Question

three quantum numbers for an electron in a hydrogen atom in a certain state are n = 4, ℓ = 1, mℓ = 1. the electron is located in what type of orbital?
4p
4s
4d
3p
question 5
1 pts
how many electrons can fill all the p orbits from n = 1 through n = 3?
18
12
3
6
question 6
1 pts
how many electrons have a +1/2 spin in the 3d, 4d and 5d orbits combined?
30
10
15
5

Explanation:

Step1: Recall orbital - quantum number relationship

The principal quantum number $n$ gives the energy level. The angular - momentum quantum number $\ell$ determines the type of orbital: $\ell = 0$ is an s - orbital, $\ell=1$ is a p - orbital, $\ell = 2$ is a d - orbital, and $\ell=3$ is an f - orbital. Given $n = 4$ and $\ell = 1$, the orbital is a 4p orbital.

Step2: Determine number of p - orbitals per energy level

For each value of $n$, the number of p - orbitals is 3 (since for $\ell = 1$, $m_{\ell}=- 1,0,1$). Each orbital can hold 2 electrons. From $n = 1$ to $n = 3$, there are 3 sets of p - orbitals. So the number of electrons that can fill these p - orbitals is $3\times2\times3=18$.

Step3: Recall d - orbital properties

A d - subshell has 5 orbitals. Each orbital can hold 2 electrons with opposite spins. The total number of electrons in 3d, 4d, and 5d subshells is $3\times5\times2 = 30$. Half of these electrons have a spin of $+\frac{1}{2}$, so the number of electrons with $+\frac{1}{2}$ spin is $\frac{3\times5\times2}{2}=15$.

Answer:

Question 1: A. 4p
Question 2: A. 18
Question 3: C. 15