University:
Massachusetts Institute of Technology
Course:
3.091SC | Introduction to Solid State Chemistry
Academic year:

2022
Views:

27

Pages:

2
Author:

carpianoig1

Session #5: Homework Solutions Problem #1 A line of the Lyman series of the spectrum of hydrogen has a wavelength of 9.50 x 10–8 m. What was the “upper” quantum state (ni) involved in the associated electron transition? Solution The Lyman series in hydrogen spectra comprises all electron transitions terminating in the ground state (n=1). In the present problem it is convenient to convert λ into ν and to use the Rydberg equation. Since we have an “emission spectrum”, the sign will be negative in the conventional approach. We can avoid the sign problem, however: ⎛ 1 ⎛ 1 ⎞ 1 ⎞ ν = R ⎜ 2 - 2 ⎟ = R ⎜1 - 2 ⎟ ⎜n ⎜ ni ⎟⎠ ni ⎟⎠ ⎝ f ⎝ ⎛ ν 1 ⎞ = ⎜1 ⎟ ⎜ R ni2 ⎟⎠ ⎝ 1 ni2 =1- ni2 = ni2 = ni = ν R- ν = R R R R- ν R R- ν ν = 1 -8 9.5 x 10 m 1.097 x 107 1.097 x 107 - 1.053 x 107 = 1.053 x 107 m-1 =5 Problem #2 List the possible values of the four quantum numbers for a 2p electron in boron. Solution For 2p n l m s 2 2 2 2 2 2 1 1 1 1 1 1 -1 -1 0 0 1 1 ½ -½ ½ -½ ½ -½