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 the

Correct answer: D. ( II ) ( ii ) ( P ) (A)(IV)(iv)(R) ⇒ incorrect, because, d _ z ^ 2 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.

JEE Advanced 2017Paper 1

Exam: JEE Advanced
Year: 2017
Paper: Paper 1
Subject: Chemistry
Chapter: Structure of Atom

JEE Advanced 2017 · Paper 1 · Chemistry · Structure of Atom

The wave function, ψ _ n, l, m _ l is a mathematical function whose...

The wave function, ${ψ}_{n, l, {m}_{l}}$ is a mathematical function whose value depends upon spherical polar coordinates $\left(r, \theta, ϕ\right)$ of the electron and characterized by the quantum numbers $n, l and {m}_{l}$ . Here $r$ is the distance from the nucleus, $\theta$ is colatitude and $ϕ$ is azimuth. In the mathematical functions given in the Table, $Z$ is the atomic number and ${a}_{o}$ is Bohr radius

Column 1	Column 2	Column 3
(I) $1s$ orbital	(i) ${ψ}_{n, l, {m}_{l}} ∝ \left(\dfrac{Z}{{a}_{o}}\right)\dfrac{3}{2}{e}^{- \left(\dfrac{Zr}{{e}_{o}}\right)}$	(P)
(II) $2s$ orbital	(ii) One radial node	(Q) Probability density at the nucleus $∝ 1{a}_{o}^{3}$ .
(III) $2{p}_{z}$ orbital	(iii) ${ψ}_{n, l, {m}_{l}} ∝ \left(\dfrac{Z}{{a}_{o}}\right)\dfrac{5}{2}{re}^{- \left(\dfrac{Zr}{2{a}_{o}}\right)}cos \theta$	(R) Probability density is maximum at the nucleus.
(IV) $3{d}_{z}^{2}$ orbital	(iv) $xy$ -plane is a nodal plane	(S) Energy needed to excite an electron from $n = 2$ state to $n = 4$ state is $\dfrac{27}{32}$ 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

Options

A $( III ) ( iii ) ( P )$
B $( I ) ( ii ) ( S )$
C $( IV ) ( iv ) ( R )$
D $( II ) ( ii ) ( P )$

Correct answer

D. $( II ) ( ii ) ( P )$

Step-by-step solution

$\left(A\right)\left(IV\right)\left(iv\right)\left(R\right) ⇒$ incorrect, because, ${d}_{{z}^{2}}$ has no nodal plane.

\left(B\right)\left(II\right)\left(ii\right)\left(P\right) ⇒ $correct, because$ 2s $orbital has$ 1 $radial node.<img src="https://cdn-question-pool.Quantrex.app/pyq/jee_advanced/33_solu_chem_pa1.jpg"/>$ \left(C\right)\left(III\right)\left(iii\right)\left(P\right) ⇒ $incorrect, because probability density for$ 2p $at nucleus is zero.\left(D\right)\left(I\right)\left(ii\right)\left(S\right) ⇒$ incorrect, because $1s$ orbital has no radial node.

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