Consider this set of quantum numbers: n = 3, l = 2, ml = -1, ms = +½
The maximum number of electrons in an atom which can share the above set of quantum numbers is
The quantum state is fixed when specifying n, l, ml and ms. Therefore, by the Pauli exclusion principle, there can be only one electron with these quantum nembers.
To determine the maximum number of electrons that can share a set of quantum numbers, we need to consider the rules governing the arrangement of electrons in an atom.
- The principal quantum number (n) represents the energy level or shell of an electron. It can have positive integer values starting from 1. In this case, n = 3.
- The azimuthal quantum number (l) represents the shape or subshell of an electron. It can have values from 0 to (n-1). In this case, l = 2.
- The magnetic quantum number (ml) represents the orientation of an electron within a subshell. It can have values from -l to +l. In this case, ml = -1.
- The spin quantum number (ms) represents the spin state or direction of an electron. It can have two possible values, +½ and -½. In this case, ms = +½.
According to the Pauli exclusion principle, no two electrons within an atom can have the same set of quantum numbers. This means that each electron within an atom must have a unique combination of n, l, ml, and ms.
Therefore, the maximum number of electrons that can share the given set of quantum numbers is 1.
To determine the maximum number of electrons that can share the set of quantum numbers you provided, we need to apply the Pauli Exclusion Principle and Hund's Rule.
The quantum numbers given are:
- Principal quantum number (n) = 3
- Azimuthal quantum number (l) = 2
- Magnetic quantum number (ml) = -1
- Spin quantum number (ms) = +½
According to the Pauli Exclusion Principle, no two electrons in an atom can have the same set of four quantum numbers. Let's analyze each quantum number and its possible values to find the maximum number of electrons that can share the provided set of quantum numbers.
1. Principal quantum number (n): Determines the energy level of the electron. For n = 3, there can be a maximum of 2n² = 2 * 3² = 18 electrons in this energy level.
2. Azimuthal quantum number (l): Determines the shape of the orbital. For l = 2, the possible values for ml are -2, -1, 0, +1, +2. Therefore, there are 5 possible orbitals for this value of l.
3. Magnetic quantum number (ml): Determines the orientation of the orbital in space. For ml = -1, there is only one possible orbital.
4. Spin quantum number (ms): Determines the spin of the electron. For ms = +½, there can be a maximum of 2 electrons in this spin state.
To find the maximum number of electrons that can share this set of quantum numbers, we need to consider the following:
- For each possible orbital (5 orbitals for l = 2) there can be a maximum of 2 electrons (one with ms = +½ and the other with ms = -½, due to the Pauli Exclusion Principle).
Therefore, the maximum number of electrons that can share this set of quantum numbers is 5 orbitals * 2 electrons = 10 electrons.
In conclusion, the maximum number of electrons in an atom that can share the provided set of quantum numbers (n = 3, l = 2, ml = -1, ms = +½) is 10 electrons.