Three of the strongest lines in the Li^2+ ion spectrum are observed at the follo

Question

Three of the strongest lines in the Li^2+ ion spectrum are observed at the following wavelengths: 11.397 nm; 54.030 nm; 72,941 nm, Find the quantum numbers of the initial and final states for the transitions that give rise to these three lines. Do this by calculating, using Equation 4, the wavelengths of lines that can originate from transitions involving any two of the four lowest levels. You calculated one such wavelength in Part b. Make similar calculations with the other possible pairs of levels. When a calculated wavelength matches an observed one, write down n_hi and n_lo for that line. Continue until you have assigned all three of the lines.

Explanation / Answer

we use Rydberg formula

1/lamda = RZ^2 ( 1/n1^2 -1/n2^2)

1/(11.397x10^-9) = ( 10967700) x 3^2 ( 1/n1^2 -1/n2^2)

0.888 = ( 1/n1^2 -1/n2^2)

n1 = 1 , n2 = 3 ,   hence transition is 3 to 1.

2) 1/(54.03 x 10^-9) = ( 10967700) x 3^2 x ( 1/n1^1 -1/n2^2)

0.1875 = 1/n1^2 -1/n2^2

n1 = 2 , n2 = 4 , hence transition is 4 to 2

3) 1/( 72.941x10^-9) = ( 10967700) x 3^2 ( 1/n1^2 -1/n2^2)

0.1389 = ( 1/n1^2 -1/n2^2)

n1 =2 , n2 = 3   hence transition is 3 to 2

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