# Atomic absorption spectrum

1. Jun 9, 2013

### unscientific

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

The following photon wavelengths are observed in absorption at room temperature from an ionized atomic gas with a single electron orbiting the nucleus: λ=
13:5 nm, 11:4 nm, 10:8 nm. Use this data to determine the effective Rydberg constant
and the nuclear charge.

2. Relevant equations

3. The attempt at a solution

I know that energy is emitted/absorbed when electron transits between different energy levels.

Thing is, I don't even know what the n=1 energy is, to find the rydberg constant. I can't tell what the energy levels are just from the photons absorbed, as they could be between any two levels.

2. Jun 9, 2013

### Staff: Mentor

Don't give up before you even started.
Did you convert the wavelength values to photon energies?
Which patterns do you expect in the energy spectrum?

3. Jun 9, 2013

### unscientific

I expect, the gaps between energy levels to become smaller as you go higher up..

4. Jun 9, 2013

### unscientific

13.5nm -> 92.1 eV
11.4nm -> 109.0 eV
10.8nm -> 115.1 eV

So

n=1 is 92.1 eV
n=2 is 109.0 eV
n=3 is 115.5 eV

Then what is the point of giving us the other 2 absorption wavelengths?

5. Jun 9, 2013

### Staff: Mentor

Photon energies are not the energies of states!

Which photon energies (not electron energy states) do you get for a hydrogen atom? Which ratios do you have between those values? Do you see a similarity to your problem?

6. Jun 9, 2013

### unscientific

For Hydrogen:

E1 = -13.6 eV
E2 = -3.4 eV
E3 = -1.51 eV
E4 = -0.850 eV

Based on the wavelengths given, 92.1eV, 109eV, 115.5eV are differences in energy between En and E1.

The ratio of first energy level between the gas and hydrogen = Z2, where Z is the proton number of the gas.

7. Jun 9, 2013

### unscientific

Ok using the relation ΔE = (1- 1/n2)

First emission:
92.1 = E1(3/4)

Second emission:
109 = E1(8/9)

Third Emission:

115.5 = E1(15/16)

These ratios match, so somehow these are the emissions from the second, third and fourth energy levels.

E1 = (13.6)Z2

Solving, Z = 3 (Lithium) and E1 = 122.4eV, R = (13.6eV)/hc = 1.09*107

Last edited: Jun 9, 2013
8. Jun 10, 2013

### Staff: Mentor

That is correct.

I think the factor of 9 is missing here, and the last value should have units.

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