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The wave function, ψn, l, ml is a mathematical function whose value depends...

The wave function, ψn, l, ml is a mathematical function whose value depends upon spherical polar coordinates (r, θ, ϕ) of the electron and characterized by the quantum numbers n, l and ml . Here r is the distance from the nucleus, θ is colatitude and ϕ is azimuth. In the mathematical functions given in the Table, Z is the atomic number and ao is Bohr radius
 

Column  1Column  2Column 3
(I) 1s orbital(i) ψn, l, ml (Zao)32 e-(Zreo)(P)
(II) 2s orbital(ii) One radial node(Q) Probability density at the nucleus 1a3o.
(III) 2pz orbital(iii) ψn, l, ml (Zao)52re-(Zr2ao)cosθ(R) Probability density is maximum at the nucleus.
(IV) 3d2z orbital(iv) xy -plane is a nodal plane(S) Energy needed to excite an electron from n=2 state to n=4 state is 2732 times the energy needed to excite are electron from n=2 state to n=6 state.
For the given orbital in column 1, the only correct combination for any hydrogen-like species is
(III) (iii) (P)
(I) (ii) (S)
(IV) (iv) (R)
(II) (ii) (P)
Solution:

(A)  (IV) (iv) (R) incorrect, because, dz2  has no nodal plane.

(B)  (II) (ii) (P) correct, because 2s orbital has 1 radial node.

(C)  (III) (iii) (P) incorrect, because probability density for 2p at nucleus is zero.

(D)  (I) (ii) (S) incorrect, because 1s orbital has no radial node.