Calculate the dimensional formula of Planck's Constant- Sciencetopia

The dimensional formula of Planck’s Constant is

[ M¹ L² T^-1 ]

where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.

From the above formula, the dimensions of Planck’s constant are (1, 2, -1).

How to calculate the dimensional formula of Planck’s constant?

We can define this formula using the mathematical formula of Plack’s constant. Mathematically,


  Planck's constant (h) = Energy / Frequency

We know that,


  Energy = Work Done

               = Force * displacement 

               = mass * acceleration * displacement

Also,

acceleration = speed / time
speed = distance / time
acceleration = distance / time²
acceleration = distance * time^-2

So, Energy = (mass * distance * displacement * time^-2)

And the formula of frequency is 1 / time = time^-1. Hence, the formula of Planck’s constant becomes


  Planck's constant = (mass * distance * displacement * time^-2) / time^-1
                       
                                   = ( mass * distance * displacement * time^-1 )

Dimensionally, we use

[M] for mass
[L] to represent both distance and displacement
and, [T] for time

Now, the formula becomes


  Planck's constant = [M¹] * [L²] * [T^-1]

Hence, the dimensional equation of Planck’s constant is h = [ M¹ L² T^-1 ].

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