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Potential/Kinetic/Total Energy of hydrogen atom absorbing photon

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data

    A hydrogen atom in the n = 2 state absorbs a photon with wavelength 380 nm.

    Q1. Find the change in the atom’s total energy.
    Q2. Find the change in the atom’s potential energy
    Q3. Find the change in the orbiting electron’s kinetic energy.
    2. Relevant equations


    3. The attempt at a solution

    Q1 I solved correctly so I know total E = 5.23×10−19 J
    Q2 I know U = E - K, but I don't know the formulas for K or for U so I'm stuck here for Q2 and Q3.

    Direction please? Also, I'm having difficulty in understanding why the kinetic energy of the electron decreases as you move away from the nucleus, and why the potential energy increases. Thanks.
  2. jcsd
  3. Sep 27, 2010 #2
    Why the kinetic energy of the electron decreases:
    KE = 1/2 mv^2
    a = v^2/r, so v = (ar)^1/2, so:
    KE = 1/2 mar, where a is given by:
    F = ma = KQq/r^2 so a = KQq/(mr^2) so:
    KE = 1/2 Kqq/r

    Why the potential energy increases:
    At r = infinity, the proton and electron would feel no attraction. Bump them a little closer than infinity, and they feel the Coulomb force, which means they experience an acceleration. If they accelerate, their kinetic energy increases. To conserve energy, we conclude that since kinetic energy increases, potential energy decreases as the distance decreases.

    I'm not sure if your text covers it, but if it does, try the Virial Theorem.
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