Show that Equation 4-19 for the radius of the first Bohr orbit and Equation 4-20 for the magnitude of the lowest energy for the hydrogen atom can be written as

where λ_c = h/mc is the Compton wavelength of the electron and a = ke²/ћc is the fine-structure constant. Use these expressions to check the numerical values of the constants a₀ and E₁.

Transcribed Image Text:

20 hc amc2 Ac Σπα E₁ = = ²mc² 2