The values #n, l, m_s and m_l# are the four electronic quantum numbers, and determine the position, angular momentum, spin and orbitals of an electron.
The value #l# is the "orbital angular momentum quantum number, and it determines the shape of an orbital, and therefore the angular distribution. The number of angular nodes is also equal to the value of #l#." https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/10%3A_Multi-electron_Atoms/Quantum_Numbers
#l# is dependent on #n#, with the rule stating that
#l<=(n-1)#. This means if #n=3#, then
#l=0 or1 or 2#, since
#3-1=2#, the highest value #l# can get to in this scenario.
In your question, you state that #n=2#, therefore
#l<= 2-1#
#l<=1#. Yet right afterwards, you then state that #l=2#, which is clearly impossible. Therefore, your electron doesn't exist, and thus exists nowhere.
I hope I helped!
