The de-Broglie wavelength associated with a particle of mass m and energy E is h/2mE. The dimensional formula for Planck's constant is :
The de-Broglie wavelength associated with a particle of mass m and energy E is h / 2 m E . The dimensional formula for Planck's constant is : Here is your right answer To determine the dimensional formula for Planck's constant, we will start by analyzing the given de-Broglie wavelength equation: λ = h 2 m E Here, λ is the wavelength, h is the Planck's constant, m is the mass of the particle, and E is the energy of the particle. First, let's derive the dimensional formula for each term involved: 1. Wavelength λ has the dimensional formula of length [ L ] . 2. Mass m has the dimensional formula M [ M ] . 3. Energy E has the dimensional formula of work, which is force times distance: MLT ML T [ E ] = [ F ] [ L ] = [ MLT − 2 ] [ L ] = [ ML 2 T − 2 ] . Now, let's rewrite the equation in terms of the dimensions: M ML T [ L ] = [ h ] 2 [ M ] [ ML 2 T − 2 ] Simplifying inside the square root: M M L T [ L ] = [ h ] 2 [ M ] [ M ] [ L 2...