Dimensional Formula of Planck’s Constant

What is the Dimensional Formula of Planck’s Constant?

The dimensional formula of the Planck constant is [ℎ] = ML²T ^-1

Planck’s constant is given as the ratio of the energy of a particle to its frequency. This ratio is constant. The value of Planck’s constant is 6.626 × 10^-34 Js. In this article, we are going to learn what is the dimensional formula of Planck’s constant with a brief introduction to the dimensional formula and Planck’s constant.

The dimensional formula represents the expression of a physical quantity in terms of the base quantities of mass M, length L, time T, electric current I, thermodynamic temperature Ө, amount of substance N, and luminous intensity J.

What is Planck’s Constant?

Planck’s constant, denoted as “h,” is a fundamental physical constant that plays a crucial role in quantum mechanics, describing the behavior of particles at the atomic and subatomic levels. Named after German physicist Max Planck, who introduced it in 1900, the constant quantifies the relationship between the energy of a photon and the frequency of its associated electromagnetic wave. Its value, approximately 6.626 x 10^-34 joule-second, underpins the understanding of phenomena such as the quantization of energy levels and the wave-particle duality of particles, forming a cornerstone in the foundation of modern physics.

Planck’s Constant Formula

Planck’s constant, denoted as “h,” is a fundamental constant in physics. Its formula is often expressed in the context of the energy-frequency relationship for electromagnetic radiation, such as light. The formula is given by:

E = hν

where,

• E represents electromagnetic radiation
• h represents Planck’s constant
• ν represents frequency of the radiation.

Dimensional Formula of Planck’s Constant

The dimensional formula of the Planck constant is [ℎ] = ML²T ^-1

In the above formula,

• M represents mass
• L represents length
• T represents time

Derivation of Planck’s Constant Dimensional Formula

To derive the dimensional formula of Planck’s constant (ℎ), we’ll use the formula

Energy[E]= Plank’s constant (h) × Frequency(ν) ….(1)

The dimensional formula for energy (E) is given by the below formula

E = [ML²T^-2]

Dimensional Formula of Frequency is given as

Frequency = 1/T = [T^-1]

Now, let’s substitute the dimensional formulas of Energy and Frequency in equation (1), we get

ML²T^-2 = [h] × [T^-1]

Now, isolate the dimensional formula of ℎ by rearranging the equation:

h = [ML²T^-2] / [T^-1]

After simplifying,

[h] = ML²T^-1

So, the derived dimensional formula for Planck’s constant (ℎ) is ML²T^-1.

Application of Planck’s Constant

The Planck constant is a crucial factor in quantum mechanics and finds applications in various areas:

• Quantization of Energy: It plays a central role in understanding the quantization of energy levels in quantum systems.
• Wave-Particle Duality: Planck’s constant is fundamental to the concept of wave-particle duality, which is a key feature of quantum mechanics.
• Quantum of Electromagnetic Action: It defines the smallest amount of action in the quantum realm.

Advantages and Disadvantages of Planck’s Constant

The advantages and Disadvantages of Planck’s Cosnstant are mentioned below:

Advantages:

• Precision in Quantum Calculations: Planck’s constant provides a precise and fundamental unit for quantum calculations.
• Consistency in Quantum Theory: It ensures consistency and accuracy in the mathematical formulations of quantum mechanics.

Disadvantages:

• Complexity: Understanding and applying Planck’s constant can be challenging due to the complexity of quantum mechanics.
• Limited Applicability: Its significance is primarily within the domain of quantum physics, and its effects are negligible in the macroscopic world.

Planck’s Constant Dimensional Formula – FAQs

1. What is Dimensional Formula of Planck’s constant?

The dimensional formula of the Planck’s constant (ℎ) is [ML²T^-1].

2. What is unit of Planck’s Constant?

The SI unit of Planck’s constant is joule-second (J⋅s)

3. Why is Planck’s constant significant in Quantum Mechanics?

Planck’s constant is fundamental in quantum mechanics, defining the quantization of energy levels, the wave-particle duality of particles, and establishing the fundamental unit of action in the quantum realm.

4. How is the Planck Constant derived Dimensionally?

The Planck constant (ℎ) is derived dimensionally by considering its role as the fundamental quantum of action. The dimensional formula is [ML²T^-1].

5. How does Planck’s Constant relate to the Uncertainty Principle?

Planck’s constant is a key factor in the Heisenberg Uncertainty Principle, which states that the precision with which certain pairs of properties (e.g., position and momentum) of a particle can be known is limited. The constant sets a fundamental limit on the precision of such measurements.