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What is Planck's constant: Units, Usage, Significance of Plank Constant

What is Planck's constant

Planck's constant is the fundamental constant in modern physics. It relates the energy of a photon to its frequency. To determine this constant we can use Light Emitting Diodes (LED) also. Diodes today come in a variety of colors. Each color is achieved by having a slightly different semiconductor material. We can choose a number of LEDs, with different colors including Blue, Green, Red and Orange.

The experiment is based on the fact that the energy of the photon relates to its frequency as:

E = h x f

Where, E is the energy of photon, h is the Planck’s constant and f is the frequency of the emitted photons. When the diode first emits light the voltage across the diode, V0, is just enough to give energy to electrons to jump between two energy levels.

Therefore, Vo.e = h x f

Where, e is the electron charge and V0 is the threshold voltage. Therefore by measuring the voltage across the diode when the first light is observed for a number of diodes, the relation between the maximum wavelength, λ, and the turn on voltage, V0, is

E = hf = hc/λ....................(1)

E = eVo.............................(2)

From (1) and (2) we get,

hc/λ = eVo

or h = eVoλ/c...................(3)

h is Planck’s constant,
e is the electronic charge,
V0 is Threshold voltage,
λ is wavelength of LED and
c is the velocity of light

Usages of Planck's constant

The Planck constant is used to describe quantization. For instance, the energy (E) carried by a beam of light with constant frequency (v) can only take on the values

E = nhv, n ∈ N

It is sometimes more convenient to use the angular frequency ω = 2πv, which gives

E = nhw, n∈ N

Many such "quantization conditions" exist. A particularly interesting condition governs the quantization of angular momentum. Let J be the total angular momentum of a system with rotational invariance, and Jz the angular momentum measured along any given direction. These quantities can only take on the values

J2 = j(j+1)h2, j = 0, 1/2, 3/2, .......

Jz= m ћ, m= -j,-j+1,…………,j

Thus, ћ may be said to be the "quantum of angular momentum".

The Planck constant also occurs in statements of Heisenberg's uncertainty principle. Given a large number of particles prepared in the same state, the uncertainty in their position, Δx, and the uncertainty in their momentum (in the same direction), Δp obey

∆x ∆p <= h/2

Where the uncertainty is given as the standard deviation of the measured value from its expected value, There are a number of other such pairs of physically measurable values which obey a similar rule.

Dirac constant

The Dirac co stant or the "reduced Planck constant", h = h/2π, differs only from the Planck constant by a factor of 2π. The Planck constant is stated in SI units of measurement, joules per hertz, or joules per (cycle per second), while the Dirac constant is the same value stated in joules per (radian per second).

In essence, the Dirac constant is a conversion factor between phase (in radians) and action (in joule-seconds) as seen in the Schrödinger equation. The Planck constant is similarly a conversion factor between phase (in cycles) and action. All other uses of Planck's constant and Dirac's constant follow from that relationship

Significance of the size of Planck's constant

Expressed in the SI units of joule seconds (J·s), the Planck constant is one of the smallest constants used in physics. The significance of this is that it reflects the extremely small scales at which quantum mechanical effects are observed, and hence why we are not familiar with quantum physics in our everyday lives in the way that we are with classical physics. Indeed, classical physics can essentially be defined as the limit of quantum mechanics as the Planck constant tends to zero.

In natural units, the Dirac constant is taken as 1 (i.e., the Planck constant is 2π), as is convenient for describing physics at the atomic scale dominated by quantum effects.

Experiment of Plank's Constant

Check the experiment of Determination of Planck's constant using Photo Vacuum Tube