Experiment 10  Problems
Use Rydberg equation to solve problems:
1. An electron de-excites from n=8 to n=3. 

    Calculate the wavelength of the emitted radiation.

      91.1nm/l = 1/m2 - 1/n2 = 1/32 - 1/82 = 0.111 - 0.0156 = 0.0954 

    l = 91.1nm/0.0854 = 945nm


2. One electron de-excites from n = 7 to n = 3, while another de-excites 

     from n = 3 to n = 2. Which emits the greater energy? Explain!

    7 to 3 l = 91.1nm/(0.111 - 0.0204) = 91.1nm/0.0906 = 1010nm

    3  to 2    l = 91.1nm/(0.250 - 0.111) = 91.1nm/0.139 = 655nm

    3 to 2 since the shorter l exhibits the greater energy!

 

3. Determine the initial and final energy levels for lines at:

   (a) 120nm  91.1nm/120nm = DIF = 0.759  Best fit is 2 to 1 (1.00 - 0.25 = 0.75)

   (b) 400nm  91.1nm/400nm = DIF = 0.223  Best fit is 7 to 2  (0.250 - 0.0204 = 0.223)

   (c) 1100nm 91.1nm/1100nm = DIF = 0.0828  Best fit is 6 to 3  (0.111 - 0.0278 = 0.0832)

4. (a)  Shortest:   91.1nm/l = 1/m2 - 1/n2 = 1/42 -  0 = 0.0625
                           l = 91.1nm/0.0625 = 1460nm

    (b)  Longest:   91.1nm/l = 1/m2 - 1/n2 = 1/52 -  1/62  = 0.0122
                           l = 91.1nm/0.0122 = 7450nm
 

5. Is it possible to emit blue light (400-450nm) if an electron returns to:

   (a) Third Shell

    Using 425nm as average for blue light, 91.1nm/425nm = 0.214 = DIF

    The maximum DIF possible for returning to third shell is 1/32 - 0 = 0.111

    NOT POSSIBLE!
 

   (b) Second Shell

    Using 425nm as average for blue light, 91.1nm/425nm = 0.214 = DIF

    The maximum DIF possible for returning to second shell is 1/22 - 0 = 0.250

    POSSIBLE if returning from 5th shell  DIF = 0.250 - 0.0400 = 0.210
 

6. Is it possible to emit red light (650-700 nm) if an electron returns to: 

   (a) Third Shell

    Using 675 nm as average for red light, 91.1nm/675nm = 0.135 = DIF

    The maximum DIF possible for returning to third shell is 1/32 -  0  = 0.111

    NOT POSSIBLE!
 

   (b) Second Shell

    Using 675nm as average for red light, 91.1nm/675nm = 0.135 = DIF

    The maximum DIF possible for returning to second shell is 1/22 - 0 = 0.250

    POSSIBLE if returning from third shell DIF = 0.250 - 0.111 = 0.139