The wave function $ψ_{n, l, m_{l}}$ 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 $m_{l}$ . Here r is distance from nucleus, $θ$ is colatitude and $ϕ$ is azimuth. In the mathematical functions given in the Table, Z is atomic number and $a_{0}$ is Bohr radius.
Column 1 Column 2 Column3
(I) Is orbital (i) $ψ_{n, l, m_{i}} α {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{- (\frac{z r}{a_{0}})}$
(P)

(II) 2S orbital (ii) one radial node
(Q) Probability density at nucleus $α \frac{1}{{a_{0}}^{3}}$

(III) $2 P_{z}$ orbital (iii) $ψ_{n, l, m_{j}} α {(\frac{Z}{a_{0}})}^{\frac{5}{2}} r e^{- (\frac{Z r}{2 a_{0}})} COS θ$ (R) Probability density is maximum at nucleus
(IV) $3 {d_{z}}^{2}$ orbital (iv) xy-plane is a nodal plane (S) Energy needed to excite electron from n=2 state to n= 4 state is $\frac{27}{32}$ times the energy needed to excite electron from n=2 state to n=6 state
For the given orbital in column I, the only CORRECT combination for any hydrogen-like species is

Difficult

Solution

1s ® 0 0 radial nodes , no angular component (Þ no cos q)
2s ® 0 1 radial node, , no angular component (Þ no cos q)
$2 p_{z} \to$ 0 radial node, angular component is present (Þ no cos q)
$3 d_{z}^{2} \to$ 0 radial node, angular component is present(Þ no cos q)
a) 1s ® 0 radial node Þ wrong as (ii),(i) 1 radial node
b) $3 d_{z}^{2} \Rightarrow d z^{2}' R' i s w r o n g p o int$
c)for $2 p_{z} g r a p h' p' i s w r o n g$
d) correct

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Column 1	Column 2	Column3
(I) Is orbital	(i) $ψ_{n, l, m_{i}} α {(\frac{Z}{a_{0}})}^{\frac{3}{2}} e^{- (\frac{z r}{a_{0}})}$	(P)
(II) 2S orbital	(ii) one radial node	(Q) Probability density at nucleus $α \frac{1}{{a_{0}}^{3}}$
(III) $2 P_{z}$ orbital	(iii) $ψ_{n, l, m_{j}} α {(\frac{Z}{a_{0}})}^{\frac{5}{2}} r e^{- (\frac{Z r}{2 a_{0}})} COS θ$	(R) Probability density is maximum at nucleus
(IV) $3 {d_{z}}^{2}$ orbital	(iv) xy-plane is a nodal plane	(S) Energy needed to excite electron from n=2 state to n= 4 state is $\frac{27}{32}$ times the energy needed to excite electron from n=2 state to n=6 state