Planck’s Constant Explained: Importance, Uses & Exam Problem Examples
Planck’s constant is a fundamental physical constant central to quantum mechanics. This constant helps describe the relationship between energy and frequency at atomic and subatomic scales, especially in the context of the particle aspect of light. Planck’s constant was introduced by the German physicist Max Planck in 1900, marking a major turning point in the understanding of physics at microscopic levels.
What is Planck’s Constant?
Planck’s constant, symbolized by h, is characteristic of quantum formulations. It appears in equations that describe how particles and waves behave on the atomic scale. The value of this constant defines the scale at which quantum effects start to become noticeable, bridging the classical and quantum views of physics.
Physically, Planck’s constant provides the proportionality factor linking a photon's energy to its frequency. This is crucial for understanding phenomena such as light emission, absorption, and quantum transitions.
Formula: The Planck-Einstein Relation
The most common equation involving Planck’s constant is:
Where:
- E = energy of a photon
- h = Planck’s constant
- f = frequency of the photon
This formula shows that the energy of a photon is directly proportional to its frequency. It is a foundational concept for quantum physics and modern understanding of light.
Units and Value of Planck’s Constant
| Expression | Unit | Symbol | Value |
|---|---|---|---|
| Standard value | Joule·second | J·s | h ≈ 6.626 × 10−34 |
The unit for Planck’s constant is Joule-second (J·s). This unit reflects the relationship between energy (Joule) and frequency (1/second).
Applications and Significance
Planck’s constant is fundamental wherever quantum behavior occurs. A few key areas include:
- Explaining the energy of photons (light particles)
- Relating to the behavior of waves and particles on the atomic scale
- Forming the basis for all modern quantum mechanical models
Worked Example: Calculating Photon Energy
Suppose the frequency of a photon is 6 × 1014 Hz. To find its energy:
E = (6.626 × 10−34 J·s) × (6 × 1014 Hz)
E = 3.9756 × 10−19 J
Thus, a photon of this frequency has an energy of approximately 3.98 × 10−19 Joules.
Key Formulas Involving Planck’s Constant
| Application | Formula |
|---|---|
| Photon energy | E = h × f |
| Energy–wavelength relation | E = hc / λ |
Dimensional Formula
| Quantity | Dimensional Formula |
|---|---|
| Planck’s Constant (h) | [M1 L2 T−1] |
This means it has the dimensions of action (energy × time).
Step-by-Step Approach: Solving Problems with Planck’s Constant
- Identify what is asked (energy, frequency, wavelength).
- Write down the known quantities.
- Select the appropriate formula (e.g., E = h × f or E = hc / λ).
- Substitute values for h and other quantities.
- Solve and check unit consistency.
Regular practice with unit conversions ensures accuracy in competitive and board exams.
Practice Questions
- Calculate the energy of a photon with frequency 8 × 1014 Hz.
- If a photon has an energy of 5 × 10−19 J, what is its frequency?
- What is the dimensional formula of Planck’s constant?
Further Learning and Related Topics
- Quantum Physics
- Energy Levels in Atoms
- Atomic Physics
- Photoelectric Effect & Threshold Frequency
- Atomic Spectra
Next Steps for Mastery
- Review more solved examples using Planck’s constant
- Solve practice sets on quantum physics topics
- Explore real-world applications in modern physics sections
Planck’s constant is a pillar of all modern atomic and quantum theory. It connects the wave-like and particle-like behaviors of energy, serving as a foundational concept for deeper study and understanding in physics.
FAQs on Planck’s Constant (h): Value, Formula, Units & Physics Applications
1. What is Planck’s constant in simple terms?
Planck’s constant (h) is a fundamental physical constant that relates the energy of a photon to its frequency. In simple terms, it sets the smallest possible unit—or quantum—of energy exchange at the atomic scale.
• Formula: E = h × f, where E is energy and f is frequency.
• Significance: It marks the boundary between classical and quantum physics and appears in many quantum equations.
2. What is the official value of Planck’s constant in SI units?
The official value of Planck’s constant (h) in SI units is:
h = 6.62607015 × 10-34 Joule·second (J·s)
This value is fixed by international agreement (CODATA 2018) and is used in all latest physics examinations and syllabi.
3. What is the formula involving Planck’s constant?
The key formula involving Planck’s constant (h) is:
Energy of a photon: E = h × f
• E = energy of the photon
• h = Planck’s constant
• f = frequency of the radiation
This formula is essential in quantum physics, the photoelectric effect, and electromagnetic radiation calculations.
4. What is the dimensional formula and SI unit of Planck’s constant?
Dimensional formula of Planck’s constant (h): [M1 L2 T-1]
SI Unit: Joule·second (J·s)
5. How is Planck’s constant used in the photoelectric effect?
Planck’s constant is crucial in the photoelectric effect, where it relates the energy of incident photons to the kinetic energy of emitted electrons.
Photoelectric Equation: Ek = h·f – φ0
• Ek = kinetic energy of electrons
• h·f = energy of photons
• φ0 = work function of material
6. Is there a difference between Planck’s constant (h) and the reduced Planck’s constant (ħ)?
Yes, there is a difference:
• Planck’s constant (h) is the standard constant used in quantum equations.
• Reduced Planck’s constant (ħ) (h-bar) is defined as ħ = h / (2π).
ħ is commonly used in advanced quantum mechanics, such as in the Schrödinger equation and angular momentum calculations.
7. What is the value of Planck’s constant in electron-volt seconds (eV·s)?
In electron-volt seconds (eV·s), Planck’s constant is:
h = 4.135667696 × 10-15 eV·s
This value is often used for photon energy calculations in atomic physics and spectroscopy problems.
8. Where is Planck’s constant used in real life and competitive exams?
Applications of Planck’s constant (h):
• Calculating photon energy in lasers, LEDs, and solar cells
• Understanding X-ray spectra and atomic structure
• Evaluating photoelectric effect problems in JEE, NEET, and board exams
• Finding de Broglie wavelength for particles
9. What are tips for remembering Planck’s constant and its formulas?
Tips to remember Planck’s constant:
• Remember h for energy per frequency (E = h·f)
• Use the shortcut: E (eV) ≈ 1240/λ (nm)
• Always check your units (J, eV) before calculation
• Practice converting between J·s and eV·s formats
10. How do you calculate the energy of a photon given its frequency or wavelength?
To calculate photon energy:
• If frequency (f) is given:
E = h × f
• If wavelength (λ) is given:
E = h × c / λ
Here, h = Planck’s constant, c = speed of light (3 × 108 m/s), λ = wavelength in meters.
11. Why is Planck’s constant considered fundamental for modern physics?
Planck’s constant is fundamental because it marks the smallest possible action in nature, setting the scale for quantum phenomena.
• It is central to quantum theory and appears in all equations describing photons, electrons, and atomic spectra.
• It distinguishes classical and quantum physics regimes.
12. What happens to the energy of a photon if its frequency is doubled?
If the frequency of a photon is doubled, its energy also doubles because energy and frequency are directly proportional (E = h × f).
• For example, if f becomes 2f, then the energy becomes 2 × (h × f).
