The electron configuration of a neutral atom is 1s22s22p63s2. Write a complete set
of quantum numbers for each of the electrons.
Please explain with answers.
To write a complete set of quantum numbers for each electron, we need to understand what quantum numbers are and how they are used to describe the electron's properties in an atom.
Quantum numbers describe various characteristics of electrons, such as their energy, orbital shape, orientation, and spin. There are four quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (ml), and spin quantum number (ms).
Here's how you can determine the quantum numbers for each electron based on their electron configuration:
1. Principal Quantum Number (n): The principal quantum number determines the energy level or shell in which the electrons reside. It takes on positive integer values (1, 2, 3, ...) starting from the innermost shell (n=1). In the electron configuration given, the electrons are found in the following energy levels:
- The first electron occupies the 1s orbital, so its principal quantum number is n=1.
- The second electron also occupies the 1s orbital, so its principal quantum number is also n=1.
- The third electron occupies the 2s orbital, so its principal quantum number is n=2.
- The fourth, fifth, and sixth electrons occupy the 2p orbitals, so their principal quantum number is also n=2.
- The seventh and eighth electrons occupy the 3s orbital, so their principal quantum number is n=3.
2. Azimuthal Quantum Number (l): The azimuthal quantum number determines the shape of the electron's orbital and ranges from 0 to (n-1). The possible values of l depend on the principal quantum number (n). Here's how you can determine the azimuthal quantum number for each electron:
- For the 1s orbital, n=1, so its azimuthal quantum number is l=0.
- For the 2s orbital, n=2, so its azimuthal quantum number is l=0.
- For the 2p orbitals, n=2, so their azimuthal quantum numbers are l=1.
- For the 3s orbital, n=3, so its azimuthal quantum number is l=0.
3. Magnetic Quantum Number (ml): The magnetic quantum number determines the orientation of the orbital in space and ranges from -l to +l. The possible values of ml depend on the azimuthal quantum number (l). Here are the possible values of ml for each orbital:
- For the 1s orbital, l=0, so its magnetic quantum number is ml=0.
- For the 2s orbital, l=0, so its magnetic quantum number is ml=0.
- For the 2p orbitals, l=1, so the magnetic quantum numbers are ml=-1, 0, and +1.
- For the 3s orbital, l=0, so its magnetic quantum number is ml=0.
4. Spin Quantum Number (ms): The spin quantum number describes the spin state of an electron and can have two values: +1/2 or -1/2, representing the electron spinning in opposite directions.
Since the electron configuration does not specify the specific spin of each electron, we assume that each electron has a different spin. Therefore, the spin quantum number for each electron can be assigned as follows:
- The first electron: ms=+1/2
- The second electron: ms=-1/2
- The third electron: ms=+1/2
- The fourth electron: ms=-1/2
- The fifth electron: ms=+1/2
- The sixth electron: ms=-1/2
- The seventh electron: ms=+1/2
- The eighth electron: ms=-1/2
So, based on the given electron configuration, the complete set of quantum numbers for each electron is as follows:
1. First electron: (n=1, l=0, ml=0, ms=+1/2)
2. Second electron: (n=1, l=0, ml=0, ms=-1/2)
3. Third electron: (n=2, l=0, ml=0, ms=+1/2)
4. Fourth electron: (n=2, l=1, ml=-1, ms=-1/2)
5. Fifth electron: (n=2, l=1, ml=0, ms=+1/2)
6. Sixth electron: (n=2, l=1, ml=+1, ms=-1/2)
7. Seventh electron: (n=3, l=0, ml=0, ms=+1/2)
8. Eighth electron: (n=3, l=0, ml=0, ms=-1/2)
Each electron is characterized by its respective set of quantum numbers, which provide information about its location and properties within the atom.