# Energy of atoms in different levels

1. Apr 13, 2012

### Noirchat

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

In a set of experiments on a hypothetical one-electron atm, you measure the wavelengths of photons emitted as electrons return to the ground state (n=1), as shown in the energy level diagram. You also observe that it takes 17.50 eV to ionise this atom.

Diagram shows:
n=5 --> n=1 ~ λ = 73.86nm
n=4 --> n=1 ~ λ = 75.63nm
n=3 --> n=1 ~ λ = 79.76nm
n=2 --> n=1 ~ λ = 94.54nm

(i) What is the energy of the atom in each of the levels n=1 to n=5

(ii) If an electron makes a transition from the n=4 to the n=2 level, what wavelength of light would it emit?

2. Relevant equations

None provided

3. The attempt at a solution

My attempt at A

I think i use this equation:
E = -hxR/n^2

where:
h is Planck's constant 6.626 x 10^-34
R is Rydbergs constant 1.097 x 10^7
and n is the energy level

at n=5 i get: -2.907 x 10^-28
at n=4 i get: -4.543 x 10^-28
at n=3 i get: -8.076 x 10^-28
at n=2 i get: -1.817 x 10^-27
at n=1 i get: -7.269 x 10^-27

I think i use balmers equation in part B?

1/λ = R(1/2^2 - 1/4^2) where R= 1.097 x 10^7

1/λ = 2056875

I have a feeling i'm doing this all wrong.

2. Apr 13, 2012

### fzero

What does ionization mean? How does the ionization energy relate to the ground state energy?

3. Apr 14, 2012

### Noirchat

Isn't it the minimum energy needed to dislodge an electron so it can move between energy states?

4. Apr 14, 2012

### fzero

For ionization, the final state is a free electron: it is no longer one of the bound energy states. This sets a reference point. Each bound state energy can be measured with respect to the lowest energy free state.

5. Apr 14, 2012

### Noirchat

Ok, that makes sense to me. So have i used the wrong equation?