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

Step-by-step solution

The number of angular nodes is equal to the azimuthal quantum number ( l ). The number of radial nodes is given by (n - l - 1) . For orbital P: Angular nodes = 1 l = 1 Radial nodes = 2 n - 1 - 1 = 2 n = 4 Orbital P is 4 p , and (n+l) = 4 + 1 = 5 . For orbital Q: Angular nodes = 2 l = 2 Radial nodes = 0 n - 2 - 1 = 0 n = 3 Orbital Q is 3 d , and (n+l) = 3 + 2 = 5 . For orbital R: Angular nodes = 2 l = 2 Radial nodes = 1 n - 2 - 1 = 1 n = 4 Orbital R is 4 d , and (n+l) = 4 + 2 = 6 . For orbital S: Angular nodes = 0 l