the Pauli exclusion principle
You did not give any numbers
Yes. Always. Otherwise they would break the fundamental rules of quantum mechanics, which say that no two electrons can have the same four quantum numbers -- and spin is the 4th quantum number. If two e- are in the same orbital, they share 3 quantum numbers, but the spin quantum number must then be different.
Pauli's exclusion principle
10 electrons.The angular momentum quantum number is l (small L). This quantum number is dependant on the principal quantum number, and has values, 0 1,2 ..(n-1), where each value of n refers to a subshell known to chemists as followsn= 0, s orbital; n=1, p orbital; n= 2, d orbital; n= 3, f orbital.So we are looking at the d orbitals.There are five d orbitals, with magnetic quantum numbers running from -l to +l, that is -2, -1, 0, +1, +2Each of these can hold 2 electrons (with spin quantum numbers -1/2, +1/2)So we have 10 electrons that can have pricipal quantum numbers of 4 and angular monmentum quantum number of 2.
Electrons do not travel in pairs. An atomic or molecular orbital can hold a pair of electrons, which is probably what you're thinking of. The reason for this is that electrons are fermions: two electrons in an atom or molecule cannot have the exact same quantum state. Specifying the orbital uses up 3 of the 4 quantum numbers for describing an electron's quantum state; the last quantum number is the spin angular momentum which can either be +1/2 or -1/2, so two electrons per orbital. After that it's full and no more electrons can go into that orbital. Note that far from "traveling in pairs", fermions really don't like to be even that close to each other. If there are three orbitals at the same energy level, one electron will go into each before they start to "double up".
An orbital may never contain 3 electrons. An orbital will contain at the most 2 electrons which have different quantum numbers.
You did not give any numbers
There are seven different possible magnetic quantum numbers or seven orbitals. In that cause the maximum number of electrons an f orbital will hold would be fourteen.
f orbital corresponds to n=4. l = n-1 = 3. The magnetic quantum numbers run from -l to l, or -3, -2,... 3. Thus there are seven possible magnetic quantum numbers, or seven orbitals. Since each orbital has 2 electrons max, an f orbital can hold 14 electrons.
By the two of them having opposite spin quantum numbers.
Yes. Always. Otherwise they would break the fundamental rules of quantum mechanics, which say that no two electrons can have the same four quantum numbers -- and spin is the 4th quantum number. If two e- are in the same orbital, they share 3 quantum numbers, but the spin quantum number must then be different.
Four quantum numbers are used to describe electrons. The principle quantum number is the energy level of an electron. The angular momentum number is the shape of the orbital holding the electron. The magnetic quantum number is the position of an orbital holding an electron. The spin quantum number is the spin of an electron.
Pauli's exclusion principle
n is the first quantum number. It is the principle quantum number. It refers to what energy level it is and will be one greater than the number of nodes in the orbital. l is the second quantum number. It is the angular momentum quantum number and refers to the shape of the orbital. ml is the third quantum number. It is the magnetic quantum number and it refers to the orientation of the orbital. ms is the fourth quantum number. It is the spin quantum number and refers to the magnetic character of the orbital.
The bottom-line answer is because that is how nature works! However, there are somewhat less profound explanations, but they are really just rules which say that this must happen -- and don't ultimately answer "Why?". The Pauli Exclusion Principle says that all electrons in an atom must have four unique quantum numbers -- no two can have all four the same. This rule forbids more than 2 electrons existing in the same orbital because there are two possible quantum numbers available for that orbital -- electron spin of +1/2 and -1/2. But again, this rule just says that there can't be more than 2 electrons per orbital because of the uniqueness of quantum numbers -- but it doesn't say why quantum numbers must be unique! In the end, it really just is the way it because that's the way it is!
An orbital can have a maximum of two electrons that have different sets of the four quantum numbers (n, l, ml, ms).
10 electrons.The angular momentum quantum number is l (small L). This quantum number is dependant on the principal quantum number, and has values, 0 1,2 ..(n-1), where each value of n refers to a subshell known to chemists as followsn= 0, s orbital; n=1, p orbital; n= 2, d orbital; n= 3, f orbital.So we are looking at the d orbitals.There are five d orbitals, with magnetic quantum numbers running from -l to +l, that is -2, -1, 0, +1, +2Each of these can hold 2 electrons (with spin quantum numbers -1/2, +1/2)So we have 10 electrons that can have pricipal quantum numbers of 4 and angular monmentum quantum number of 2.