Indicate which of the following quantum states are allowed and which are
disallowed under the rules governing the electronic structure of atoms.
n = 2, l = 1, ml = 0, ms = ½
n = 3, l = 3, ml = -2, ms = -½
n = 4, l = 3, ml = -2, ms = ½
n = 3, l = 2, ml = 2, ms = ⅓
n = 2, l = 1, ml = -2, ms = -½
n = 3, l = 2, ml = -1, ms = -½
John/Sara/Robert/et al.
You must know the rules which are
n may be any whole number >1.
l may be a whole number from 0 to n-1; i.e., 0, 1, 2, 3, etc.
m may be any whole number from -l to +l including zero
s may be either +1/2 or -1/2.
For example, 1 is allowed but 2 is not.
(2 is not allowed because if n = 3 then l may not be larger than n-1 = 2.)That's how it's done.
To determine whether a quantum state is allowed or disallowed under the rules governing the electronic structure of atoms, we need to consider a few principles:
1. Principle of Quantum Numbers: Each electron in an atom is described by a set of four quantum numbers - n, l, ml, and ms.
2. Principle of Principal Quantum Number (n): The principal quantum number (n) defines the energy level or shell in which the electron resides. It can have integer values ranging from 1 to infinity.
3. Principle of Angular Momentum Quantum Number (l): The angular momentum quantum number (l) determines the shape or type of orbital within a given energy level. It can have integer values ranging from 0 to n-1.
4. Principle of Magnetic Quantum Number (ml): The magnetic quantum number (ml) specifies the orientation or spatial distribution of an orbital within a subshell. It can have integer values ranging from -l to +l.
5. Principle of Spin Quantum Number (ms): The spin quantum number (ms) describes the intrinsic angular momentum or spin of an electron. It can have two possible values: +½ (spin-up) or -½ (spin-down).
Now, let's analyze each of the given quantum states:
1. n = 2, l = 1, ml = 0, ms = ½
This state is allowed because all the quantum numbers fall within their permissible ranges.
2. n = 3, l = 3, ml = -2, ms = -½
This state is disallowed because the value of l is greater than n-1, which violates the principle of Angular Momentum Quantum Number.
3. n = 4, l = 3, ml = -2, ms = ½
This state is allowed because all the quantum numbers fall within their permissible ranges.
4. n = 3, l = 2, ml = 2, ms = ⅓
This state is disallowed because the value of ml is greater than l, violating the principle of Magnetic Quantum Number.
5. n = 2, l = 1, ml = -2, ms = -½
This state is allowed because all the quantum numbers fall within their permissible ranges.
6. n = 3, l = 2, ml = -1, ms = -½
This state is allowed because all the quantum numbers fall within their permissible ranges.
In summary, the allowed states are:
1. n = 2, l = 1, ml = 0, ms = ½
2. n = 4, l = 3, ml = -2, ms = ½
3. n = 2, l = 1, ml = -2, ms = -½
4. n = 3, l = 2, ml = -1, ms = -½
The disallowed states are:
1. n = 3, l = 3, ml = -2, ms = -½
2. n = 3, l = 2, ml = 2, ms = ⅓