Question

How would you find the quantum numbers for an atom?

Answer 1

See explanation.

Explanation:

Quantum numbers are considered as the coordinates that will give an idea about the location of an electron in an atom.

There are four different quantum numbers:

1. Principal Quantum Number (n) has integral values 1, 2, 3, ... This number determines the size and energy of the orbital.

2. Angular Momentum Quantum Number (`l`) associated with the number of different types of subshells in an energy level. `l=0, 1, 2, 3, ... (n - 1)`.
   

3. Magnetic Quantum Number (`m_l`) describes the orientation (direction) in space of each orbital and can have integral values from `- l` through `+l`.
   

4. Electron Spin Quantum Number (`m_s`) describes the direction of spin of the electron(s) in an orbital. There are only two values of `m_s, +1/2 "and" -1/2`.

Note that no two electrons may have identical sets of all 4 quantum numbers.

Consider the electron configuration of sodium `""_11Na`:

`""_11Na:1s^(2)2s^(2)2p^(6)color(red)(3)color(blue)(s)^(color(green)(1))`

What would be the set of quantum numbers of the valence electron of sodium:
`color(red)(n=3)`: third energy level.
`color(blue)(l=0)`: sublevel or subshell `s`.
`color(blue)(m_l=0)`: one possible orbital.
`color(green)(m_s=+1/2) or color(green)(-1/2)`: the electron spin.