Question

Consider the following set of quantum numbers.
\(n \,|\, m_|\)
A. 3 3 –3
B. 3 2 –2
C. 2 1 +1
D. 2 2 +2
The number of correct sets of quantum numbers is _____.

Answer 1

Correct Answer: 2

The quantum numbers \(n\), \(l\), and \(m_l\) describe the state of an electron in an atom. The rules are: 1. \(n\) must be a positive integer (principal quantum number). 2. \(l\) (azimuthal quantum number) ranges from 0 to \(n-1\). 3. \(m_l\) (magnetic quantum number) ranges from \(-l\) to \(+l\). Now, evaluate the given sets:
A. \(n=3\), \(l=3\), \(m_l=-3\). Here, \(l\) should be \(0 \leq l \leq n-1\), hence valid \(l\) values for \(n=3\) are 0, 1, 2. Since \(l=3\) is not valid, this set is incorrect.
B. \(n=3\), \(l=2\), \(m_l=-2\). For \(l=2\), valid \(m_l\) values are \(-2, -1, 0, 1, 2\). Therefore, this set is correct.
C. \(n=2\), \(l=1\), \(m_l=+1\). For \(l=1\), valid \(m_l\) values are \(-1, 0, 1\). Hence, this set is correct.
D. \(n=2\), \(l=2\), \(m_l=+2\). For \(n=2\), acceptable \(l\) values are 0, 1. Since \(l=2\) is invalid, this set is incorrect.
So, the correct sets are B and C, totaling two correct sets. This fits the range 2,2, confirming the solution.