Fine Structure Constant Expression · CAP 2001 #10

Physics · modern-physics

Problem

In problems involving electromagnetism it is often convenient and informative to express answers in terms of a constant, α, which is a combination of the Coulomb constant, ke=1/4πϵ0k_e = 1/4π\epsilon_0, the charge of the electron, e, and hˉ=h/2π\bar{h} = h/2π, h being Planck's constant. For instance, the lowest energy that a hydrogen atom can have is given by E=−12α2mc2E = −\frac{1}{2}α^2mc^2, where m is the mass of the electron and c is the speed of light. Which of the following is the correct expression for α? (HINT: non-relativistic kinetic energy is 12mv2\frac{1}{2}mv^2, where v is speed.) (a) kee2hˉc\frac{k_e e^2}{\bar{h}c} (b) hˉkee2c\frac{\bar{h}}{k_e e^2 c} (c) kee2hˉc\frac{k_e e^2 \bar{h}}{c} (d) kee2chˉ\frac{k_e e^2 c}{\bar{h}}

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