What is Planck's Constant 'h'?
Max Planck, a German scientist, was interested in understanding the electromagnetic radiation emitted by a blackbody. A body emits and absorbs electromagnetic radiation incident on it. But a blackbody can absorb and emit all the incident radiation on it. A blackbody emits the incident radiation at a constant temperature. Planck was keen on understanding the spectrum of this emission or the amount of energy radiated at a specific wavelength. Before Planck, it was assumed that the energy associated could take any value and the energy emission is continuous. But it was later observed that more energy is produced at higher frequencies; in other words, a heated body would radiate more blue than red. This was contrary to what was observed before. Planck later theorized that if he assumes energy to be radiated in packets, the model can produce the same outcome as in Black Body radiation without violating already proven physics principles.
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He then derived the value of a constant, later known as Planck's constant 'h,' which relates the energy of a photon to its frequency. When Planck's constant is multiplied by a photon's frequency, the result is the specific photon's energy. The value of Planck's constant 'h' is 6.626070 * 10-34 JS. Planck calculated this value of h from the experimental data obtained from black body radiations.
Value of 'hc' and its Importance
Planck's constant' h' and speed of light' c' can be used to find a photon's energy. A photon's energy is directly proportional to the frequency and thus is inversely proportional to its wavelength. Higher photon frequency denotes higher energy, and the longer is the photon particle's wavelength, the lower is the energy.
The value of 'hc' is 1.986445 * 10-25 J m. The equation for the energy of a photon is given as E=hc/λ. Here E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ denotes the wavelength of the photon. The value of 'hc' in eV comes out to be 1.23984193 * 10-6 eV.m. The value of 'hc' is also used to find out the energy of a specific atomic orbit by using the formula, E= - hcR/n2
Role of hc in Photoelectric Effect
hc plays a vital role in the photoelectric effect. But to understand this first we have to know what is photoelectric effect? Photoelectric Effect is when electrons are ejected out from a metal surface when light is incident on it. It was then believed that the more the intensity of incident light, the more energy it possesses regardless of the color of the light. The light was considered and treated to be a wave, but the wave phenomena didn't explain the photoelectric effects of light. The photoelectrons emitted during the phenomenon of the photoelectric effect have a definite and measurable kinetic energy. The Kinetic energy also depends linearly on the frequency along with the intensity. If the frequency is too low, there is no discharge of photoelectrons. A threshold frequency is needed to take the electrons in atoms of their orbit. After the threshold frequency is crossed, the number of photoelectrons emitted increases with the intensity of radiation.
Constant h in Atomic Structure
To overcome Rutherford's classical model's drawbacks, Neils Bohr introduced the first quantized model of an atom in 1913. In classical mechanics, particles spiraling around should emit electromagnetic radiation, thus losing energy and gradually spiral down into the nucleus. To solve this paradox, Bohr took reference from Planck's work and postulated that an electron would spiral around the nucleus only in orbits having pre-defined energies. The formula gives the energy of a specific orbit, E= -hcR/n2, where R is the experimentally determined Rydberg's constant and 'n' is the orbit number. When the electron reaches the lowest energy level, i.e., n=1, it cannot move any closer to the nucleus. The constant 'h' is also used in the uncertainty principle given by Heisenberg.
Overall Significance of h
Planck's Constant establishes a relation between photon energy and frequency and gives a quantitative value to light in the microscopic context where classical mechanics fails. The order of Planck's Constant, in a way, says that macroscopic bodies around us are made of billions and trillions of small microscopic bodies, which are in turn governed by a new set of laws altogether. Planck's Constant had a significant effect on our understanding of reality and life itself. The value also has an essential role in the construction of transistors, Integrated Circuits, and chips. Planck's quantization of energy was a revolutionary step to the destination of quantum mechanics, i.e., the way particles behave at the minor level.
Points to Remember
hc = 12,400 eV
Å = 1240 eV
nm = 1240 MeV
fm
Dimension of hc = [M1L3T-2]
Solved Numerical Type Questions
Q1. The work function of a metal is 3 eV. Will this metal give photoelectric emission for incident radiation of wavelength 350 nm? (h=6.63 x 10-3 J s, c = 3 x 108 m/sec)
Sol. The energy of the incident radiation
E=hc/λ
= (6.63 x 10-34 x 3 x 108)/(350 x 10-9)
= 0.0568 x 10-17 J
= 5.68 x 10-19 / 1.6 x 10-19
= 3.55 eV
Since the work function of the given metal is 3 eV. Therefore, when the photon of high energy incident on the metal, photoemission occurs.
2. A radio transmitter operates on a wavelength of 2500 m at a power of 500 kW. Find the energy of radio photons in joules. (h = 6.64 x 10-34 J s, c = 3 x 108 m/sec)
Solution. The energy of a photon emitted by a radio transmitter that operates on a wavelength of 2500 m is given by
E = hc/λ
= (6.64 x 10-34 J s x 3 x 108 m/s)/(2500 m)
= 0.7968 x 10-28 J
So, the energy of photoelectron emitted from a radio transmitter is 79.68 x 10-30 J.
