1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Hydrogen bound by only grav force (Bohr theory etc)

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data
    If electric charge did not exist, and protons and electrons were only bound together by gravitational forces to form hydrogen, derive the expressions for a_0 and E_n and compute the energy and frequency of the H_alpha line and limit of Balmer series.

    2. Relevant equations
    E_n=mc^2 * alpha * 1 / (2n^2)

    3. The attempt at a solution
    If electric charge did not exist, then the balance of electron orbit and distance would change. Bohr's radius would just be zero i would imagine since it depends on electron charge. E_n would suffer the same fate... Would E_n just become mc^2? The radius would have to still be a number as the two do still have mass and gravity would affect them.

    F=Gm1m2/r^2 is the force on either exerted by the other and
    E=-Gm1m2/r is the gravitational potential energy

    The energy of the electron E_n must be strictly dependent on this.

    How do I "derive" an expression from E_n or a_0 when their original formulas must be completely nixed?

    Is there supposed to be a way of expressing it with n levels?

    Otherwise I propose the energy of the electron is -Gm1m2/r as there is no kinetic energy.
    Last edited: Apr 3, 2009
  2. jcsd
  3. Apr 3, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    One of the key components of the Bohr model is the electron's angular momentum must be an integer multiple of Planck's constant divided by 2 pi:

    L = n h / 2 π . . . with n = 1, 2, 3, ... ​
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook