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

Correct answer: D. ( I ) ( i ) ( S ) We have to select only correct combination hence, the option (iv) is correct. For 1s orbital : ψ _ n, l, m α( Z a _ 0 )(3)/(2)e - zr a _ 0 Energy needed to excite an electron : from n = 2 to n = 4 Δ E _ 2 - 4 = 13 .6 Z ^ 2 × (3)/(16)eV Energy needed to excite an electron : from n = 2 to n = 6 Δ E _ 2 - 6 = 13 .6 Z ^ 2 × (8)/(36) Δ E _ 2 - 4 = (27)/(32) E _ 2 - 6 (hence, true)

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 distance from nucleus, $\theta$ is colatitude and $ϕ$ is azimuth. In the mathematical functions given in the Table, Z is atomic number and ${a}_{o}$ is Bohr radius.

Column – 1	Column – 2	Column – 3
(I) Is 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 nucleus $∝ \dfrac{1}{{a}_{o}^{3}}$
(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 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 electron from $n = 2$ state to $n = 6$ state.

For hydrogen atom, what is the only CORRECT combination?

Options

A $( I ) ( i ) ( P )$
B $( II ) ( i ) ( