write down the possible terms of one electron system corresponding to n=2
To determine the possible terms of a one-electron system corresponding to n=2, we need to consider the quantum numbers associated with a hydrogen-like atom or ion. These quantum numbers are the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml).
For n=2, the principal quantum number tells us that the electron is in the second energy level (shell).
The azimuthal quantum number, l, determines the shape of the electron's orbital and can have values from 0 to (n-1). So for n=2, l can be 0 or 1.
The magnetic quantum number, ml, specifies the orientation of the orbital and can have values from -l to +l. Therefore, for l=0, ml is 0, and for l=1, ml can be -1, 0, or +1.
Combining the values of l and ml for n=2, we can list the possible terms:
1. For l=0 (s orbital):
- Term: 2s (ml=0)
2. For l=1 (p orbital):
- Terms: 2p₀ (ml=-1), 2p₁ (ml=0), and 2p₂ (ml=+1)
These are the possible terms for a one-electron system corresponding to n=2. Each term corresponds to a different orbital and represents the different possible configurations of the electron in the second energy level.