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This problem is killing me [calculation of electron transition]

  1. May 7, 2010 #1
    this problem is killing me!! [calculation of electron transition]

    i've been trying to solve this problem.. the answer should be 7.. my answer is 0.7 !!

    What is the value of n_i for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the H atom?

    my solution..

    n_f=1
    λ=93.14 nm×(10^(-9) m)/(1 nm)=93.14×10^(-9) m
    ∆E=hν=hc/λ=(6.63×10^(-34)×3.00×10^8)/(93.14×10^(-9))≈2.14×10^(-18)
    ∆E=-2.18×10^(-18) (1/(n_f^2 )-1/(n_i^2 ))
    2.14×10^(-18)=-2.18×10^(-18) (1/1^2 -1/(n_i^2 ))
    -2.14/2.18=1-1/(n_i^2 )
    1.982= 1/(n_i^2 )
    n_i^2=0.5045
    n_i=√0.5045≈0.7

    n_i = n initial
    n_f = n final
    λ = wavelength ( lambda )
    ∆E = energy of the transition
    h = plank's constant
    ν = frequency ( nu )
    c = speed of light

    if reading the solution is an issue.. just past it in microsoft word and activate the equation mode..
     
    Last edited: May 7, 2010
  2. jcsd
  3. May 7, 2010 #2

    Borek

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    Staff: Mentor

    Re: this problem is killing me!! [calculation of electron transition]

    We have something called LaTeX for such situations. And I don't have, use, nor want to use Microsoft Word.

    When I solve

    [tex]\frac 1 {93.14nm} = R_{\infty} (\frac 1 {1^2} - \frac 1 {n^2})[/tex]

    for n, I get 6.85 - close enough to 7. No idea what is 2.18x10-18, as far as I can tell Rydberg constant is 1.097x107 m-1.

    --
    methods
     
  4. May 7, 2010 #3
    Re: this problem is killing me!! [calculation of electron transition]

    2.18x10-18 is the Rhydberg constant in joules.
     
  5. May 8, 2010 #4

    Borek

    User Avatar

    Staff: Mentor

    Re: this problem is killing me!! [calculation of electron transition]

    OK, I know what have happened. Check your math, you made a simple error when solving.

    --
    methods
     
  6. May 8, 2010 #5
    Re: this problem is killing me!! [calculation of electron transition]

    i already figured it out.. since the electron is returning to its ground state.. it is releasing energy.. which means that ∆E is negative.. after taking that into consideration.. the answer should be 7..

    wow.. it makes more sense to me now!

    thank you.
     
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