# Ionisation Energy of Hydrogen

1. May 26, 2009

### mrausum

1. The problem statement, all variables and given/known data

The wavelengths λ of spectral lines produced by the Hydrogen atom are given by the expression:

.

Calculate the Energy in eV required to ionise the atom

2. Relevant equations

p=h/$$\lambda$$

3. The attempt at a solution

n2 = 1 and n1 = infinity, therefore $$\lambda$$=1/R.

E = p2/2m = h2/($$\lambda$$^2*2Me)

Subbing in $$\lambda$$=1/R. and rearranging gives:

E = (h2R2)/(2Me)

Why doesn't this give me the right answer?

Last edited: May 26, 2009
2. May 26, 2009

### Redbelly98

Staff Emeritus
In that equation, λ is the deBroglie wavelength of the electron, and not the wavelength of the photon. So I'm afraid it isn't relevant here.

Instead, what other equation do you have that relates the energy and wavelength of a photon?

3. May 26, 2009

### mrausum

So it's just as simple as using E = hc/lamda = hcR?

4. May 26, 2009

### Redbelly98

Staff Emeritus
Yes.

5. May 26, 2009

### mrausum

ah i see what's going on now - the equation gives the wavelength of the emitted photon not the wavelength of the electron? Thanks.

6. May 26, 2009

### Redbelly98

Staff Emeritus
Yup!

You're welcome.