Value of Planck's Constant - Formula, Definition, Unit, Application, FAQs

Q: What is Planck's constant's dimensional formula?

Planck's constant has the dimensional formula ML 2 T -1

Value of Planck's Constant

Edited By Team Careers360 | Updated on Jul 02, 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.

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What is Planck's constant?
Value of Plank’s Constant
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.

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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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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^-34J/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.

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

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Frequently Asked Questions (FAQs)

1. What is Planck's constant's dimensional formula?

Planck's constant has the dimensional formula ML²T^-1

2. Calculate the Dimensional Formula for energy'.

ML²T⁻²

3. What is the significance of Planck's constant?

Planck's constant is used to describe particle and wave dynamics on an atomic scale. One of the causes for the creation of quantum mechanics is Planck's constant.

4. What do you understand by Planck's law?

The energy of electromagnetic radiation, according to Planck's rule, is limited to quanta that cannot be divided and have an energy equal to the product of the Planck constant and the frequency of the radiation.

5. Why do we use Planck's constant?

Planck's constant is used to calculate Planck length and Planck time.

6. What is Planck's constant and why is it important in quantum physics?

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.

7. How does Planck's constant relate to the wave-particle duality of light?

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).

8. What is the relationship between Planck's constant and the uncertainty principle?

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.

9. How does Planck's constant affect the energy levels in atoms?

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.

10. How is Planck's constant used in calculating the energy of a photon?

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.

11. How was Planck's constant discovered?

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.

12. What is the reduced Planck's constant, and how does it differ from the regular Planck's constant?

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.

13. Why is Planck's constant so small?

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.

14. Can Planck's constant change over time?

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.

15. How does Planck's constant relate to the de Broglie wavelength?

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).

16. What is the numerical value of Planck's constant?

The value of Planck's constant is approximately 6.626 × 10^-34 joule-seconds (J⋅s) or 4.136 × 10^-15 electron volt-seconds (eV⋅s). It's important to note that the exact value has been refined over time with more precise measurements.

17. How does Planck's constant relate to the photoelectric effect?

Planck's constant is crucial in explaining the photoelectric effect. Einstein used it to show that the energy of ejected electrons is directly proportional to the frequency of incident light, with Planck's constant as the proportionality factor. This relationship is expressed as E = hf - W, where W is the work function of the metal.

18. How does Planck's constant affect the spacing of energy levels in a quantum well?

The energy levels in a quantum well are quantized, with their spacing determined by Planck's constant. The smaller the well, the larger the energy spacing between levels, as described by the equation ΔE ∝ h²/(mL²), where m is the particle mass and L is the well width.

19. How does Planck's constant influence the behavior of Bose-Einstein condensates?

Planck's constant is crucial in determining the conditions for Bose-Einstein condensation. The de Broglie wavelength of particles, which must be comparable to their inter-particle spacing for condensation to occur, is calculated using Planck's constant. This relationship highlights the quantum nature of this state of matter.

20. What role does Planck's constant play in the Bohr model of the atom?

In the Bohr model, Planck's constant is used to determine the allowed energy levels and orbital radii of electrons. The angular momentum of electrons in these orbits is quantized in integer multiples of ħ (reduced Planck's constant), leading to discrete energy states.

21. Why is Planck's constant considered a universal constant?

Planck's constant is considered universal because it applies to all quantum phenomena, regardless of the type of particle or interaction involved. It is fundamental to the structure of the universe and plays a crucial role in many areas of physics, from atomic physics to quantum field theory.

22. How does Planck's constant affect the behavior of electrons in a conductor?

Planck's constant influences the behavior of electrons in a conductor by determining their allowed energy states. It plays a role in phenomena like the quantization of electrical conductance and the spacing of energy levels in nanostructures, which are important in modern electronics.

23. What is the significance of Planck's constant in blackbody radiation?

Planck's constant is crucial in explaining blackbody radiation. It appears in Planck's law, which describes the spectral energy distribution of radiation emitted by a blackbody. This law resolved the ultraviolet catastrophe predicted by classical physics and led to the development of quantum theory.

24. How does Planck's constant relate to the Compton effect?

In the Compton effect, Planck's constant is used to describe the change in wavelength of a photon when it scatters off an electron. The Compton wavelength, a characteristic length for particles, is defined as h/mc, where m is the particle's mass and c is the speed of light.

25. What is the role of Planck's constant in quantum tunneling?

Planck's constant is essential in quantum tunneling, a phenomenon where particles can pass through energy barriers that classical physics forbids. The probability of tunneling depends on the particle's mass, the barrier's properties, and Planck's constant, highlighting the quantum nature of this effect.

26. How does Planck's constant affect the stability of atoms?

Planck's constant is crucial for atomic stability. It determines the quantized energy levels of electrons in atoms, preventing them from spiraling into the nucleus as classical physics would predict. This quantization, governed by Planck's constant, explains why atoms have discrete emission and absorption spectra.

27. What is the connection between Planck's constant and the zero-point energy?

Zero-point energy, the lowest possible energy a quantum system can have, is directly related to Planck's constant. For a simple harmonic oscillator, the zero-point energy is given by E = ½hf, where f is the oscillator's frequency. This shows that even at absolute zero, quantum systems retain some energy due to Planck's constant.

