Three fundamental constants of physics, which we will encounter at various times, are: mp, the mass of the proton, whose dimension is [M]; c, the speed of light, whose dimension is [L/T]; and h, Planck's constant, whose dimension is [ML2/T]. What combination of these constants will produce a quantity whose dimension is [L]? Show me explicitly what the correct combination of constants is. ([M] represents mass, [T] represents time, and [L] represents length.)

Given data: mp - Mass of the proton c- Speed of light h- Planck's constant The dimension wise, Dimension of mass is [ M] Dimension of speed of light is [ M/T] Dimension of Planck's constant is [ ML2/T]Calculation: In the given problem it is asked to make the combinationation of above physical constant to get the dimension of length. The quantity which made up of all these three quantities is the Compton wavelength. Let us check whether it will produce the correct result of not. M = hmpc Expand dimensionally, M = ML2TMLTM = ML2TMTLM =M Therefore it is correct choice of combination. And hmpc- Compton wavelength. And wavelength has dimension of length.Answer: Therefore, correct combination of given constant quantity which results into the quantity whose dimension is [M] is, hmpc

Answered: Three fundamental constants of physics,…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter34: Maxwell’s Equations And Electromagnetic Waves

Section34.1: Light: One Last Classical Topic

Problem 34.1CE

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Three fundamental constants of physics, which we will encounter at various times, are: m_p, the mass of the proton, whose dimension is [M]; c, the speed of light, whose dimension is [L/T]; and h, Planck's constant, whose dimension is [ML²/T]. What combination of these constants will produce a quantity whose dimension is [L]? Show me explicitly what the correct combination of constants is. ([M] represents mass, [T] represents time, and [L] represents length.)

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