how many combinations are possible with the four quantum numbers?

San K

1. how many combinations are possible with the four quantum numbers?

2. Does Pauli's exclusion principle apply only to electrons within the same atom?

can it apply across atoms as well? how is the exclusion principle generalized across atoms?

mfb

1.: Which quantum numbers do you mean? Electrons in an atom? The number is (countable) infinite.

2.: No, it is valid for all electrons, but in systems with multiple atoms you get different energy eigenstates and therefore different quantum numbers.

jtbell

In principle, an infinite number. In practice, it depends on how high you can go with the principal quantum number (n) in a particular physical situation. As n increases, it becomes easier to ionize an atom and more difficult to keep it together. Look at the energy levels for hydrogen, for example, and see how they approach E = 0 as n increases.

San K

Thanks mfb and jtbell.

1. How many combinations are possible with the four quantum numbers, with/when principal quantum number (n) = 1?

Assume these are electrons around a nucleus.

2. In a system with multiple atoms:

Is n=1 different than n=1 in a neighbouring atom, for determining the combinations and permutations of the four quantum numbers?

jtbell

Have you looked up the rules for the hydrogen quantum numbers?

http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html

Try it for yourself and tell us what you get.