Which of the following combinations of quantum numbers (n,l,m_l,m_s)do not represent permissible solutions of the Schrödinger equation for the electron in the hydrogen atom (i.e. ,which combination of quantum numbers is not allowed)? A)9,8,-4,1/2 B)8,2,2,1/2 C)6,-5,-1,1/2 D)6,5,-5,1/2 E)All are allowed.

Question

Quizplus · Accepted Answer

There are three rules that determine which combinations of quantum numbers are allowed:
1) The principle quantum number (n) must be a positive integer (1, 2, 3, ...).
2) The angular momentum quantum number (l) must be an integer between 0 and n-1.
3) The magnetic quantum number (mL) must be an integer between -l and l.

In addition, there are two possible spin states for the electron, each with a magnetic quantum number of either +1/2 or -1/2.

In choice C, the combination of (n=6, l=-5, mL=-1, mS=1/2) violates the second rule, as -5 is not a valid value of l. Therefore, choice C is not allowed.

All the other choices satisfy the rules and are allowed.

Which of the Following Combinations of Quantum Numbers (N,l,ml,ms)do Not

Which of the Following Combinations of Quantum Numbers (N,l,m_l,m_s)do Not