Which set of quantum numbers(n, l, ml, ms) could describe the highest-energy electron in a ground-state potassium ion, K?
a) (4, 1, -1, 1/2)
b) (4, 1, 0, 1/2)
c) (4, 0, 1, 1/2)
d) (4, 0, 0, 1/2)
e) (4, 1, 1, 1/2)
1s2 2s2 2p6 3s2 3p6 4s1
So n = 4
l = 0 because it's an s electron
ml = 0 because l = 0
ms = 1/2
To determine the set of quantum numbers that could describe the highest-energy electron in a ground-state potassium ion (K), we need to understand the rules for assigning quantum numbers.
The quantum numbers describe various properties of an electron, including its energy level (n), orbital shape (l), orientation in space (ml), and spin (ms). Here's a brief explanation of each quantum number:
1. Principal quantum number (n): This quantum number determines the energy level and size of an orbital. It can have integer values greater than or equal to 1.
2. Angular momentum quantum number (l): This quantum number determines the shape of an orbital. It can have integer values ranging from 0 to n-1.
3. Magnetic quantum number (ml): This quantum number determines the orientation of an orbital in space. It can have integer values ranging from -l to l.
4. Spin quantum number (ms): This quantum number describes the spin of an electron. It can have values of either +1/2 (spin-up) or -1/2 (spin-down).
In a ground-state potassium ion (K+), which has lost one electron, the highest-energy electron will be found in the next available energy level. The electronic configuration of neutral potassium (K) is [Ar] 4s^1, indicating that the highest-energy electron is in the 4s orbital.
Now, let's evaluate each option:
a) (4, 1, -1, 1/2): This set of quantum numbers is invalid since the magnetic quantum number (ml) cannot have a negative value.
b) (4, 1, 0, 1/2): This set of quantum numbers is valid. It represents the 4s orbital, with ml = 0 indicating that the orbital is not oriented in any specific direction.
c) (4, 0, 1, 1/2): This set of quantum numbers is invalid since the angular momentum quantum number (l) cannot be zero for an electron in the 4s orbital.
d) (4, 0, 0, 1/2): This set of quantum numbers is valid. It represents the 4s orbital, with both l and ml equal to zero.
e) (4, 1, 1, 1/2): This set of quantum numbers is invalid since the magnetic quantum number (ml) cannot exceed the value of the angular momentum quantum number (l).
Based on the analysis, the only valid set of quantum numbers that could describe the highest-energy electron in a ground-state potassium ion (K+) is option (d) - (4, 0, 0, 1/2).
Remember, these answers are based on the principles of quantum mechanics and the specific electronic configuration of potassium.
To determine the set of quantum numbers that describes the highest-energy electron in a ground-state potassium ion (K), we need to consider the electron configuration of potassium.
The electron configuration of potassium (K) is: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1.
In a ground-state ion, the highest-energy electron is the one that gets removed. In the case of a potassium ion (K+), the 4s^1 electron gets removed, as it has the highest energy level.
The quantum numbers are as follows:
- Principal quantum number (n): The principal quantum number for the 4s^1 electron is 4.
- Azimuthal quantum number (l): The azimuthal quantum number for the 4s^1 electron is 0.
- Magnetic quantum number (ml): The magnetic quantum number for the 4s^1 electron is 0.
- Spin quantum number (ms): The spin quantum number for all electrons, including the 4s^1 electron, is always 1/2.
Therefore, the correct set of quantum numbers is (4, 0, 0, 1/2).
Out of the given options, the correct answer is: d) (4, 0, 0, 1/2).