Which sets of the wuantum numbers are not allowed in the hydrogen atom? For the sets that are incorrect state what is wrong with them.
A) n= 4 l=3 ml=4
B) n= 0 l= 0 ml= 0
To determine if a set of quantum numbers is allowed in the hydrogen atom, we need to consider the specific rules and restrictions for each quantum number:
1. Principal quantum number (n): It represents the energy level or shell of the electron and can take on positive integer values (1, 2, 3, etc.). It cannot be zero or a negative number.
2. Azimuthal quantum number (l): It describes the orbital angular momentum of the electron and can take on values from 0 to (n-1). It represents the shape of the orbital, where l = 0 corresponds to an s-orbital, l = 1 corresponds to a p-orbital, l = 2 corresponds to a d-orbital, and so on.
3. Magnetic quantum number (ml): It gives the orientation of the orbital in space and can take on values ranging from -l to l, including zero. For example, if l = 1 (p-orbital), ml can be -1, 0, or 1.
Now let's analyze each set of quantum numbers provided:
A) n = 4, l = 3, ml = 4
In this case, the principal quantum number (n) and azimuthal quantum number (l) are within the allowable range. However, the magnetic quantum number (ml) cannot be larger than the azimuthal quantum number (l). Since ml = 4 is greater than l = 3, this set is not allowed.
B) n = 0, l = 0, ml = 0
The principal quantum number (n) cannot be zero or negative, as it represents the energy level or shell of the electron. Therefore, this set of quantum numbers is not allowed.
In summary, the set (A) is not allowed because the magnetic quantum number (ml) is larger than the azimuthal quantum number (l), and the set (B) is not allowed because the principal quantum number (n) cannot be zero.