Planck's Constant

Planck's Constant is one of the smallest constants used in physics. It is a fundamental constant in quantum mechanics which relates the energy of a photon to its frequency. Planck constant stands as one of the most elegant and pivotal values in the realm of physics, where constants shape the very essence of this physical world.

Further in this article, we will learn about its definition, who Max Planck was, explore methods for calculating its value in various units, its formula, dimension, and unit. We will look into what's a Reduced Planck Constant and discuss the application of Planck's constant across various scientific disciplines.

👁 Planck's-Constant

What is Planck Constant?

Planck's constant, symbolized as ℎ, is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency, now known as the Planck-Einstein relation:

E = ℎf

Where,

• E represents the energy of the light,
• f is the frequency of the light, and
• ℎ is referred to as the Planck constant.

Planck Constant tells us that energy exchanged at the quantum level occurs in some specific amount, known as quanta. The Planck's constant says how much of that energy is in these quanta. One quanta is defined by the value of the Planck's Constant value (we will learn about this value later in this article.)

Discovery of Planck Constant

German physicist Max Planck introduced the constant in 1900 when he was working on a formula to describe the distribution of radiation emitted by a blackbody, also known as blackbody radiation. This constant, now known as Planck's constant, was crucial in resolving a problem known as the ultraviolet catastrophe, a point where classical physics failed to explain the observed physics.

Who is Max Planck?

Max Planck was a German physicist who pioneered the field of quantum theory. Planck's most famous contribution was quantization of energy packets, which gave birth to the revolutionary idea that energy is not emitted or absorbed continuously but in discrete quantities. This constant came to be known as Planck's constant and is now denoted by the symbol 'ℎ'.

Value of Planck's Constant

Planck's constant, symbolized as ℎ, is a fundamental universal constant. From the data, its value is calculated and it came to be

6.62607015 × 10⁻³⁴ Joule seconds

Value of Planck's Constant in eV

Its value when calculated in terms of electron volts (eV) is very useful for quantum level calculations.

4.135667696 × 10⁻¹⁵ eV seconds

Planck Constant Formula

Its value can be easily calculated by putting values in the Planck-Einstein relation for the Photoelectric effect energy:

E = ℎf

Where E is the energy of the light, and f is the known frequency of the light.

Unit of Planck Constant

Planck's constant is a very small value can be written in two formats:

Planck Constant = 6.62607015 × 10⁻³⁴ Joule seconds

Here, 10^-34 is a very small value, which is 1 in its 34^th digit.

Planck Constant = 4.135667696 × 10⁻¹⁵ eV seconds

Here, 10^-15 is a slightly larger but equivalently smaller quantity, which is 1 in its 15^th digit.

Planck Constant Dimensions Formula

Dimension of Planck Constant is [ML²T^-1]

Experimental Determination of Planck's Constant

Experimental determination of Planck's constant is done by the photoelectric effect. In this experiment, the energy of the electron emitted from a metal surface is precisely measured when light strikes it.

Also measuring the frequency of the incident light, a direct relationship can be found between the energy of the photons and the frequency of the light, that's Planck's constant. Accuracy of these experiments perfectly validate Max Planck's theory, and in turns strengthening our understanding of the quantum world.

Reduced Planck Constant

Frequency is measured using hertz. A 360° cycle or one full Bohr introduced the quantity ℏ = ℎ/2π , Its value is 1.054571817×10⁻³⁴ joule seconds, known as the reduced Planck constant, represents the quantum of angular momentum and more commonly used in modern physics.

Application of Planck’s Constant Different Fields

Planck's constant plays a unique and foundational role across various scientific fields. Here's a few perspectives that highlights its distinct and direct contributions:

In Quantum Mechanics, Planck's constant (ℎ) acts as a bridge between the macroscopic and microscopic worlds, defining the granularity of energy at the quantum level. It's the fundamental quantum unit that underpins numerous phenomena, making it unparalleled in its significance.

Planck's Constant in Different Fields

There are various uses of Planck's Costant in different fields of physics, some of these applicationa are listed as follows:

• Black Body Radiation

Formula for spectral radiance B(v, T) is revolutionary, describing how objects emit light at different temperatures, and it is given by,

B(v, T) = 2ℎv³⁄c² × 1 ⁄[e^ℎv/KT -1]

• Photoelectric Effect

Planck-Einstein relation revolutionized our understanding of light's interaction with matter, and it is given by,

E = ℎf

• Atomic Structure

Within atomic models, Planck's constant appears in equations describing the energy levels of electrons in orbits around the nucleus, and it is given by,

E_n = -ℎc₀R_∞ ⁄ n²

• Uncertainty Principle

The uncertainty principle embodies a fundamental limitation in measuring both the position and momentum of a particle simultaneously, and it is given by,

ΔxΔp ≥ ℏ⁄ 2

• Matter-Wave Duality

The de Broglie wavelength equation relates a particle's momentum to its associated wavelength, and it is given by,

λ= ℎ⁄p

Read More,

• Planck's Quantum Formula
• Dual Nature of Light
• Dimensional Formula of Planck's Constant