Electromagnetic emission lines for a hydrogen atom

[Jdraper]

Homework Statement

Hi, I've been unable to find a relevant thread for a question that I've been stuck on for a couple of days now.

Here it is;

One of the electromagnetic emission lines for a hydrogen atom has wavelength 389nm. Assiming that this is a line from one of the Lyman (n_f =1 ), Balmer (n_f = 2) or Paschen (n_f =3) series, what is the initial principle quantum number associated with the transitions? The Rydberg energy can be assumed to be 13.6eV

Homework Equations

ΔE=Ry(1/(n_i)² - 1/(n_f)²))
Ry=13.6eV

This is the formula used to attempt a solution

There is another formula in my notes that may be helpful but i do not understand the symbols within it, it is;
E_n,l = -Ry/(n-δ_l)²

The Attempt at a Solution

Using the equation ΔE=Ry(1/(ni)2 - 1/(nf)2)) and then equating this change in energy to the energy of light E=hc/λ.
Ry=13.6eV
Then I insert various n_f 's e.g. n_f =1 for Lyman, then i would solve this for n_i to see if i get an integer number, indicating that this is correct. I do this for n_f =1,2 and 3 and I have never got an integer number leading me to believe my method is incorrect.

Any help or insight would be appreciated,

Thanks in advance, John.

 

[MisterX]

You should have gotten something close to an integer if you tried the right $n_f$ but perhaps a simpler way is to just search tables which have already been complied.

http://hyperphysics.phy-astr.gsu.edu/hbase/tables/hydspec.html

 

[Jdraper]

I forgot to mention doing these questions are purely for exam practice. So having the tables will no be an option.

How would i do this in an exam? Simply put the numbers in as i have done and then chose the one which is closest to an integer value to be the correct one?

Thank, John

 

[TSny]

Using the equation ΔE=Ry(1/(ni)2 - 1/(nf)2))

Check your equation in regard to the placement of ni and nf.

I think your approach to the problem is good.

 

[Jdraper]

Ahh, yes, the n_i and n_f are the wrong way around. Thanks for your help :)