Question

question 12 (0.25 points) listen which of the following is a correct set of quantum numbers for an electron in a 4f orbital? a) $n = 4, l = 0, m_l = -1$ b) $n = 4, l = 3, m_l = +2$ c) $n = 4, l = 2, m_l = 3$ d) $n = 4, l = 1, m_l = +1$ e) $n = 4, l = 2, m_l = -2$

Explanation:

Step1: Define principal quantum number

For a 4f orbital, the principal quantum number $n=4$.

Step2: Define azimuthal quantum number

For f orbitals, $l=3$ (since $l=0=s, l=1=p, l=2=d, l=3=f$).

Step3: Define magnetic quantum number

$m_l$ ranges from $-l$ to $+l$, so for $l=3$, $m_l$ can be $-3,-2,-1,0,+1,+2,+3$.

Step4: Match valid set

Check options: only option b has $n=4, l=3, m_l=+2$ (which falls in the valid range for $m_l$ when $l=3$).

Answer:

b) $n = 4, l = 3, m_l = +2$