Chapter 28, Problem 14P

To determine

The possible values of $m_l$ and $m_s$

Answer to Problem 14P

The magnetic quantum numberis $m_l=-3,-2,-1,0,1,2,3$

The possible values of $m_s$ are $-\frac{1}{2},+\frac{1}{2}$

Explanation of Solution

Given info: The principal quantum number $\text{n = 5}$

The orbital quantum number $l=3$

Formula used:

The principal quantum number $n$ can take on any integer value $\left(1,2,3,\mathrm{...}\right)$ and also, corresponds to the quantum number of the old Bohr theory. The orbital quantum number $l$ can take on values from $0$ to $\text{n-1}$ .

The magnetic quantum number, $m_l$ , can take on the integer values from $-l$ to $+l$

The spin quantum number, $m_s$ , can be $+\frac{1}{2}$ to $-\frac{1}{2}$

Calculation:

Note that the value of $m_l$ can range from $-l$ to $+l$ .

So, for $l=3$ , it is having that $m_l=-3,-2,-1,0,1,2,3$

And the possible values ofthe spin quantum number, $m_s$ , are $-\frac{1}{2},+\frac{1}{2}$

Conclusion:

All the required values are calculated.