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Homework Help: Energy of atoms in different levels

  1. Apr 13, 2012 #1
    1. The problem statement, all variables and given/known data

    In a set of experiments on a hypothetical one-electron atm, you measure the wavelengths of photons emitted as electrons return to the ground state (n=1), as shown in the energy level diagram. You also observe that it takes 17.50 eV to ionise this atom.

    Diagram shows:
    n=5 --> n=1 ~ λ = 73.86nm
    n=4 --> n=1 ~ λ = 75.63nm
    n=3 --> n=1 ~ λ = 79.76nm
    n=2 --> n=1 ~ λ = 94.54nm

    (i) What is the energy of the atom in each of the levels n=1 to n=5

    (ii) If an electron makes a transition from the n=4 to the n=2 level, what wavelength of light would it emit?

    2. Relevant equations

    None provided

    3. The attempt at a solution

    My attempt at A

    I think i use this equation:
    E = -hxR/n^2

    h is Planck's constant 6.626 x 10^-34
    R is Rydbergs constant 1.097 x 10^7
    and n is the energy level

    at n=5 i get: -2.907 x 10^-28
    at n=4 i get: -4.543 x 10^-28
    at n=3 i get: -8.076 x 10^-28
    at n=2 i get: -1.817 x 10^-27
    at n=1 i get: -7.269 x 10^-27

    I think i use balmers equation in part B?

    1/λ = R(1/2^2 - 1/4^2) where R= 1.097 x 10^7

    1/λ = 2056875

    I have a feeling i'm doing this all wrong.
  2. jcsd
  3. Apr 13, 2012 #2


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    What does ionization mean? How does the ionization energy relate to the ground state energy?
  4. Apr 14, 2012 #3

    Isn't it the minimum energy needed to dislodge an electron so it can move between energy states?
  5. Apr 14, 2012 #4


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    For ionization, the final state is a free electron: it is no longer one of the bound energy states. This sets a reference point. Each bound state energy can be measured with respect to the lowest energy free state.
  6. Apr 14, 2012 #5
    Ok, that makes sense to me. So have i used the wrong equation?
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