Identifying Spin Direction

Spin multiplicity = (n +1) = (1+1) = 2 (spin state = doublet); (2+1) = 3 (spin state = triplet) and (3 + 1) = 4 (spin state = quartet) respectively.

Intrinsic Spin Angular Momentum Is Quantized in Magnitude and Direction. S=√s(s+1)h2π(s= 1/2 for electrons) S = s ( s + 1 ) h 2 π ( s = 1/2 for electrons ) , for electrons. Sz is the z-component of spin angular momentum and ms is the spin projection quantum number.

1. Determine the number of electrons the atom has.
2. Draw the electron configuration for the atom. See Electronic Configurations for more information.
3. Distribute the electrons, using up and down arrows to represent the electron spin direction.

Table of Allowed Quantum Numbers

For a 4d orbital, the value of n (principal quantum number) will always be 4 and the value of l (azimuthal quantum number) will always be equal to 2. The values of the magnetic quantum number range from -l to l, so the possible values of ml for the 4d orbital are -2, -1, 0, 1, and 2.

Indicate the number of subshells, the number of orbitals in each subshell, and the values of l and ml for the orbitals in the n = 4 shell of an atom. For n = 4, l can have values of 0, 1, 2, and 3. Thus, s, p, d, and f subshells are found in the n = 4 shell of an atom. For l = 0 (the s subshell), ml can only be 0.

Because n=3, the possible values of l = 0, 1, 2, which indicates the shapes of each subshell.

There is an electron with n=4. Therefore there is individual shells of electrons, each with a larger energy level than the previous. Since ℓ can be from any positive integer 0 all the way to n-1, and if n=4, then ℓ can be 0, 1, 2, and 3. So, there are 4 subshells of 4 different shapes within the n=4 shell.

So adding the possibilities gives 1 + 3 + 5 = 9 orbitals in total.

Maximum number of orbitals in an energy level (n2)