Single Electron Ions Homework: Find Wavelengths

[AnniB]

Homework Statement

In a hot star, a multiply ionized atom with a single remaining electron produces a series of spectral lines as described by the Bohr model. The series corresponds to electronic transitions that terminate in the same final state. The longest and shortest wavelengths of the series are 63.3 nm and 22.8 nm, respectively. a.) What is the ion? b.) Find the wavelengths of the next three spectral lines nearest to the line of longest wavelength.

Homework Equations

E_n = -13.6 Z²/n²
1/ $$\lambda$$ = R((1/n_f²) - (1/n_o²))

The Attempt at a Solution

To be honest, I'm not even sure where to start. I did try finding n_f for the shortest wavelength assuming that the electron started at n = infinity, but it gave a decimal value. The only other thing I can think of is somehow assuming the n in the first equation and the n_f in the second are equivalent.

 

[Borek]

What do you mean "it gave a decimal value"?

Second equation you are using is probably wrong - depends on what R value you are using. I guess you used R for hydrogen atom.

 

[AnniB]

I got an answer for n_f which was something like .50034, which I know can't be right since it has to be an integer.

I used R = 1.097 * 10^-7. I don't know how I'd find it for the ion I have especially since I don't even know what it is. My professor also said the only unknowns should be Z and n_f.

 

[Borek]

http://en.wikipedia.org/wiki/Rydberg_equation#Rydberg_formula_for_any_hydrogen-like_element

http://en.wikipedia.org/wiki/Rydberg_constant

 

[AnniB]

Okay. I'm using the new equation but for some reason when I try to solve all the variables end up canceling somehow.

I'm assuming that the longest and shortest wavelengths correspond to shifts from n_o = $$\infty$$ to n_f and n_o = n_f + 1 to n_f respectively. Is that valid?

 

[Borek]

I'm assuming that the longest and shortest wavelengths correspond to shifts from n_o = $$\infty$$ to n_f and n_o = n_f + 1 to n_f respectively. Is that valid?

Probably yes.

$n_\infty$ wavelength should let you calculate final state - just solve for n_f, as

$$\frac 1 {n_\infty}$$

is 0.