What are the possible sets of quantum numbers for the following orbitals
7p
6d
5s
4d
What is your problem in answering this. You just memorize those values. Here is an example for 7p
n = 7
l = 1 for p, 0 for s, 2 for d, 3 for f electrons.
ml = -l to + l in steps of 1 including 0. For example for the p electron ml may have values of -1 or 0 or +1.
ms = +1/2 or - 1/2
For 5s, n = 5, l = 0, ml = 0, ms = +1/2 or -1/2
I'll be glad to check your answers for the others.
To determine the possible sets of quantum numbers for a given orbital, we need to understand the rules that govern the quantum numbers.
The four quantum numbers are:
1. Principal Quantum Number (n): Represents the energy level or shell of an electron. It can take any positive integer value greater than or equal to 1.
2. Azimuthal Quantum Number (l): Determines the shape of the orbital. It can take integer values from 0 to n-1.
3. Magnetic Quantum Number (ml): Specifies the orientation of the orbital in space. It can take integer values between -l and +l, including zero.
4. Spin Quantum Number (ms): Represents the spin of the electron in the orbital. It can take two values: +1/2 for "spin-up" and -1/2 for "spin-down."
Now let's determine the possible sets of quantum numbers for each of the given orbitals:
1. 7p:
- Principal Quantum Number (n) = 7
- Azimuthal Quantum Number (l) can be either 1 or 0 since the lowest energy p orbital has l = 1.
- Magnetic Quantum Number (ml) can be -1, 0, or +1 since the p orbital has three orientations in space.
- Spin Quantum Number (ms) can be +1/2 or -1/2.
Therefore, the possible sets of quantum numbers for 7p orbital are:
- (7, 1, -1, +1/2)
- (7, 1, 0, +1/2)
- (7, 1, +1, +1/2)
- (7, 1, -1, -1/2)
- (7, 1, 0, -1/2)
- (7, 1, +1, -1/2)
2. 6d:
- Principal Quantum Number (n) = 6
- Azimuthal Quantum Number (l) can be either 2, 1, or 0 since the lowest energy d orbital has l = 2.
- Magnetic Quantum Number (ml) can be -2, -1, 0, +1, or +2 since the d orbital has five orientations in space.
- Spin Quantum Number (ms) can be +1/2 or -1/2.
Therefore, the possible sets of quantum numbers for 6d orbital are:
- (6, 2, -2, +1/2)
- (6, 2, -1, +1/2)
- (6, 2, 0, +1/2)
- (6, 2, +1, +1/2)
- (6, 2, +2, +1/2)
- (6, 2, -2, -1/2)
- (6, 2, -1, -1/2)
- (6, 2, 0, -1/2)
- (6, 2, +1, -1/2)
- (6, 2, +2, -1/2)
3. 5s:
- Principal Quantum Number (n) = 5
- Azimuthal Quantum Number (l) can be 0 since the lowest energy s orbital has l = 0.
- Magnetic Quantum Number (ml) is always 0 for an s orbital.
- Spin Quantum Number (ms) can be +1/2 or -1/2.
Therefore, the possible sets of quantum numbers for 5s orbital are:
- (5, 0, 0, +1/2)
- (5, 0, 0, -1/2)
4. 4d:
- Principal Quantum Number (n) = 4
- Azimuthal Quantum Number (l) can be 2 since the lowest energy d orbital has l = 2.
- Magnetic Quantum Number (ml) can be -2, -1, 0, +1, or +2 since the d orbital has five orientations in space.
- Spin Quantum Number (ms) can be +1/2 or -1/2.
Therefore, the possible sets of quantum numbers for 4d orbital are:
- (4, 2, -2, +1/2)
- (4, 2, -1, +1/2)
- (4, 2, 0, +1/2)
- (4, 2, +1, +1/2)
- (4, 2, +2, +1/2)
- (4, 2, -2, -1/2)
- (4, 2, -1, -1/2)
- (4, 2, 0, -1/2)
- (4, 2, +1, -1/2)
- (4, 2, +2, -1/2)
To determine the possible sets of quantum numbers for each orbital, we need to know the rules for assigning quantum numbers.
The four quantum numbers are:
1. Principal quantum number (n)
2. Azimuthal quantum number (l)
3. Magnetic quantum number (ml)
4. Spin quantum number (ms)
The principal quantum number (n) describes the energy level or shell of the electron and can have any positive integer value (1, 2, 3, ...).
The azimuthal quantum number (l) describes the shape of the orbital and can range from 0 to (n-1). The values of l correspond to specific subshells:
- l = 0 corresponds to the s subshell
- l = 1 corresponds to the p subshell
- l = 2 corresponds to the d subshell
- l = 3 corresponds to the f subshell
... and so on.
The magnetic quantum number (ml) describes the orientation of the orbital within a subshell. It can have integer values ranging from -l to +l. For example, if l = 2 (d subshell), then ml can be -2, -1, 0, +1, or +2.
The spin quantum number (ms) describes the spin of the electron and can have values of +1/2 or -1/2.
Now, let's determine the possible sets of quantum numbers for each of the given orbitals:
1. 7p orbital:
- For the principal quantum number (n), we know it is 7.
- For the azimuthal quantum number (l), since it is a p orbital, l = 1.
- For the magnetic quantum number (ml), it can have values of -1, 0, or 1.
- For the spin quantum number (ms), it can have values of +1/2 or -1/2.
So, the possible sets of quantum numbers for the 7p orbital are:
(7, 1, -1, +1/2), (7, 1, 0, +1/2), (7, 1, 1, +1/2), (7, 1, -1, -1/2), (7, 1, 0, -1/2), (7, 1, 1, -1/2)
2. 6d orbital:
- For the principal quantum number (n), we know it is 6.
- For the azimuthal quantum number (l), since it is a d orbital, l = 2.
- For the magnetic quantum number (ml), it can have values of -2, -1, 0, 1, or 2.
- For the spin quantum number (ms), it can have values of +1/2 or -1/2.
So, the possible sets of quantum numbers for the 6d orbital are:
(6, 2, -2, +1/2), (6, 2, -2, -1/2), (6, 2, -1, +1/2), (6, 2, -1, -1/2), (6, 2, 0, +1/2), (6, 2, 0, -1/2), (6, 2, 1, +1/2), (6, 2, 1, -1/2), (6, 2, 2, +1/2), (6, 2, 2, -1/2)
3. 5s orbital:
- For the principal quantum number (n), we know it is 5.
- For the azimuthal quantum number (l), since it is an s orbital, l = 0.
- For the magnetic quantum number (ml), it can only have a value of 0.
- For the spin quantum number (ms), it can have values of +1/2 or -1/2.
So, the possible set of quantum numbers for the 5s orbital is:
(5, 0, 0, +1/2), (5, 0, 0, -1/2)
4. 4d orbital:
- For the principal quantum number (n), we know it is 4.
- For the azimuthal quantum number (l), since it is a d orbital, l = 2.
- For the magnetic quantum number (ml), it can have values of -2, -1, 0, 1, or 2.
- For the spin quantum number (ms), it can have values of +1/2 or -1/2.
So, the possible sets of quantum numbers for the 4d orbital are:
(4, 2, -2, +1/2), (4, 2, -2, -1/2), (4, 2, -1, +1/2), (4, 2, -1, -1/2), (4, 2, 0, +1/2), (4, 2, 0, -1/2), (4, 2, 1, +1/2), (4, 2, 1, -1/2), (4, 2, 2, +1/2), (4, 2, 2, -1/2)