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    1. The problem statement, all variables and given/known data
    hi
    i came across this problem on an aqa physics a past question.

    How many different wavelengths of electromagnetic radiation can be emitted after
    atomic hydrogen is excited to level 4?



    2. Relevant equations



    3. The attempt at a solution
    i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
    from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
    i calculated in this manner for level 3 to the ground, 2 to the ground state etc.

    can someone someone clarify where i am going wrong?
    thanks
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    the answer (6) implies ground state is n=1
    so there are 3 gaps:
    ______________ 4

    ______________ 3

    ______________ 2

    ______________ 1

    and so 6.
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      (Original post by aurao2003)
      1. The problem statement, all variables and given/known data
      hi
      i came across this problem on an aqa physics a past question.

      How many different wavelengths of electromagnetic radiation can be emitted after
      atomic hydrogen is excited to level 4?



      2. Relevant equations



      3. The attempt at a solution
      i was looking at transitions from level 4 to the ground. i obtained 10 but the answer suggested 6. this was my conclusion;
      from level 4 (4 wavengths. this was calculating from 4 to 3, 4 to 2, 4 to 1 etc)
      i calculated in this manner for level 3 to the ground, 2 to the ground state etc.

      can someone someone clarify where i am going wrong?
      thanks
      If the hydrogen is in n = 4, then the possible ways it can return to the ground state are:
      4 --> 3 --> 2 --> 1
      4 --> 3 --> 1
      4 --> 2 --> 1
      4 --> 1

      Radiation is emitted when each of these transitions between levels occurs, and the wavelength of the radiation is related to the energy difference between the levels n and m by:

      \displaystyle E_{nm} = E_n - E_m = \frac{\text{hc}}{\lambda_{nm}}

      So the number of different wavelengths of radiation we can get is the same as the number of distinct transitions, which is 6:
      4 --> 3
      4 --> 2
      4 --> 1
      3 --> 2
      3 --> 1
      2 --> 1
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      thanks a million!
     
     
     
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