 # Planck’s Constant

What is Planck’s Constant?

The energy that is released in the form of packets or chunks in a discontinuous manner are known as Photons where the energy of each photon is directly proportional to the frequency i.e. E and depends upon f.

E  ∝  f ,   E = k x  h x u….(1)   (k is no of photons, and is an integer)

Here, ‘h’  is called the Planck’s constant.

• Planck’s constant

• Value of planck’s constant

• Deriving Planck’s constant formula in both MKS and CGS unit

• Planck’s constant units and dimensional formula

• Planck’s constant symbol

• Applications of Planck’s constant with examples

• Illustrative examples to understand the basics of this topic.

What Planck’s Quantum Theory is all about?

A German theoretical physicist, Dr. Max Planck had put forth a theory known as Planck’s quantum theory. This theory states: Energy radiated or enwrapped is not perpetual, but in the form of packets called quanta. This energy is known as “Quantum of energy.” For a single packet, we call it quanta, where quanta is an integer value, unlike continuous energy supply which has varying values: 1 or 1.1 or 1.2.

Packets are units of energy and they are called Quanta in general terms whereas Photons is a term used for packets in terms of visible light.

Consider this equation:

E = h x c / λ….(2)

h = 6.626 x 10^ - 34

c = 3 x 10 ^ 8 m/s

Put this value in the above equation(2)

6.626 x 10 ^ - 34 * 3 x 10 ^ 8 /λ

19.878 x 10 ^ -26 /   ∽   2 x 10 ^ 25 /λ

We get,

M = 2 x 10 ^ 25 /λ

This is the value for energy of a single photon, and for ‘k’ no of photons, it would be:

 E = k x 2 x 10 ^ 25 /λ

The value of E is calculated only when wavelength, λ is given in meters. If λ is given in any other unit let’s say in Angstrom, simply, we can convert 1 Angstrom to meters (1 Angstrom = 10 ^ -10 m) where h is the Planck’s constant, and h = Energy of a quantum of electromagnetic radiation divided by its frequency.

Planck’s constant ‘h’  is measured in Joule-seconds in the SI system.

h  = 6.626 x 10 ^ - 34

and Electronvolt or (eV) in the M.K.S system.

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 so Special about Planck’s Constant?

A blackbody is an idealized physical body, which assimilates all the electromagnetic radiation. Upon heating, it reflects the light falling on it, but that too of varying amounts of wavelengths.

Here in this graph, we can observe that less is the wavelength, lesser is the emission of waves, then a time comes when we get the maximum wavelength, Vmax, which means maximum emission.

The Vmax is the position shown as a peak in the graph is the visible light.

What happens here is when we go further, the wavelength keeps on increasing, but the emission of waves keeps on decreasing and continues further, we see that the emission of waves is negligible, but not zero. (All the wavelengths of whatever amount and irrespective of frequencies are radiated).

But from theoretical derivation, you must have observed in the curve that from the starting till the point when the wavelength is maximum, the graph shows symmetry, but what happens thereafter? The emission of waves is maximum even when the wavelength is less.

There’s a lot of difference when the wavelength is less. The modification in the above concept was brought up by a great German theoretical physicist, named Dr. Max Planck.

Where he considered light as a form of ‘k’ no of chunks or packets called photons by the relation.

 E = k x h x f, k being the no of photons.

After his experimentation, the experimental and theoretical curves which were not symmetrical to each other, got into symmetry infers that the theory given by Dr. Planck was correct.

Summary

• When an iron rod is heated, lights of all wavelengths are emitted, but a human eye can perceive only that light which is of maximum wavelength Vmax.

• We estimate the temperature of stars by observing the Vmax of the light emitted.

Q1: Why is Light Called an Electromagnetic Wave?

Ans: Light is formed by the combination of the Magnetic and Electric field, and these two fields are perpendicular to each other, which means these two waves are oscillating in a direction perpendicular to each other and the wave is propagating in the direction perpendicular to these two fields.

Q2: Derive the Dimensional Formula for Planck’s Constant ‘h’.

Ans: Dimensional formula for h

Since  h  =  E / f

E  = [M L ^ 2 T ^ -2]

f= [M ^ 0 L ^0 T ^ -1]

h  = [M L ^ 2 T ^ -2] / [ M^0  L^ 0 T ^ -1]

[M L ^ 2 T ^ -1]

Q3: Calculate the Ratio of Energies of Two Sources which Emit Light of Wavelength 4000 and 5000 Å to show the Relation of Energy (E) is Inversely Proportional to the Wavelength (λ).

Ans:  E1 = h x v / λ1  …..(1)

E2 = h x v /λ2 ….(2)

eq (1) / eq (2)

We get:  E1 / E2 = λ2 / λ1 =  4000/ 5000 = 4/5 = 4: 5

We conclude that more is the energy, lesser is the wavelength and vice-versa.

Q4: A Light Source of λ = 3000 Å Emits 0.6 J of Energy. Calculate the Number of Photons.

Ans: Given E = 0.6 J, λ  = 3000 Å ... (1)

We know that  E = k x h x c/ λ  = k x 2 x 10 ^ -25/ v

Now putting the values in eq(1)

0.6 = k x 2 x 10 ^ -25 / 3000 x 10 ^ - 10

k = 3000 x 0.6 x 10 ^ - 10 / 2 x 10 ^ - 25

k=  900 x 10 ^ 15 = 9 x 10 ^ 17 photons