Five lines in the H atom spectrum have the following wavelengths in Ǻ: a). 1212.7, b). 4340.5, c).
4861.3 d). 6562.8 and e). 10938. Three lines result from transitions to the nf = 2. The other two
result from transitions in different series, one with nf = 1, and the other with nf = 3. Identify the initial
state for each line.
1/wavelength = R*(1/N1^2 - 1/N2^2)
R = 1.0973732 x 10^7 when wavelength is in meters. This will allow you to solve for either N1 or N2. In this formula, N1<N2.
Im confused though, it says three lines result from transitions to the nf=2, which three lines?
Redi
h.atomspectrumwavelengthin(A):-A/1212.7transefertoN,final=2
To identify the initial state for each line in the H-atom spectrum, we need to understand the energy level transitions that correspond to the given wavelengths. The energy levels in the hydrogen atom are represented by quantum numbers, with the ground state having the lowest energy level (n=1) and higher energy states represented by increasing values of n.
Let's analyze each line and determine the initial state:
a) Wavelength: 1212.7 Å - This corresponds to the transition nf = 2 to ni = ???
To find the initial state (ni), we need to recognize that this wavelength corresponds to a transition ending at nf = 2. The possible initial states will have ni = nf + 1. Therefore, ni = 2 + 1 = 3.
So, the initial state for this line is n = 3.
b) Wavelength: 4340.5 Å - This corresponds to the transition nf = 2 to ni = ???
Again, we are looking for the initial energy level (ni) that corresponds to a transition ending at nf = 2. The initial state will be ni = nf + 1. Therefore, ni = 2 + 1 = 3.
So, the initial state for this line is n = 3.
c) Wavelength: 4861.3 Å - This corresponds to the transition nf = 2 to ni = ???
Following the same logic as before, the initial state (ni) will be ni = nf + 1. In this case, ni = 2 + 1 = 3.
So, the initial state for this line is n = 3.
d) Wavelength: 6562.8 Å - This corresponds to the transition nf = 2 to ni = ???
Once again, the initial state (ni) is obtained by ni = nf + 1. Here, ni = 2 + 1 = 3.
So, the initial state for this line is n = 3.
e) Wavelength: 10938 Å - This corresponds to the transition nf = 3 to ni = ???
For this line, the final state is nf = 3. To find the initial state, we need to recognize that ni = nf + 1. Therefore, ni = 3 + 1 = 4.
So, the initial state for this line is n = 4.
In summary:
a) Initial state: n = 3
b) Initial state: n = 3
c) Initial state: n = 3
d) Initial state: n = 3
e) Initial state: n = 4
Thus, the initial states for the five lines in the H-atom spectrum are identified.
I would plug in N1 = 2, then N2 = 3 and calculate the wavelength. Perhaps that will give you 1 of the lines. Then N = 4 (their running numbers like that, all whole numbers) and you can identify another of the lines. Then n = 5 and you can identify the next one. If nothing fits one of the number you insert, just make sure your arithmetic is ok and go to the next. Rydberg (the R in the formula) did that strictly on an empirical basis and found the constant R and the running series of the Balmer (which ends in N = 2), the Lyman (which ends in N = 1), the Paschen (which ends in N = 3) etc. It must have been tedious. You can read more about it here. In fact, you probably can pick out the lines you have from this site, also.
http://en.wikipedia.org/wiki/Hydrogen_spectral_series