Consider the last electron in Li: Values n,l,ml,and ms of 1,1,0, +1/2 are not allowable. Why not.
I do not understand this question. I am not sure what the values for the last electron would be.
n = 1,
l = 0
ml = 0
ms = +1/2 and -1/2 for the first two electron in Li. The last electron will be
n = 2
l = possible 0 and 1
ml = 0 for the 0
ms = +1/2
l = 1 is a higher energy level and starts filling with the first p electron (which is 5 = B) but Li ground state can't have l=1 since it has no p electrons.
In order to understand why certain values are not allowable for the last electron in Li (Lithium), let's review the principles of quantum numbers. Quantum numbers are used to describe various properties of an electron's position and energy within an atom.
The four quantum numbers used to describe an electron are:
1. Principal quantum number (n): This quantum number represents the energy level or the shell in which the electron resides. It can have integer values from 1 to infinity. In the case of the last electron in lithium, the value of n is given as 1.
2. Azimuthal quantum number (l): This quantum number relates to the shape or subshell of the orbital. The values of l depend on the value of n and can range from 0 to (n-1). For the last electron in lithium, the value of l is given as 1.
3. Magnetic quantum number (ml): This quantum number determines the orientation of the orbital within a subshell. It can take integer values within the range of -l to +l. For the last electron in lithium, the value of ml is given as 0.
4. Spin quantum number (ms): This quantum number describes the spin orientation of an electron. It can either be +1/2 (spin up) or -1/2 (spin down).
Based on the given values for n, l, ml, and ms (1, 1, 0, +1/2), we can analyze why they are not allowable for the last electron in lithium:
1. The value of n being 1 is acceptable since it represents the first energy level or shell.
2. The value of l being 1 is also acceptable since it corresponds to the p orbital, which is a possible subshell in the first energy level.
3. The value of ml being 0 is allowed since it falls within the range of -l to +l.
4. However, the value of ms being +1/2 is not acceptable. According to the Pauli exclusion principle, within an orbital, two electrons must have opposite spins (one +1/2 and one -1/2) to minimize their mutual repulsion. Therefore, the last electron in lithium should have a spin of -1/2 (spin down) rather than +1/2.
In summary, the given values for n, l, ml, and ms (1, 1, 0, +1/2) are not allowable for the last electron in lithium because the spin quantum number, ms, should be -1/2 (spin down) rather than +1/2 (spin up) according to the Pauli exclusion principle.
In the atomic structure of an atom, electrons are arranged in energy levels or shells around the nucleus. Each electron in an atom is characterized by four quantum numbers: n, l, ml, and ms.
The quantum number n represents the principal energy level or shell in which the electron is found. It can have values of 1, 2, 3, and so on, with higher values indicating higher energy levels.
The quantum number l represents the orbital shape or subshell in which the electron is located. It can have values ranging from 0 to n-1, indicating different shapes such as s, p, d, or f orbitals.
The quantum number ml represents the orientation of the orbital in space. It can have values from -l to +l, indicating different orientations within the subshell.
The quantum number ms represents the spin of the electron. It can have two possible values: +1/2 and -1/2, representing two opposite spin directions.
Now, let's consider the case of the last electron in a lithium (Li) atom. The atomic number of lithium is 3, meaning it has 3 electrons. When we fill the electrons in increasing energy levels, we find that the last electron of lithium occupies an energy level with n=2.
In this case, the possible values for l can be 0 or 1, as the second energy level has both s and p subshells. The possible values for ml would be -l to +l, which means -1, 0, or 1. Lastly, the possible values for ms can be +1/2 or -1/2.
Now, let's analyze the given values of n=1, l=1, ml=0, and ms=+1/2, and understand why they are not allowable for the last electron in Li.
1. n=1: This value is not valid for the last electron of Li because, as mentioned earlier, the last electron occupies the second energy level (n=2).
2. l=1: This value is not valid for the last electron of Li because the second energy level (n=2) has both s and p subshells. The p subshell corresponds to l=1, but since the last electron occupies the s subshell, the value of l for the last electron is 0.
3. ml=0: This value is not valid for the last electron of Li because, as mentioned earlier, the last electron occupies the s subshell, and the s subshell has only one orbital with ml=0. So ml can only be 0 for the last electron in Li.
4. ms=+1/2: This value is not invalid for the last electron of Li. The spin quantum number can have values of +1/2 or -1/2, indicating the two possible spin directions.
In summary, the values n=1, l=1, ml=0, and ms=+1/2 are not allowable for the last electron in Li because they do not correspond to the correct energy level, orbital shape, orbital orientation, and spin for that particular electron.