Question

which of the following is not an allowable set of quantum numbers n, l, m_l
a. 2, 2, -2
b. 3, 2, 0
c. 4, 1, -2
both a and c are not allowed.
none are allowed.

Explanation:

Step1: Analyze option A

For a given \(n = 2\), the possible values of \(l\) are \(l=0,1\) (since \(l\) ranges from \(0\) to \(n - 1\)). Here \(l = 2\) when \(n=2\), which is not allowed.

Step2: Analyze option C

For \(l = 1\), the possible values of \(m_l\) range from \(-l\) to \(+l\), i.e., \(m_l=- 1,0,1\). Here \(m_l=-2\) when \(l = 1\), which is not allowed.

Step3: Analyze option B

For \(n = 3\), \(l\) can be \(0,1,2\). When \(l = 2\), \(m_l\) can range from \(-2\) to \(+2\). So \(m_l = 0\) is allowed.

Answer:

D. Both A and C are NOT allowed.