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  Physics Constants Matching Quiz Match the following physical constants with their correct dimensional formulas. This quiz tests your understanding of Boltzmann's constant, coefficient of viscosity, thermal conductivity, and Planck's constant. 14. Match the following physical constants with their dimensional formulas: (i) Boltzmann's constant (a) ML 2 T -1 (ii) Coefficient of viscosity (b) ML 2 T -2 K -1 (iii) Thermal conductivity (c) ML -1 T -1 (iv) Planck's constant (d) MLT -3 K -1 (1) (i)-(c), (ii)-(b), (iii)-(a), (iv)-(d) (2) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a) (3) (i)-(b), (i...

  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...