Question

question 13 (0.25 points) listen which of the following is a correct set of quantum numbers for an electron in a 4d orbital? a) n = 4, l = 0, m_l = -1 b) n = 4, l = 1, m_l = +3 c) n = 4, l = 3, m_l = +2 d) n = 4, l = 2, m_l = 3 e) n = 4, l = 2, m_l = -2

Explanation:

Step1: Define principal quantum number

For a 4d orbital, the principal quantum number $n$ corresponds to the coefficient, so $n=4$.

Step2: Define azimuthal quantum number

For a d orbital, the azimuthal quantum number $l=2$ (since $l=0$=s, $l=1$=p, $l=2$=d, $l=3$=f).

Step3: Define magnetic quantum number

The magnetic quantum number $m_l$ ranges from $-l$ to $+l$. For $l=2$, $m_l$ can be $-2, -1, 0, +1, +2$.

Step4: Match options to rules

Check each option against the above values:

• a) $l=0$ (incorrect, needs $l=2$)
• b) $l=1$, $m_l=+3$ (both incorrect)
• c) $l=3$ (incorrect, needs $l=2$)
• d) $m_l=3$ (incorrect, exceeds $+2$)
• e) $n=4, l=2, m_l=-2$ (all values valid)

Answer:

e) $n=4, l=2, m_l= -2$