How many electrons can have the quantum numbers n=4; l=2; ml=2 in an atom?
two electrons: (4, 2, 2, +1/2) and (4, 2, 2, -1/2)
To determine the maximum number of electrons that can have the given quantum numbers, we need to consider the allowed range of the magnetic quantum number (ml).
The magnetic quantum number (ml) describes the orientation of the orbital and can have values ranging from -l to +l. In this case, the quantum number ml is given as 2. Since the value of ml cannot exceed the value of l, there can only be a maximum of 3 orbitals with ml = 2.
Since each orbital can accommodate only 2 electrons (due to the Pauli exclusion principle), the maximum number of electrons with the given quantum numbers is:
3 orbitals * 2 electrons/orbital = 6 electrons
Therefore, a maximum of 6 electrons can have the quantum numbers n=4; l=2; ml=2 in an atom.
To determine the number of electrons that can have the given quantum numbers n=4, l=2, ml=2, we need to understand the rules governing electron distribution.
1. The quantum number "n" represents the principal energy level or shell of an atom.
2. The quantum number "l" represents the orbital angular momentum quantum number, which determines the type of orbital (s, p, d, f) within a particular energy level.
3. The magnetic quantum number "ml" indicates the specific orientation or shape of the orbital.
Now, let's break down the values of the quantum numbers:
1. n = 4 represents the fourth energy level or shell.
2. l = 2 indicates a d-type orbital.
3. ml = 2 denotes a specific orientation within that d orbital.
For a d-type orbital, the possible values of ml range from -2 to +2 (including zero). This means that for ml=2, we have:
ml = 2, 1, 0, -1, -2
Each orientation can accommodate two electrons due to the spin quantum number (ms), which can be either +1/2 or -1/2. Therefore, for each ml value, there can be two electrons. Thus, for ml = 2, we would have 2 x 2 = 4 electrons.
Therefore, the number of electrons that can have the quantum numbers n=4, l=2, ml=2 in an atom is 4.