The four quantum numbers for the last electron placed in the orbitals of a certain element are: n=3 l=2 m of l=0 and m of s=-1/2. What is the element?
I need help with this part of chemistry I have NEVER understood this ever. I know how to do the configurations but not this. I need some explanation on how to do it.
I'm sorry I can draw this thing out on the board but I'll try to explain it. First, however, you must learn the rules.
n = principal quantum number and can have any whole number beginning with 1.
l = any whole number beginning at 0 but can be no larger than n-1
ml = any whole number (including zero) and it can be as small as -l and as large as +l
ms can be +1/2 or -1/2.
Get all of this in your mind and we go to the set up.
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Here is what we do. We count by n until we get to n=3, l=2, ml = 0 and ms = 1/2
n = 1
l can be 0 (only)
ml can be 0 (only)
ms can be +1/2 and -1/2. So we put two electrons in for the +1/2 and -1/2 and that spells He.
n=2
l = 0................or 1
ml = 0............or -1...0...+1
ms = +/-1/2
We put electrons into each of these holes or 8 electrons total. Together with the two we had above makes 10 and we are to Ne.
n = 3
l = 0........or 1..........or 2
ml = 0.....-1, 0, +1.....-2,-1,0,+1,+2
ms +/-1/2
Add electrons in pairs (two for the ml = 0, 6 for the ml of -1,0,+1, and 2 for ml of -2, 2more for ml = of -1 and ONE more for ml = 0.
Remembering we had 10 from n = 2, that plus what we have added here makes 13 more or 23 total. Must be V.
It might help if you drew something like this on a sheet of paper; however, it get laborious to do this every time and you don't need to do that. You can take a shortcut. How?
We take a little stock and look at the periodic table.
n = 1 (period 1 takes you through He)=2e
n = 2 (period 2 takes you through Ne)=10e
n = 3(you wanted n = 3 so we know the element is somewhere after Na.
For l=2, that's a d electron (s electrons are l = 0, p electrons are l =1, d electrons are l = 2, f electrons are l = 3). So a d electrons means it must be somewhere in the 3d transition series (n = 3, l =2). Remembering to fill the 4s next, we add those to get us through K and Ca, then we count what we have so far. Through Ca is 20, adding 1 more gives us Sc, another gives Ti, and the last one gives V. What makes Ti and Sc different.
Sc is n = 3, l = 2, ml = -2
Ti is n = 3, l = 2, ml = -1
V is n = 3, l = 3, ml = 0
etc.
I hope this helps. If you draw something like I did above two or three times I can assure you it gets easier.
Well I'm studying for my final and he gave us an answer key and with a spin down it says that the answer is nickel.. SOO I'm trying to make sense of it but I understand what n is what l is but how do you figure out what the elements are from ml? And all of that put together?
To determine the element based on the given quantum numbers, we need to understand the quantum mechanical model of the atom and the rules for assigning quantum numbers.
The four quantum numbers for an electron are:
1. Principal Quantum Number (n): It represents the energy level or shell in which the electron is located. It determines the size of the orbital. The allowed values for n are positive integers (1, 2, 3, ...).
2. Azimuthal Quantum Number (l): It defines the shape of the orbital within a given energy level. It ranges from 0 to (n-1) for a given value of n. The values of l correspond to different sublevels: 0 = s sublevel, 1 = p sublevel, 2 = d sublevel, 3 = f sublevel, and so on.
3. Magnetic Quantum Number (m of l): It represents the orientation of the orbital within a given sublevel. It can have integer values ranging from -l to +l, including zero. For example, if l = 2, then the allowed values for m of l are -2, -1, 0, 1, 2.
4. Spin Quantum Number (m of s): It indicates the direction of the electron's spin, either clockwise or counterclockwise. It can have only two values: +1/2 (spin-up) or -1/2 (spin-down).
Based on the given quantum numbers: n = 3, l = 2, m of l = 0, and m of s = -1/2, we can determine the element as follows:
The value of n = 3 indicates that the electron is in the third energy level.
The value of l = 2 indicates that the electron is in the d sublevel.
The value of m of l = 0 indicates that the electron is in one of the five d orbitals, specifically the d orbital with no angular momentum along the z-axis.
The value of m of s = -1/2 indicates that the electron has a spin-down orientation.
Combining all the quantum numbers, we can conclude that the last electron is located in the 3d orbital with a spin-down orientation.
Therefore, the element with the given configuration is in the 3d block of the periodic table. Without additional information, we cannot determine the specific element.
To determine the element based on the given quantum numbers, we need to understand the meaning of each quantum number.
1. Principal Quantum Number (n): This quantum number defines the energy level or shell in which the electron is located. The values of n are positive whole numbers (1, 2, 3, etc.), with larger values indicating higher energy levels farther from the nucleus.
2. Azimuthal Quantum Number (l): This quantum number determines the orbital shape or subshell in which the electron is found. The values of l range from 0 to (n-1) and correspond to different subshells: 0(s-subshell), 1(p-subshell), 2(d-subshell), 3(f-subshell), and so on.
3. Magnetic Quantum Number (m[sub]l[/sub]): This quantum number specifies the orientation or orbital within a subshell. The values of m[sub]l[/sub] range from -l to +l, including zero. For example, if l = 2, the values of m[sub]l[/sub] can be -2, -1, 0, +1, or +2, corresponding to the five different d orbitals.
4. Spin Quantum Number (m[sub]s[/sub]): This quantum number describes the direction of electron spin. It can have one of two values: +1/2 (spin-up) or -1/2 (spin-down).
Now, let's analyze the given quantum numbers:
n = 3 (principal quantum number)
l = 2 (azimuthal quantum number)
m[sub]l[/sub] = 0 (magnetic quantum number)
m[sub]s[/sub] = -1/2 (spin quantum number)
To determine the element, we consider the last electron placed in orbitals with these quantum numbers. The values of n, l, and m[sub]l[/sub] determine the specific orbital. In this case, n = 3 tells us that the electron is in the third energy level. l = 2 indicates it is in the d-subshell, and m[sub]l[/sub] = 0 specifies that it is in the central d orbital, the d[sub]0[/sub] orbital.
Now, let's find the element by looking at the Periodic Table. Locate the 3rd row (corresponding to the 3rd energy level) and find the d-block (corresponding to the d-subshell). In the d-block, the central d orbital (d[sub]0[/sub]) is associated with the transition metals. The element where the last electron resides will be one of the transition metals in the 3rd period.
Therefore, based on the given quantum numbers, the element in question is a transition metal in the 3rd period, specifically in the d-block with an electron configuration ending in d[sub]0[/sub]. The exact element needs to be determined from experimental data, such as atomic number or other characteristics.