28. How does Planck's constant influence the behavior of lasers?

Planck's constant is fundamental to laser operation. It determines the energy of the photons emitted during stimulated emission, which is the basis of laser light. The frequency (and thus wavelength) of laser light is related to the energy difference between atomic levels, which is quantized according to Planck's constant.

29. What is the significance of Planck's constant in quantum entanglement?

While Planck's constant doesn't directly appear in the mathematical description of quantum entanglement, it underlies the quantum mechanical principles that make entanglement possible. The quantization of angular momentum and spin, crucial for entanglement, is governed by Planck's constant.

30. How does Planck's constant relate to the Heisenberg microscope thought experiment?

The Heisenberg microscope thought experiment illustrates the uncertainty principle, which is directly related to Planck's constant. The experiment shows that the act of measurement affects the system being measured, with the minimum uncertainty determined by Planck's constant.

31. What role does Planck's constant play in the quantum Hall effect?

In the quantum Hall effect, the Hall conductance is quantized in integer multiples of e²/h, where e is the elementary charge and h is Planck's constant. This quantization demonstrates the fundamental role of Planck's constant in quantum transport phenomena.

32. What is the relationship between Planck's constant and the fine structure constant?

The fine structure constant, α, is a dimensionless quantity that characterizes the strength of the electromagnetic interaction. It can be expressed in terms of fundamental constants, including Planck's constant: α = e²/(ħc), where e is the elementary charge and c is the speed of light.

33. How does Planck's constant influence the operation of scanning tunneling microscopes?

Scanning tunneling microscopes rely on quantum tunneling, which is governed by Planck's constant. The tunneling current between the microscope tip and the sample surface depends exponentially on their separation, with the decay constant related to Planck's constant and the work function of the material.

34. What is the significance of Planck's constant in the study of quantum dots?

In quantum dots, Planck's constant determines the discrete energy levels of confined electrons. The energy level spacing is inversely proportional to the dot size and depends on Planck's constant, leading to size-dependent optical and electronic properties that are crucial for various applications.

35. How does Planck's constant relate to the concept of wave packets in quantum mechanics?

Wave packets in quantum mechanics represent localized particles. The relationship between the spread in position (Δx) and momentum (Δp) of a wave packet is governed by the uncertainty principle: ΔxΔp ≥ ħ/2. This fundamental limit on localization is a direct consequence of Planck's constant.

36. What role does Planck's constant play in the quantum mechanical description of angular momentum?

Planck's constant is fundamental to the quantization of angular momentum in quantum mechanics. The angular momentum of a particle is quantized in units of ħ (reduced Planck's constant). This quantization leads to discrete values for orbital angular momentum and spin, crucial for understanding atomic structure and particle physics.

37. How does Planck's constant affect the behavior of electrons in a periodic potential?

In a periodic potential, such as in a crystal lattice, Planck's constant influences the formation of energy bands and band gaps. The width of these bands and gaps depends on the interplay between the lattice potential and the quantum mechanical wavelength of electrons, which is determined by Planck's constant.

38. What is the connection between Planck's constant and the Casimir effect?

The Casimir effect, a quantum mechanical force between conducting plates in a vacuum, is directly related to Planck's constant. The force arises from quantum fluctuations of the electromagnetic field, with its magnitude depending on Planck's constant, the speed of light, and the plate separation.

39. What role does Planck's constant play in the quantum mechanical description of harmonic oscillators?

In quantum mechanics, the energy levels of a harmonic oscillator are quantized, with the spacing between levels given by hf, where f is the oscillator frequency. This quantization, a direct result of Planck's constant, leads to phenomena like zero-point energy and affects the behavior of systems from molecules to quantum fields.

40. How does Planck's constant relate to the concept of quantum superposition?

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.

41. What is the significance of Planck's constant in the study of quantum optics?

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.

42. How does Planck's constant affect the behavior of electrons in semiconductors?

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.

43. What is the relationship between Planck's constant and the quantization of magnetic flux?

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).

44. How does Planck's constant influence the operation of quantum computers?

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.

45. What role does Planck's constant play in the quantum mechanical description of the hydrogen atom?

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.

46. How does Planck's constant relate to the concept of quantum vacuum fluctuations?

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.

47. What is the significance of Planck's constant in the study of quantum field theory?

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.

48. How does Planck's constant affect the behavior of electrons in graphene?

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.

49. What role does Planck's constant play in the quantum mechanical description of the photoelectric effect?

Planck's constant is central to Einstein's explanation of the photoelectric effect. The energy of ejected electrons is given by E = hf - W, where h is Planck's constant, f is the frequency of incident light, and W is the work function of the metal. This equation directly demonstrates the quantized nature of light energy.

50. How does Planck's constant relate to the concept of quantum coherence?

Quantum coherence, the ability of quantum systems to exist in superposition states, is fundamentally related to Planck's constant. The timescale over which coherence can be maintained is often inversely proportional to the energy differences between states, which are quantized according to Planck's constant.

51. What is the significance of Planck's constant in the study of quantum cryptography?

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.