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Scholar
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Date Posted: 5/16/2008 7:19:57 AM  Status: Live
physcics problem....help....
Course Textbook Chapter Problem
Calculus Based Physics Physics for Scientists and Engineers A Strategic Approach 1st by Knight N/A N/A
Question Details:
1. The wavelengths in the hydrogen spectrum with m = 5 form a series of spectral lines called the Pfund series. Calculate the wavelengths of the first four members of the Pfund series.

2.indicate the m and n values when the wavelength is 1282.2

please,... help.....
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Oracle
Karma Points: 21,464
(Ohio University Main Campus)
Date Posted: 5/16/2008 10:57:07 AM  Status: Live
Asker's Rating: This answer has not been rated. If you asked this question, then please login.   
Response:
This is pretty lengthy. Pl do not forget to Rate.
 
Wavelength, λ = ? ΔE = hc/λ; λ = hc/ΔE
The lowest energy level for Pfund series is,
         E5 = E1/5x5 = 13.6 eV/25 = 0.544 eV
         E6= E1/6x6 = 13.6 eV/36 = 0.3778 eV
         E7 = E1/7x7 = 13.6 eV/49 = 0.2775 eV
         E8= E1/8x8 = 13.6 eV/64 = 0.2125 eV
         E9 = E1/9x9 = 13.6 eV/81 = 0.1679 eV
     ΔE65 = 0.1662 eV;      ΔE75 = 0.26645 eV
     ΔE85 = 0.3315 eV;      ΔE95 = 0.3761 eV
 
Wavelength λ = hc/ΔE ; On substitution
 λ = 7474 nm, 4663 nm, 3748 nm, and 3303 nm.
 
(b) Given λ = 1282 nm
Corresponding ΔE = hc/λ = 1.5505x10-19 J
                             = 0.9691 eV
By inspection of the values E in eV for various values of m, n we find,
this ΔE = 0.969 eV = E5 - E3 = (-0.544 - -1.511 ) = 0.967 eV
So, the values of m, n are 3 and 5
 
 
 
Kayen (Enjoys helping you uderstand..)
Please do not forget to Rate my Response.

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Mentor
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(Howard University)
Date Posted: 5/16/2008 5:29:31 PM  Status: Live
Asker's Rating: This answer has not been rated. If you asked this question, then please login.   
Response:
Using Rydberg's formula:   1 / λ = R ( 1 / m2  - 1 / n2  )
 
  1.                                        1 / λ = R ( 1 / 52 - 1/ 62 ) =
                                          1 / λ = R ( 1 / 52 - 1 / 72 ) =
                                          1 / λ = R ( 1/ 52  - 1 / 82 ) =
                                          1 / λ = R ( 1 / 52 - 1/ 92 ) =
   2.  We can't have two unknowns m and n ... also 1282.2 ? What units nm , angstrums, ?
            Substitute λ and m; solve for n using formula.



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