What is the maximum number of electrons that can have n=4, mi= -1 in an atom?
Also, explain how you got that answer. I am confused.
N = 4 is set.
l may have values of 0, 1, 2, etc up to a maximum of n-1; therefore, l may be
0, 1, 2, or 3,
ml can have values of -l to +l in increments of 1 including 0.
If l = 0, ml must be 0.
If l = 1, ml can be -1, 0, +1; therefore, you can place 2 electrons there.
If l = 2, ml can be
-2, -1, 0, +1, +2; therefore, there can be two more electrons in this -1.
If l = 3, ml can be
-3, -2, -1, 0, +1, +2, +3; therefore, we can place two more electrons in this -1.
If I understand the problem correctly, we can place six (6) electrons in those three orbitals.
So, the maximum electrons is 6 right?
That's what I count. But you need to go through the reasoning and confirm that.
To determine the maximum number of electrons that can have a specific set of quantum numbers, we need to consider the limitations imposed by the Pauli exclusion principle and the Aufbau principle.
The quantum numbers specify the energy level (n), the orbital shape (l), the orientation (ml), and the spin (ms) of an electron. In this case, we are given n = 4 and ml = -1.
The ml quantum number represents the orientation of the orbital, which includes the values of -l to +l. Therefore, for ml = -1, the allowed values for l would be +1 or -1, corresponding to the p or d orbitals.
According to the Aufbau principle, electrons fill the lowest-energy orbitals first. In the case of n=4, the order of filling would be 4s, 3d, and 4p orbitals.
In the 4s orbital, there are a maximum of 2 electrons.
In the 3d orbital, there are a maximum of 10 electrons.
In the 4p orbital, there are a maximum of 6 electrons.
Since the ml quantum number only determines the orientation within a specific orbital, it does not affect the number of electrons that can occupy that orbital. Therefore, for ml = -1, the maximum number of electrons that can exist in the 4p orbital is 6.
Hence, the maximum number of electrons that can have n=4, ml= -1 in an atom is 6.
To arrive at this answer, we considered the available orbitals and their respective maximum electron capacities based on the principles of quantum mechanics, specifically the Pauli exclusion principle and the Aufbau principle.