1. Not finding help here? Sign up for a free 30min 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!

Total energy of Coulomb model of Hydrogen atom

  1. Sep 5, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi, my question is regardng a Coulomb model of an H atom specified with Hamiltonian operator, Hhat, by spherical coordinates of energy eigenfunction
    ψ2,1,-1 (r,θ, ∅) =(1/ 64∏a02)1/2 r/a0 e-r/2a0 sinθ e-iθ

    Principal quantum numer n = 2
    orbital an mom l = 1
    magnetic quantum number m = -1

    I must specify magnitude of orbital ang momentum, Lhat2, and z-component of orbital ang momentum as well as total energy.

    2. Relevant equations
    Lhat2 = l (l + 1) hbar2
    Lz = m hbar (1/ √2∏) eim∅

    3. The attempt at a solution
    Lhat2 = 1 (1 + 1)hbar2
    Lhat2 = 2 hbar2

    Lz = m hbar (1/ √2∏) eim∅
    Lz = -1 hbar / √2∏ ei-1∅
    = -1 hbar

    but what about total energy?
    I'm lost in the forest again and can't see the wood for the trees.
  2. jcsd
  3. Sep 5, 2013 #2


    User Avatar
    2016 Award

    Staff: Mentor

    There is a relation between principal quantum number and energy that you should know.
  4. Sep 6, 2013 #3

    Well, En = (n + 1/2) hbar ω0


    En = n22 hbar2 / 2mL2
    where principal quantum number n = 0, 1, 2 . . .

    but I can't evaluate ω0 and I don't have the mass for the other one . . do I?
  5. Sep 6, 2013 #4
    n = principal quantum number
    m = mass of electron
    L2 = square of magnitude of orbital ang momentum.

    so . . . .

    E = 22 ∏2 hbar2 / 2(9.1x10-31) 2 hbar2
    E = -2∏hbar/m

    er! surely too messy and probably wrong.
  6. Sep 6, 2013 #5


    User Avatar
    2016 Award

    Staff: Mentor

    Why? Your formula (edit: wait, those are the wrong formulas) assumes an infinite central mass, which is usually a reasonable approximation in a hydrogen atom.

    The total energy of the system does not matter unless you want to consider special relativity.
    Last edited: Sep 6, 2013
  7. Sep 6, 2013 #6


    User Avatar
    Homework Helper
    Gold Member

    Does either of these formulas apply to the hydrogen atom?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Total energy of Coulomb model of Hydrogen atom