The 3f orbital is not possible due to the rules of quantum mechanics that govern the behavior of electrons in atoms. According to the principles of quantum mechanics, each electron in an atom is described by a set of quantum numbers, which include the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (ml).
The principal quantum number (n) indicates the energy level of the electron. The azimuthal quantum number (l) describes the shape of the orbital and can take on integer values from 0 to (n-1). This means that for the 3rd energy level (n=3), the possible values of l are 0, 1, and 2, corresponding to the s, p, and d orbitals, respectively. Therefore, the values of l for n=3 are:
- l = 0 (s orbital)
- l = 1 (p orbital)
- l = 2 (d orbital)
The value l = 3, which would correspond to the f orbital, is not allowed in the 3rd energy level because it would require n to be at least 4 (as l can only take values from 0 to n-1). Thus, the f orbitals only appear starting from the 4th energy level (n=4), where l can equal 3, leading to the existence of 4f and higher orbitals.
In summary, the 3f orbital does not exist because the allowed values of l for n=3 do not reach 3, which means no f orbitals are possible at this principal energy level.