This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Fresh day Adebayo, let's solve. To find the dimensions of Planck's constant h, we use the given energy equation: E = (hc)/() where E is energy, h is Planck's constant, c is the velocity of light, and is wavelength. Step 1: Rearrange the equation to solve for h. h = (E )/(c) Step 2: Determine the dimensions of each known quantity. Energy (E): Energy has the dimensions of work, which is force times distance. Force is mass times acceleration (F=ma). [E] = [M][L T^-2][L] = [M L^2 T^-2] Wavelength (): Wavelength is a measure of length. [] = [L] Velocity of light (c): Velocity is distance over time. [c] = [L T^-1] Step 3: Substitute these dimensions into the equation for h. [h] = [M L^2 T^-2] [L][L T^-1] Step 4: Simplify the expression. [h] = M L^2+1 T^-2L T^-1 [h] = M L^3 T^-2L T^-1 [h] = M L^3-1 T^-2 - (-1) [h] = M L^2 T^-2+1 [h] = M L^2 T^-1 Comparing this with the given options: A. MLT^-1 B. ML^1T^-1 C. ML^2T^-1 D. ML^2T^-2 The calculated dimension matches option C. The final answer is C. ML^2T^-1. Got more? Send 'em!