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 1 | Column 2 | Column 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. |
(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.
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