Question 1

What are the permitted values of the four quantum numbers?

Accepted Answer

The principal quantum number n can be any positive integer. For a given n, l ranges from 0 to n-1. For a given l, m_l takes integer values from -l to +l, and the spin quantum number m_s is only +1/2 or -1/2.

Question 2

How many orbitals are present in an s, p, d, or f subshell?

Accepted Answer

A subshell contains 2l+1 orbitals. Therefore s has 1 orbital, p has 3, d has 5, and f has 7. These are spatial orbitals; m_s does not create another spatial orbital.

Question 3

Is p_x simply the m_l = +1 orbital?

Accepted Answer

No. An m_l value labels an angular-momentum eigenstate about the chosen z-axis. Real p_x and p_y orbitals are linear combinations of the m_l=+1 and m_l=-1 states, while p_z corresponds to m_l=0.

Question 4

How many orbitals are present in the nth shell?

Accepted Answer

The nth shell contains n^2 orbitals because its allowed l values contribute 2l+1 orbitals each. Thus shells 1, 2 and 3 contain 1, 4 and 9 spatial orbitals respectively.

Question 5

Does a 3D orbital shape show the path of an electron?

Accepted Answer

No. An atomic orbital is a one-electron wave function, and its rendered volume represents spatial probability rather than a fixed trajectory. An orbital can contain two electrons with opposite spin values, +1/2 and -1/2.

Quantum Numbers Audit — Build a Valid Electron State

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