Question

An electron in a multi-electron atom is known to have the quantum number I = 3. What are its possible $\mathbf{n}\mathbf{,}\mathbf{}{\mathbf{m}}_{\mathbf{1}}\mathbf{,}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{m}}_{\mathbf{s}}$quantum numbers?

Short answer

The possible quantum numbers are given by:

The values of are any value greater than 3.

The values of ${\mathrm{m}}_1\mathrm{are}-3,-2,-1,0,-1,2,\mathrm{or}3$.

The values of ${\mathrm{m}}_{\mathrm{s}}\mathrm{are}+\frac{1}{2}\mathrm{or}-\frac{1}{2}$.

Step-by-step solution

The given data

The given quantum state, I = 3

Understanding the concept of quantum numbers:

A quantum number is a value used to describe the energy levels that atoms and molecules have.

For a given orbital quantum number I, the principal quantum can have values greater than I . Again, for the given I , the magnetic orbital quantum numbers range from -I to +I. Now, irrespective of all quantum numbers, the spin quantum number has only two values due to the case of Pauli's exclusion Principle.

Calculation of the possible quantum numbers:

From the concept, we can say that the value of the principal quantum number n can have values greater than 3 for I = 3 .

Now, the possible values for considering the concept are -3,-2,-1,0,-1,2, or 3 .

Now, using the concept, the possible values for ${\mathrm{m}}_{\mathrm{s}}\mathrm{is}+\frac{1}{2}\mathrm{or}-\frac{1}{2}$.