If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is?

By Ritesh|Updated : November 13th, 2022

(a) c1/2 G1/2 h1/2

(b) c1/2 G1/2 h-½

(c) c1/2 G-½ h1/2

(d) c-½ G1/2h1/2

The dimensions of mass in the new system are c1/2 G-½ h1/2. Let m ∝ cx Gy hz:

Now by substituting the following dimensions for the above proportions we get:

[c] = LT-1; [G] = [M-1 L3 T-2]; [h] = [ML2T-1]

On comparing both sides we get:

x = ½; G = -½; h = ½

So m ∝ c1/2 G-½ h1/2

Planck’s constant

Planck's constant is the physical constant that connects the energy carried by a single photon to its corresponding frequency in the quantum theory of electromagnetic. measured with J.s in the SI system and eV in the MKS system, and represented by the symbol h.

In quantum mechanics, the Planck constant's value is of utmost significance. Therefore, the definition of Planck's constant is a universal constant that is the product of the energy of an electromagnetic radiation quantum and its frequency.

Application:

Several applications, including Planck's equation, make use of the Planck constant value. For instance, the Planck constant(h) and the frequency of a photon are multiplied to determine its energy.

Summary:

If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system is?

If the velocity of light (c), gravitational constant (G) and Planck's constant (h) are chosen as fundamental units, then the dimensions of mass in new system are c1/2 G-½ h1/2.

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