the fourth number?

[Annie Chantasirivisal_4G]

hi guys!

can anyone explain to me the significance of the fourth quantum number aka the spin magnetic quantum number? I'm having trouble understanding why it would be significant to know how the electrons are reacting in an atom compared to the other three numbers... like what more does it tell us aside from the size, shape and axis that the other three numbers already tell us?

[Chem_Mod]

The first three quantum numbers (n, l, m_l) are essentially the describing the environment in which the electron is located. Namely, which energy shell (i.e. n=3), the shape of the energy subshell it is in (i.e. p-orbital), and the orientation of the orbital it is in (i.e. p_z orbital).
The fourth quantum number, m_s, is distinct in that it tells about the electron itself, not its location. It tells us whether the electron is spinning clockwise( spin down, m_s = -1/2) or counterclockwise (spin up, m_s = + 1/2)

[Alvaro Chumpitaz 4D]

I believe the 4th number is arbitrary as all you have to know is if there are 2 electrons in a box diagram then one is +1/2 and the other is -1/2. And if it is a single electron in the box it is still arbitrary.

[Rida Ismail 2E]

the 4th number does not tell you anything about the placement of the e-. It only states that in the pairs of e- in orbitals the e- must be spinning in different directions. So in order to fill the e- shell in an orbital the arrows (representing 1/2 and -1/2) must go in the opposite directions

[madijohnson_4A]

The fourth number is really just there to demonstrate that the electrons are not identical: they are spinning in opposite directions.That is why the options for ms are +1/2 and -1/2.