Energy of atoms in different levels

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.

fzero

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

Noirchat

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

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.

Noirchat

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