To demonstrate the relative strengths of the electrical and gravitational forces of at- traction between the electron and the proton in the Bohr atom, suppose the hydrogen atom were held together solely by the force of gravity. Determine the radius of the ground-state orbit (in units of both nm and AU) and the energy of the ground state and the first excited state (in eV). Restate each of these quantities in units of their corresponding values for the true (i.e. electromagnetic) Bohr atom. What would be the wavelength of light emitted by such an atom if the electron were to drop from the first excited state to the ground state? (This last request is nonsensical, since the photon is associated solely with electromagnetic transitions and not the hypothetical gravi- tational transition discussed here, but you should proceed nonetheless simply using E = hc/?) To what part of the electromagnetic spectrum would this correspond?
To demonstrate the relative strengths of the electrical and gravitational forces of at- traction between the electron and the proton in the Bohr atom, suppose the hydrogen atom were held together solely by the force of gravity. Determine the radius of the ground-state orbit (in units of both nm and AU) and the energy of the ground state and the first excited state (in eV). Restate each of these quantities in units of their corresponding values for the true (i.e. electromagnetic) Bohr atom. What would be the wavelength of light emitted by such an atom if the electron were to drop from the first excited state to the ground state? (This last request is nonsensical, since the photon is associated solely with electromagnetic transitions and not the hypothetical gravi- tational transition discussed here, but you should proceed nonetheless simply using E = hc/?) To what part of the electromagnetic spectrum would this correspond?