FAQs on Value of hc
1. What does 'hc' represent in physics and why is it significant?
In physics, 'hc' represents the product of two fundamental physical constants: Planck's constant (h) and the speed of light in a vacuum (c). This combination is highly significant because it directly links the energy of a photon (E) to its wavelength (λ) through the pivotal formula E = hc/λ. It forms the cornerstone of quantum mechanics and is essential for studying phenomena like the photoelectric effect, atomic spectra, and black-body radiation as per the CBSE 2025-26 syllabus.
2. What is the standard value of hc in SI units (Joule-meter)?
The standard value of the product hc in SI units is calculated by multiplying the values of h and c.
- Planck's constant (h) ≈ 6.626 x 10⁻³⁴ Joule-seconds (J·s)
- Speed of light (c) ≈ 3.0 x 10⁸ meters per second (m/s)
3. What is the value of hc in electron-volt nanometers (eV·nm) and why is this unit useful?
The value of hc is approximately 1240 electron-volt nanometers (eV·nm). This unit is extremely useful in atomic and nuclear physics because the energies of particles are often measured in electron-volts (eV) and their wavelengths in nanometers (nm). Using this value simplifies calculations significantly, allowing students to quickly find a photon's energy in eV if its wavelength is known in nm, using the formula E(eV) = 1240 / λ(nm). A similar value, 12400 eV·Å, is used when wavelength is given in angstroms (Å).
4. How is the value of hc applied in the photoelectric effect formula?
In the photoelectric effect, the value of hc is central to Einstein's photoelectric equation. The equation states that the maximum kinetic energy (K.E.max) of an emitted electron is the energy of the incident photon (E) minus the work function (Φ) of the material. The photon's energy is given by E = hc/λ. Therefore, the full equation becomes: K.E.max = (hc/λ) - Φ. Here, 'hc' allows us to calculate the energy supplied by a single photon of light with a specific wavelength (λ), which determines if an electron can be ejected.
5. Why is hc often used as a single combined constant in quantum physics calculations instead of using h and c separately?
The product 'hc' is frequently treated as a single constant for two main reasons:
- Conceptual Link: The combination hc fundamentally connects a particle's wave property (wavelength λ) to its energy (E) in the equation E = hc/λ. Using it as a single block reinforces this core concept of wave-particle duality.
- Calculation Efficiency: In many problems involving atomic and particle physics, energy and wavelength are the primary variables. Pre-calculating hc in convenient units like eV·nm (approx. 1240) or J·m (approx. 1.988 x 10⁻²⁵) saves time and reduces the chance of calculation errors, especially in multi-step problems.
6. What is the dimensional formula for hc, and what physical quantity does it relate to?
To find the dimensional formula for hc, we multiply the dimensions of Planck's constant (h) and the speed of light (c).
- The dimension of Planck's constant (h) is [ML²T⁻¹].
- The dimension of the speed of light (c) is [LT⁻¹].
7. How do you convert the value of hc from Joule-meter to eV-angstrom? Explain the steps.
To convert the value of hc from Joule-meter (J·m) to electron-volt angstrom (eV·Å), you need to use the conversion factors for energy and length. The steps are as follows:
- Start with the value in J·m: hc ≈ 1.988 x 10⁻²⁵ J·m.
- Convert Joules (J) to electron-Volts (eV): We know that 1 eV = 1.602 x 10⁻¹⁹ J. Therefore, 1 J = 1 / (1.602 x 10⁻¹⁹) eV.
- Convert meters (m) to angstroms (Å): We know that 1 Å = 10⁻¹⁰ m. Therefore, 1 m = 10¹⁰ Å.
- Combine the conversions: Substitute the conversion factors into the original value: hc ≈ (1.988 x 10⁻²⁵) × [1 / (1.602 x 10⁻¹⁹) eV] × [10¹⁰ Å]
- Calculate the final value: Performing the arithmetic gives hc ≈ 12409 eV·Å. For most physics problems, this is approximated as 12400 eV·Å.
8. How does the role of 'hc' differ when calculating the energy of a photon versus the energy levels in the Bohr model of an atom?
While 'hc' is used in both contexts, its role is slightly different:
- Energy of a Photon: For a free photon, the product 'hc' is used to directly calculate its total energy based on its wavelength (λ) using the formula E = hc/λ. Here, 'hc' relates energy to a wave property.
- Energy Levels in Bohr Model: In the Bohr model, 'hc' appears in the formula for the energy (Eₙ) of an electron in a specific orbit 'n': Eₙ = -hcR/n², where R is the Rydberg constant. In this case, 'hc' is part of a larger expression that quantifies the discrete energy levels an electron can occupy within an atom. It helps determine the energy of emitted or absorbed photons when an electron transitions between these fixed levels.
