Question

How many different 3d states are there? What physical property (as opposed to quantum number) distinguishes them, and what different values may this property assume?

Short answer

There are five states in the case of 3d states.

The angular momentum could be 0 or$\pm h$ or$\pm 2h$ .

Step-by-step solution

Given data

The principal quantum number, n = 3, and the subshell is d.

To find different 3d states and angular momentum

The state 3d means principal quantum number n = 3 , the azimuthal quantum number l=n-1=2 so that magnetic quantum number ${\mathit{m}}_{\mathbf{l}}$, can take values from -l to +l as -2, -1, 0, 1 2.

So, there are five states.

The states that have differentrole="math" localid="1659781123812" ${\mathit{m}}_{\mathbf{l}}$ have different orbits and electron probability densities. They have different angular momentum in the z-direction, that is${\mathit{L}}_{\mathbf{z}}\mathbf{=}{\mathit{m}}_{\mathbf{i}}\sout{\mathbf{h}}$ .

The angular momentum could be 0 or$\mathbf{\pm }\mathit{h}$ or$\mathbf{\pm }\mathbf{2}\mathit{h}$ .

Conclusion

There are five states in the case of 3d states.

The angular momentum could be 0 or$\pm h$ or$\pm 2h$