Question

which is a set of valid quantum numbers?
( n = 4, l = 4, m = 4 )
( n = 1, l = -2, m = 0 )
( n = -1, l = 0, m = 0 )
( n = 4, l = 3, m = 3 )

Explanation:

Step1: Check the principal quantum number \(n\)

The principal quantum number \(n\) must be a positive integer (\(n = 1,2,3,\cdots\)).

• For \(n=- 1\), it is invalid since \(n>0\) is required.

Step2: Check the angular - momentum quantum number \(l\)

The angular - momentum quantum number \(l\) satisfies \(0\leq l\leq n - 1\).

• When \(n = 4\), \(l\) can be \(0,1,2,3\). So \(l = 4\) (when \(n = 4\)) is invalid.
• \(l=-2\) is invalid because \(l\geq0\)

Step3: Check the magnetic quantum number \(m\)

The magnetic quantum number \(m\) satisfies \(-l\leq m\leq l\)

• For \(n = 4\) and \(l = 3\), \(m\) can be \(-3,-2,-1,0,1,2,3\). So \(m = 3\) is valid

Answer:

\(n = 4,l = 3,m = 3\)