SCI 270: On Nuclear Technology Practice Problems  

3. Atoms - the tiny wonders

  1. When heated to very high temperature or passing a electric discharge through, a hydrogen gas glows, emitting a purplish light. When analyzed by a prism, the light consists of a few lines with wavelengths listed in the Table.

    Wavelength, l Wavenumber, 1/l Frequency, c/l Photon energy, h v n in Balmer series.
    nm 106 m-1 1014 Hz 10-19 J Integer
    656.3       
    486.1       
    434.0       
    410.1       
    396.9       
    389.0       

    Convert the wavelengths l to wavenumbers and frequencies using the given formulas in multiples and units as indicated. Also evaluate the n in the Balmer series.

  2. From the values above, draw a spectrum indicating where the lines will be observed based on a linear frequency scale.

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    |4____________________5____________________6____________________7___________/e14 Hz
    

    The Rydberg relationship is usually given in the form as follows:

    1
    ---
    l
    = - R (1
    ---
    n2
     - 1
    --- )
     4

    The Rydberg constant R is
    ________________________ m-1

    However, the Rydberg relationship can be written for frequency (v) as follows:

    v = - R (1
    ---
    n2
     - 1
    --- )
     4

    The Rydberg constant R is
    ________________________ Hz

  3. The Bohr model and the quantum mechanical approach result in an expression for the Rydberg constant R:

            2 p2 m Z2 e4
    R = --------------- = 10967700 m-1
                c h3

    where m, Z, c, h and e are the mass of the electron, atomic number, speed of light, Planck's constant, and charge of an electron respectively.

    Apply this number to calculate the wave numbers of the 5 lines (nf = 2, 3, 4, 5, and 6; ni = 1) of the Lyman series.

    The formula used:
    _____________________________
    Wave numbers of the five lines

    _____________

    _____________

    _____________

    _____________

    _____________

    In what regions are these lines within the electromagnetic radiation spectrum, visible, UV, IR, Microwave, or X-ray?

    These lines are in the region of

    _______________________________

  4. The characteristic X-rays of some elements are listed here,

    Atomic
    number
    ElementWavelength Frequency Frequency(1/2) Photon energy, h v
        nm 1018 Hz 109 Hz(1/2) 10-15 J
    23 V 0.2503 1.199    
    24 Cr 0.2289 1.310    
    25 Mn 0.2102 1.427    
    26 Fe 0.1936 1.550    
    27 Co 0.1789 1.677    
    28 Ni 0.1657 1.810    
    29 Cu 0.1541 1.947    
    30 Zn 0.1435 2.090    
    42 Mo 0.0746 4.020    
    47 Ag 0.0559 5.363    
    79 Au 0.0180 16.650   

    Complete the Table by taking the square root of the frequencies, and plot them against the atomic number Z on a graph to see if these data obey the Moseley's law.

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    Evaluate the photon energies and plot them against Z2 to see if they fit a straight line.

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  5. Apply the Moseley's law to estimate the wavelength of characteristic X-rays from hydrogen, (H, Z = 1), aluminium (Al, Z = 13), tin (Sn, Z = 50), and uranium (U, Z = 92).

    The wavelengths are given below
    H Al Sn U

    _____________

    _____________

    _____________

    _____________

Answers to Assignment 3 is available, but do your part first. Your skills are your best friends they are yours forever.

© cchieh@uwaterloo.ca