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Value of Planck's Constant

Value of Planck's Constant

Team Careers360Updated on 02 Jul 2025, 05:08 PM IST

The Planck's constant, often known as Planck's constant, is a fundamental physical constant in quantum physics that is symbolized by the letter h. A photon's energy is calculated by multiplying its frequency by the Planck's constant. The Planck's constant also connects mass to frequency due to mass-energy equivalence.
At the end of the nineteenth century, precise measurements of the spectrum of black body radiation were available, but estimates of the frequency distribution of the radiation based on current theories deviated significantly at higher frequencies. Max Planck developed an empirical formula for the observed spectrum in 1900. He thought that an electrically charged oscillator in a cavity filled with black-body radiation could only modify its energy by a little amount, E, proportional to the frequency of the accompanying electromagnetic wave.

This Story also Contains

  1. What is Planck's constant?
  2. Value of Plank’s Constant
  3. Application of Planck's constant

From the experimental observations, he was able to derive the proportionality constant, which is now named after him. Albert Einstein discovered a "quantum" or minimum constituent of the electromagnetic wave's energy in 1905. The photon was named after the light quantum, which behaved in some ways like an electrically neutral particle. "In acknowledgement of the contributions he contributed to the advancement of Physics by his discovery of energy quanta," Max Planck was awarded the Nobel Prize in Physics in 1918.

Max Planck's successful effort to construct a mathematical expression that precisely anticipated the observed spectrum distribution of thermal radiation from a closed furnace resulted in the formulation of Planck's constant (black-body radiation). Planck's law is the name given to this mathematical equation.

NCERT Solution

What is Planck's constant?

Planck's constant is the physical constant in quantum electromagnetism that connects the energy carried by a single photon to its associated frequency. In the SI system, it is represented by h, and it is measured using J.s, and in the MKS system, it is measured using eV.s. In quantum physics, the value of Planck's constant is extremely important.

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What is the significance of Planck's Quantum Theory?

Dr. Max Planck, a German theoretical physicist, proposed a theory known as Planck's quantum theory. According to this idea, energy is emitted or enwrapped in quanta, not in a continuous state. "Quantum of energy" is the name given to this type of energy. We call it quanta for a single packet, where a quantum is an integer value, as opposed to continuous energy supply, which has to change values: 1, 1.1, or 1.2...

Packets are energy units that are referred to as Quanta in general, whereas Photons refer to packets in terms of visible light.

Consider the following equation:

E = h x c/λ…. (2)

h = 6.626 x 10⁻³⁴

c = 3 x 10⁸ m/s

Now put the values in the above equation (2)

E=(6.626 x 10⁻³⁴) * (3 x 10⁸)/λ

=(19.878 x 10⁻²⁶)/λ ∽ (2 x 10-²⁵)/λ

We get,

E = (2 x 10-²⁵)/λ

This is the value for a single photon's energy, and for a group of k photons, it would be:

E = (k x 2 x 10²⁵)/λ

Only when the wavelength is supplied in meters is the value of E calculated. It is supplied in a different unit, such as Angstrom, we can easily convert 1 Angstrom to meters (1 Angstrom = 10^-10m), where h is the Planck's constant.

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Commonly Asked Questions

Q: How was Planck's constant discovered?
A:
Planck's constant was discovered by Max Planck in 1900 while studying black body radiation. He found that energy could only be emitted or absorbed in discrete packets, which he called "quanta." This discovery led to the development of quantum theory and revolutionized our understanding of the microscopic world.
Q: What is the reduced Planck's constant, and how does it differ from the regular Planck's constant?
A:
The reduced Planck's constant, denoted by ħ (h-bar), is equal to Planck's constant divided by 2π. It is often used in quantum mechanics equations to simplify calculations. While h is measured in joule-seconds, ħ is measured in joule-seconds per radian.
Q: Why is Planck's constant so small?
A:
Planck's constant is extremely small because it describes phenomena at the atomic and subatomic scales. Its small value explains why quantum effects are not noticeable in our everyday macroscopic world but become significant at very small scales.
Q: Can Planck's constant change over time?
A:
Current scientific evidence suggests that Planck's constant is truly constant and does not change over time. However, some theories propose that fundamental constants might vary over extremely long cosmological timescales, but this has not been observed for Planck's constant.
Q: How does Planck's constant relate to the de Broglie wavelength?
A:
The de Broglie wavelength, which describes the wave-like nature of particles, is calculated using Planck's constant. The formula λ = h/p, where λ is the wavelength and p is the momentum, shows how Planck's constant connects particle properties (momentum) to wave properties (wavelength).

Value of Plank’s Constant

The Planck's constant has angular momentum dimensions. The Planck constant is measured in joules per hertz. In mathematics and science, an angular frequency in radians per second is typically more intuitive, therefore many calculations utilize a lower Planck constant (pronounced h-bar).

Value of h = 6.62607015×10-34 J/Hz

What Makes Planck's constant so Unique?

A blackbody is a hypothetical physical body that absorbs all electromagnetic radiation. It reflects the light that falls on it when heated, but only of various wavelengths.

From the theoretical reasoning, you must have noticed in the curve that the graph is symmetric from the beginning to the point where the wavelength is maximum, but what happens beyond that? Even though the wavelength is shorter, the emission of waves is at its peak.

When the wavelength is shorter, there is a significant difference. Dr. Max Planck, a prominent German theoretical physicist, proposed the adjustment to the above principle.

