Write a set of quantum numbers for each of the electrons with an n of 4 in a Se atom.
The correct answer and explanation is:
In a selenium (Se) atom, the electron configuration is:
$\text{Se}: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^{10} 4s^2 4p^4$
Now, considering the electrons in the fourth energy level (n = 4), we need to focus on the 4s and 4p orbitals. The 4s orbital contains 2 electrons, and the 4p orbital contains 4 electrons, as part of the atom’s overall configuration.
Quantum Numbers
Each electron can be described using a set of four quantum numbers:
- Principal Quantum Number (n): It denotes the energy level or shell the electron occupies. For Se, we are interested in the electrons in the 4th energy level, so n = 4 for all of them.
- Angular Momentum Quantum Number (l): This defines the shape of the orbital.
- For the 4s orbital, l = 0 (s orbitals have l = 0).
- For the 4p orbital, l = 1 (p orbitals have l = 1).
- Magnetic Quantum Number (mₗ): This describes the orientation of the orbital in space.
- For the 4s orbital, since l = 0, there is only one possible orientation, so mₗ = 0.
- For the 4p orbitals, there are three possible orientations (since l = 1), so mₗ can be -1, 0, or +1.
- Spin Quantum Number (mₛ): This describes the electron’s spin, which can be either +½ or -½.
- For the 4s orbital, both electrons will have opposite spins, so their mₛ values will be +½ and -½.
- For the 4p electrons, each of the four electrons will also have spins of +½ or -½. Because there are four electrons, two will have spin +½, and two will have spin -½, following Hund’s rule of maximum unpaired electrons in degenerate orbitals.
Quantum Numbers for Se Electrons in n = 4:
For the 4s electrons (2 electrons):
- n = 4, l = 0, mₗ = 0, mₛ = +½
- n = 4, l = 0, mₗ = 0, mₛ = -½
For the 4p electrons (4 electrons):
- n = 4, l = 1, mₗ = -1, mₛ = +½
- n = 4, l = 1, mₗ = 0, mₛ = +½
- n = 4, l = 1, mₗ = +1, mₛ = +½
- n = 4, l = 1, mₗ = -1, mₛ = -½
- n = 4, l = 1, mₗ = 0, mₛ = -½
- n = 4, l = 1, mₗ = +1, mₛ = -½
Thus, the set of quantum numbers for the electrons with n = 4 in a selenium atom are those listed above. These quantum numbers give a full description of each electron’s energy state, orbital shape, orientation, and spin within the atom.