Solutions

1) The logic for this problem is pretty straightforward (Isn't that always what the instructor says?). Big energy differences between orbits mean higher energy photons. High-energy photons have shorter wavelengths and hence more blue colors than low energy photons. The answer to question 1.1 is (a), the jump from orbit 4 to Orbit 3. This is true because you were asked to make the spacing between these orbits (the energy difference) large. The answer to question 1.2 is also (a), the jump from Orbit 1 to Orbit 2 since the spacing between these orbits (the energy difference) should be small.

There is one subtle but important point to notice. If two sets of orbits have the same difference in spacing from the nucleus, they will not have the same energy difference. You can see this by playing with the applet. The reason is simple: the energy difference between the orbits depends not only about how far each orbit is from the other, but also how far each orbit is from the nucleus.

2) If the source moves away from the atom, its light is ?doppler-shifted? towards the red, making the wavelength longer. The atom would not be able to absorb these photons, since the energy jump between its third and fourth orbits no longer corresponds to the (now reduced) energy of the red-shifted photons. If the orbits could be brought closer together, the energy difference of the jump would be smaller and the atom might be able to absorb the red-shifted photons.

3) The algebraic steps are given below. Start with energy in a jump,

Then consider the energy in a photon,

The two are equal so,

Solving for wavelength gives you

which is also,

4) If the energy of the photon is 1.8 eV then using the formula we dervied above gives us

or

This is in the red region of the spectrum.