An electron in a multi-electron atom is present in an orbital 'X'. It is known that the energy of orbital 'X' is strictly greater than the energy of a 4 s orbital, but strictly less than the energy of a 4 p orbital. What are the principal ( n ) and azimuthal ( l ) quantum numbers for the orbital 'X'?

Step-by-step solution

The energy of an orbital in a multi-electron atom is determined by the (n+l) rule. For the 4 s orbital: n=4, l=0 (n+l) = 4 For the 4 p orbital: n=4, l=1 (n+l) = 5 According to the Aufbau principle, the orbital that fills between 4 s and 4 p is the 3 d orbital. For the 3 d orbital: n=3, l=2 (n+l) = 5 Since the 3 d and 4 p orbitals both have (n+l) = 5 , the orbital with the lower principal quantum number ( n ) has lower energy. Thus, the energy of 3 d is less than that of 4 p . Therefore, the orbital 'X' is 3 d , whi