of every wavelength are produced, but only the light of (Vmax) maximum wavelength can be seen by the human eye. We can measure the temperature of twinkling stars by measuring the maximum amount of light emitted.