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.
I HAVE NO IDEA
To identify the initial state for each line in the H atom spectrum, we need to understand the energy level transitions involved. The energy levels in the hydrogen atom are described by the Rydberg equation:
1/λ = R_H * (1/n_i^2 - 1/n_f^2)
where λ is the wavelength of the electromagnetic radiation, R_H is the Rydberg constant for hydrogen, n_i is the initial energy level, and n_f is the final energy level.
Let's analyze each line:
a). Wavelength = 1212.7 Å
This line corresponds to a transition where n_f = 2. We can set up the Rydberg equation using this information:
1/λ = R_H * (1/n_i^2 - 1/2^2)
To find the initial state (n_i), we need to rearrange the equation and solve for n_i:
n_i = √(1 / (1/2^2 - 1/λ*R_H))
b). Wavelength = 4340.5 Å
This line also corresponds to a transition where n_f = 2. Using the Rydberg equation, we have:
1/λ = R_H * (1/n_i^2 - 1/2^2)
Rearranging the equation, we get:
n_i = √(1 / (1/2^2 - 1/λ*R_H))
c). Wavelength = 4861.3 Å
This line corresponds to a transition where n_f = 2. We can use the Rydberg equation:
1/λ = R_H * (1/n_i^2 - 1/2^2)
Rearranging, we find:
n_i = √(1 / (1/2^2 - 1/λ*R_H))
d). Wavelength = 6562.8 Å
For this line, the transition is to nf = 3. Applying the Rydberg equation:
1/λ = R_H * (1/n_i^2 - 1/3^2)
And solving for n_i:
n_i = √(1 / (1/3^2 - 1/λ*R_H))
e). Wavelength = 10938 Å
The transition for this line is to nf = 1. Using the Rydberg equation:
1/λ = R_H * (1/n_i^2 - 1/1^2)
Solving for n_i:
n_i = √(1 / (1/1^2 - 1/λ*R_H))
Now you can substitute the values of λ and R_H into the equations to find the initial energy levels (n_i) for each line.