How many possible sets of quantum number values are there for a 2p electron?
The correct answer and explanation is:
For a 2p electron, there are 6 possible sets of quantum number values.
To explain how this works, let’s break down the four quantum numbers associated with an electron:
- Principal Quantum Number (n): This number describes the energy level or shell of the electron. For a 2p electron, the principal quantum number is n = 2. This indicates that the electron is in the second energy level.
- Azimuthal Quantum Number (l): This quantum number determines the shape of the orbital. For a p orbital, l = 1. Therefore, for a 2p electron, the value of l is fixed at 1, representing a p-type orbital.
- Magnetic Quantum Number (ml): The magnetic quantum number defines the orientation of the orbital in space. For a p orbital, ml can take values ranging from -l to +l. In this case, since l = 1, the possible values for ml are -1, 0, and +1.
- Spin Quantum Number (ms): The spin quantum number specifies the direction of the electron’s spin. It can take one of two values: +1/2 (spin-up) or -1/2 (spin-down).
Now, combining these values:
- The n is fixed at 2.
- The l is fixed at 1 (since it’s a p orbital).
- The ml has three possibilities: -1, 0, +1.
- The ms has two possibilities: +1/2 or -1/2.
Therefore, the total number of possible sets of quantum numbers is calculated by multiplying the number of possibilities for each quantum number: 1 (for n=2)×1 (for l=1)×3 (for ml=−1,0,+1)×2 (for ms=+1/2 or −1/2)=6.1 \text{ (for } n = 2) \times 1 \text{ (for } l = 1) \times 3 \text{ (for } ml = -1, 0, +1) \times 2 \text{ (for } ms = +1/2 \text{ or } -1/2) = 6.
Thus, there are 6 possible sets of quantum number values for a 2p electron.