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Application of Planck's constant

Planck's equation, for example, uses the Planck's constant value. The product of Planck's constant h and frequency, for example, gives the energy associated with a photon.

  1. The spectral radiance of a body in black body radiation.
  2. The classic Planck Einstein relation in the photoelectric effect.
  3. The energy of the nth orbit in atomic structure.
  4. The relationship between location and momentum in the uncertainty principle.
  5. The de Broglie wavelength is calculated using the matter-wave equation.

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NCERT Notes

Commonly Asked Questions

Q: What is Planck's constant and why is it important in quantum physics?
A:
Planck's constant, denoted by h, is a fundamental physical constant that relates the energy of a photon to its frequency. It is crucial in quantum physics because it describes the quantization of energy at the atomic and subatomic levels. Planck's constant helps explain phenomena like the photoelectric effect and atomic spectra, which cannot be explained by classical physics.
Q: How does Planck's constant relate to the wave-particle duality of light?
A:
Planck's constant is central to the wave-particle duality of light. It appears in the equation E = hf, where E is the energy of a photon and f is its frequency. This equation shows that light behaves both as a wave (with a frequency) and as a particle (with discrete energy packets).
Q: What is the relationship between Planck's constant and the uncertainty principle?
A:
Planck's constant is a key component of Heisenberg's uncertainty principle. The principle states that the product of the uncertainties in position and momentum of a particle must be greater than or equal to h/4π. This fundamental limit on precision in quantum mechanics is directly related to the value of Planck's constant.
Q: How does Planck's constant affect the energy levels in atoms?
A:
Planck's constant determines the discrete energy levels in atoms. The allowed energy states of an electron in an atom are quantized, with the energy differences between levels being multiples of Planck's constant times the frequency of the associated electromagnetic radiation.
Q: How is Planck's constant used in calculating the energy of a photon?
A:
The energy of a photon is calculated using the equation E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. This equation directly links the particle-like property of energy to the wave-like property of frequency.

Frequently Asked Questions (FAQs)

Q: What is the significance of Planck's constant in the study of quantum cryptography?
A:
In quantum cryptography, Planck's constant underlies the security of protocols like quantum key distribution. The impossibility of perfectly measuring both the polarization and phase of a photon, a consequence of the uncertainty principle involving Planck's constant, ensures the security of information transmitted using quantum states.
Q: What is the relationship between Planck's constant and the quantization of magnetic flux?
A:
Magnetic flux in superconducting loops is quantized in units of the flux quantum, Φ₀ = h/(2e), where e is the elementary charge. This quantization, a direct consequence of Planck's constant, is fundamental to the behavior of superconductors and devices like SQUIDs (Superconducting Quantum Interference Devices).
Q: How does Planck's constant relate to the concept of quantum superposition?
A:
While Planck's constant doesn't directly appear in the mathematical description of quantum superposition, it underlies the wave-like nature of quantum entities that makes superposition possible. The wavelength associated with a particle's momentum, λ = h/p, is fundamental to understanding interference and superposition effects.
Q: What is the significance of Planck's constant in the study of quantum optics?
A:
In quantum optics, Planck's constant is crucial for understanding phenomena like single-photon interference, squeezed light states, and photon antibunching. It determines the energy of individual photons and sets the scale for quantum fluctuations in electromagnetic fields.
Q: How does Planck's constant affect the behavior of electrons in semiconductors?
A:
Planck's constant plays a key role in semiconductor physics. It influences the effective mass of charge carriers, the density of states in energy bands, and quantum confinement effects in nanostructures. These quantum mechanical effects, governed by Planck's constant, are essential for modern electronic devices.
Q: How does Planck's constant influence the operation of quantum computers?
A:
Planck's constant is fundamental to quantum computing. It determines the energy scales of qubit operations, the strength of quantum entanglement, and the timescales over which quantum coherence can be maintained. Understanding and controlling these quantum effects, all related to Planck's constant, is crucial for developing practical quantum computers.
Q: What role does Planck's constant play in the quantum mechanical description of the hydrogen atom?
A:
In the quantum mechanical model of the hydrogen atom, Planck's constant is essential for determining the allowed energy levels and the probabilities of transitions between them. It appears in the Schrödinger equation and in the expressions for the quantized energy levels, demonstrating its fundamental importance in atomic physics.
Q: How does Planck's constant relate to the concept of quantum vacuum fluctuations?
A:
Quantum vacuum fluctuations, temporary changes in the amount of energy in a point in space, are a direct consequence of the uncertainty principle, which involves Planck's constant. The energy-time uncertainty relation, ΔEΔt ≥ ħ/2, allows for the brief creation and annihilation of virtual particles in the vacuum.
Q: What is the significance of Planck's constant in the study of quantum field theory?
A:
In quantum field theory, Planck's constant plays a crucial role in the quantization of fields. It appears in the commutation relations between field operators and their conjugate momenta, and it sets the scale for quantum fluctuations in fields. These quantum effects, governed by Planck's constant, are essential for understanding particle physics and quantum electrodynamics.
Q: How does Planck's constant affect the behavior of electrons in graphene?
A:
In graphene, a two-dimensional material, Planck's constant is crucial for understanding the unique electronic properties. The linear dispersion relation of electrons in graphene leads to behavior mimicking massless Dirac fermions, with the Fermi velocity replacing the speed of light in equations involving Planck's constant.
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