Four orbitals P , Q , R , and S in a multi-electron atom are described by their respective numbers of radial and angular nodes as follows: P : 1 radial node, 1 angular node Q : 0 radial nodes, 2 angular nodes R : 2 radial nodes, 0 angular nodes S : 3 radial nodes, 0 angular nodes The correct increasing order of energy for these four orbitals is:

Step-by-step solution

The number of angular nodes is given by l , and the number of radial nodes is given by n - l - 1 . For orbital P : angular nodes = 1 l=1 . Radial nodes = n - 1 - 1 = 1 n=3 . This is the 3 p orbital ( n+l=4 ). For orbital Q : angular nodes = 2 l=2 . Radial nodes = n - 2 - 1 = 0 n=3 . This is the 3 d orbital ( n+l=5 ). For orbital R : angular nodes = 0 l=0 . Radial nodes = n - 0 - 1 = 2 n=3 . This is the 3 s orbital ( n+l=3 ). For orbital S : angular nodes = 0 l=0 . Radial nodes = n - 0 - 1 = 3 n=4 . This is the 4 s