What do the four quantum numbers stand for?

Answer 1

Principal quantum number (#n#) - the energy the electron occupies, where #nge1, and ninZZ#.

Angular momentum quantum number (#ℓ#) - This describes the type of orbitals the electron resides in, where #ℓge0, ℓinZZ, and ℓltn#. It also gives the number of angular nodes, and therefore describe its shape.

If #ℓ=0# it is the s-orbital, if it is 1 then it is the p-orbital, 2 means d-orbital, etc. This number is often pair with n, so that if #n=4, and ℓ=2#, it is in the 4d subshell.

Magnetic quantum number (#m_ℓ#) - describes the orientation of the orbital, where #m_ℓ# can be anywhere from #-ℓ to +ℓ#, and #m_ℓinZZ#

There are #2l+1# orbitals per subshell. This is proven as if #ℓ=1#, then #2(1)+1=3#, there are three orbitals for the p subshell. If #ℓ=2#, then #m_ℓ =-2, -1, 0, 1, 2#, 5 orbitals for d-subshells.

Spin quantum number (#m_s#) - describes the spin of an electron where #m_s = -1/2 or +1/2#, where #-1/2# means spin down, and #+1/2# means spin up.

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Answer 2

Natalie Anton

The electron's energy level is represented by its principal quantum number (n). Its orbital shape and angular momentum are indicated by its azimuthal quantum number (l). Its orbital orientation within a subshell is specified by its magnetic quantum number (m_l). Its intrinsic spin is described by its spin quantum number (m_s).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.