Correct option is (C)
To determine the dimensional formula for Planck's constant, we will start by analyzing the given de-Broglie wavelength equation:
Here, is the wavelength, is the Planck's constant, is the mass of the particle, and is the energy of the particle.
First, let's derive the dimensional formula for each term involved:
1. Wavelength has the dimensional formula of length .
2. Mass has the dimensional formula .
3. Energy has the dimensional formula of work, which is force times distance:
.
Now, let's rewrite the equation in terms of the dimensions:
Simplifying inside the square root:
Since the constants like 2 do not affect the dimensional formula, we can simplify further:
Cross multiplying to solve for the dimensional formula of :
Therefore, the dimensional formula for Planck's constant is:
Hence, the correct option is:
Option C