Hydrogen -Energy State Transitions

[Berdi]

Homework Statement

Find the (algebraic) relationship between the wavelengths of the equivalent transitions (i.e. same n1 and n2) for hydrogen-like ions of atomic number Z and hydrogen itself.

Homework Equations

I know:

$$h\nu (n_{1} , n_{2} ) = C_{1}Z_{1}^2(\frac{1}{n_{2}^2} - \frac{1}{n_{1}^2})$$

And

$$\nu = \frac{c}{\lambda}$$

The Attempt at a Solution

But that's as far as I can get really. I know putting Z as 1 will give me the simplest case for Hydrogen, but I'm still a bit perplexed at what the question actually wants. I could rearrange for $$\lambda$$, but I'm still unsure if that's on the right lines?

Thanks.

 

[Delphi51]

Use lambda = h/v = h^2/(hv) = h^2/(C*Z^2*X)
where X is the big pair of brackets with the transition numbers in it.
You want to compare this with the same expression for hydrogen which is h^2/(C*1*X) unless the C is different for hydrogen, too.
They are the same except for the Z^2 so you'll end up with
lambda = 1/Z^2 * (lambda for H)

 

[Berdi]

Sorry, I just realized I've written rubbish:

$$\nu = \frac{c}{\lambda}$$ Is what is meant to be there!

Sorry