Question 1:

Question

In the Balmer-Rydberg equation, what value of m is used to determine the wavelengths of the Balmer series?
m=?
Question 2:
List a possible set of four quantum numbers (n,l,ml,ms) in order, for the highest energy electron in gallium,Ga.

Answer 1

In the equation, which can be seen here,
http://en.wikipedia.org/wiki/Rydberg_formula
m is an integer. The Balmer series consists of lines from the transition 3 to 2, 4 to 2, 5 to 2, 6 to 2, etc.
For the second question, click on Ga, scroll down to the electronic structure, and look at the outside electron(s). Then you can write n, l, ms and ml.

Answer 2

m=2