answer the following questions assuming that m (subscript s) could have three values rather than two and the rules for n, l and m (subscript l) are the normal ones.

Question

1. how many electrons would an orbital be able to hold?

2. how many elements would the first period in the periodic table contain?

3. how many elements would the second period in the periodic table contain?

4. how many elements would be contained in the first transitional metal series?

5. how many electrons would the set of 4f orbitals be able to hold?

Answer 1

Here is what you should do.
First, make a table containing the normal values.
Remember:
N can be 1, 2,......etc. whole numbers.
l can be 0, 1, 2....N-1
m_l can be -l to +l in whole increments.
M_s can be +/- 1/2.

Then count up
period 1 = 1s2 = 2 elements.
period 2 = 2s2 2p6 = 8 elements.
period 3 = 3s2 3p6 = 8 elements.
period 4 = 4s2 3d10 4p6 = 18 elements.
etc.

The answer to 1 is 3.
The answer to 2 is 3.
The answer to 3 is 12.
You get the idea how to do this. Just follow the chart you made at the beginning and you can count up to get 4 and 5. Check my thinking and my counting.