Which one of the following sets of quantum numbers can correctly represent a 3p orbital?
a) (n = 3 l = 1, ml = 2)
b)(n = 1, l = 3, ml = 3)
c) (n = 3, l = 2, ml = 1)
d) (n = 3, l = 1, ml = -1)
e) (n = 3, l = 0, ml = 1)
The answer should be Option (d) (n = 3, l = 1, mₗ = -1).
This is because a 3p orbital must have n = 3.
*That eliminates Option (b), because it has n = 1*
A p orbital must have l = 1.
*That eliminates Options (c), and (e), because they have l = 2, and 0*
The mₗ is required to be an integer satisfying −l ≤ m ≤ l, so mₗ could be any of −1, 0, or +1.
*That eliminates Option (a), because they have mₗ = 2*
The only correct option is:
(d) n = 3, l = 1, mₗ = -1
Well, let me give this a whirl! And by whirl, I mean let me spin some jokes related to quantum numbers to help you remember which one represents a 3p orbital.
a) (n = 3, l = 1, ml = 2) - This one is all twisted up, like a pretzel. Definitely not a 3p orbital!
b) (n = 1, l = 3, ml = 3) - Oh boy, we have a winner! Just kidding, this one has more l's than a lemonade stand. Not a 3p orbital either!
c) (n = 3, l = 2, ml = 1) - This is a great attempt, but this set of quantum numbers doesn't fit the 3p orbital shape. So close, yet so far!
d) (n = 3, l = 1, ml = -1) - Aha! Now we're getting somewhere. This set of quantum numbers represents a 3p orbital. We've hit the jackpot!
e) (n = 3, l = 0, ml = 1) - Nope, this set of quantum numbers doesn't match a 3p orbital. You're drifting away!
So, the correct answer is d) (n = 3, l = 1, ml = -1). Congrats! You've got the right quantum numbers for a 3p orbital. Keep up the great work!
The correct set of quantum numbers that represent a 3p orbital is:
d) (n = 3, l = 1, ml = -1)
The quantum numbers indicate the following:
- n represents the principal quantum number and indicates the energy level of the electron. In this case, it is 3.
- l represents the azimuthal quantum number and indicates the shape of the orbital. In this case, it is 1, which corresponds to the p orbital.
- ml represents the magnetic quantum number and indicates the orientation of the orbital in space. In this case, it is -1, which corresponds to the p orbital along the y-axis.
To determine which set of quantum numbers represents a 3p orbital, we first need to understand the meaning of each quantum number.
1. Principal quantum number (n): It represents the energy level or shell of an electron. It can have positive integer values (1, 2, 3, etc.).
2. Angular momentum quantum number (l): It describes the shape of the orbital and determines the sublevel (s, p, d, f). It can have values from 0 to (n-1).
3. Magnetic quantum number (ml): It specifies the orientation of the orbital in three-dimensional space. It can have values from -l to +l.
For a 3p orbital:
- The principal quantum number (n) must be 3 because it indicates the third energy level.
- The angular momentum quantum number (l) must be 1 because there is only one p orbital in this energy level (n=3).
- The magnetic quantum number (ml) must have a value of -1, 0, or +1 because there are three p orbitals (-1, 0, +1) that can occupy this energy level.
From the given options:
a) (n = 3, l = 1, ml = 2) - Incorrect, as the value of ml exceeds the maximum possible value (+1).
b) (n = 1, l = 3, ml = 3) - Incorrect, as the value of l exceeds the maximum possible value (n-1).
c) (n = 3, l = 2, ml = 1) - Incorrect, as the value of l is incorrect for a p orbital.
d) (n = 3, l = 1, ml = -1) - Correct, as all the quantum numbers align with the criteria for a 3p orbital.
e) (n = 3, l = 0, ml = 1) - Incorrect, as the value of l is incorrect for a p orbital.
Therefore, the correct answer is d) (n = 3, l = 1, ml = -1).
3p so
n = 3
l = 1 because it's a p
ml can be -1 or 0 or +1
You take it from here.
You can immediately rule out a because of mL, b because of n, c because l, etc.