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Absorbtion/Emmision Spectra

  1. Nov 10, 2007 #1
    1. The problem statement, all variables and given/known data

    An atom of element Q can only absorb two photons of frequency 6.40E14 Hz and 9.05E14 Hz.

    Explain how atoms of element Q could absorb or emit photons of particular frequencies.


    2. The attempt at a solution

    OK I think I am missing something in my understanding of absorbtion and emission ....
    I don't really understand what the question is asking.

    But, perhaps;

    The element Q has set energy levels; n=1, n=2 ...
    Hence the element can only absorb or emit photons with energies equal to the energies of these energy levels.
    These energies are 6.40E14 Hz and 9.05E14 respectively.


    As I said, I'm having trouble. If someone could please explain the concept of the problem, it would be greatly appreciated.

    Thanks
    Steven
     
    Last edited: Nov 10, 2007
  2. jcsd
  3. Nov 10, 2007 #2

    Astronuc

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    Staff: Mentor

  4. Nov 10, 2007 #3
    Astronuc, thanks for your reply :)

    For the second part of the question,
    I am required to draw the energy level diagram of the element, showing the known levels.
    Then, calculate the longest wavelength photon that the element could emit.

    [​IMG]

    ok so the longest possible photon will be that of the smallest frequency photon.
    From the question, it says the element can absorb photons of the the specifc frequencies.

    Now from here
    http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html#c2
    I can see that the downward transition gives an emission of E2 - E1.

    So we are looking for the downward transition with the smallest possible frequency, which is;
    9.05E14 - 6.04E14 = 3.01E14 Hz
    [tex]
    \begin{array}{l}
    \lambda = \frac{c}{f} \\
    \lambda _{\max } = \frac{{3 \times 10^8 }}{{3.01 \times 10^{14} }} = 9.97 \times 10^{ - 7} m \\
    \end{array}
    [/tex]

    How am I looking?

    Thanks for your help,
    Steven
     
    Last edited: Nov 10, 2007
  5. Nov 10, 2007 #4

    Astronuc

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    Staff: Mentor

    The energy level at n=2 is closer to n=1 than n=3 is to n=2.

    Refer to the last link I cited -
    http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html

    If 9.05E14 Hz represents n=3 to n=1 and 6.04E14 n=2 to n=1, then the n=3 to n=2 transition would be the difference. This is based on the statement "An atom of element Q can only absorb two photons of frequency 6.40E14 Hz and 9.05E14 Hz." It would be unlikely that a photon would absorbed by an electron in the excited n=2 state.

    Looks OK.
     
  6. Nov 10, 2007 #5
    OK for the diagram, the 2.5eV should be less than the 3.75eV (elementary mistake)

    I'm not really fully understanding what you mean.
    But are you trying to say that those frequencies do not represent those transitions?
    Am I sort of on the right track?

    Thanks for your patience.
    Steven.
     
  7. Nov 10, 2007 #6

    Astronuc

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    Staff: Mentor

    Note the different groups and emission lines in this -
    http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html#c4


    I was saying those energies do represent those transitions.

    The two absorption energy would correspond to n=3 to n=1 (more energetic) and n=2 to n=1 less energetic, and these would be approximately equal to emission lines. There is also a possible n=3 to n=2 emission, which is the difference between 3-1 and 2-1.

    The 2->3 would be an unlikely absorption because the transition 2->1 would occur very quickly.
     
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