Frequently Asked Questions about PS-1

Question 1-32

> > Hello!  I'm one of your quantum students and I was wondering about one of
> > the questions in the first assignment.  In question 1-32, it asks for the
> > derivation of an equation describing the wavelengths of the Pickering
> > series.  Does the extra proton come into consideration anywhere?   Thanks
> > for your time.

Yes.  The Z (atomic number) does come into play here.  You need to do 1-31
first.  Follow the derivation for the H atom but modify the electrostatic
(Coulomb) force for Ze (Z protons, where Z is the atomic number) and e (1
electron).   Eventually, you can show that we have to modify the normal
Rydberg formula for the H atom by 

Z to the "x" power (you have to find x here - Hint x is an integer and is
less than 10).

The Rydberg formula for any atom with Z atomic number looks exactly the
same as that for H atom except for this modification.  Once you get this,
then you are home free.  Plug in the n and m and compute the transition
energy and hence find the amount of radiation that the atom will absorb.

Note the mass remains to be the same as the mass of the electron because we
are calculating the force acting on a single electron in its "Bohr orbit".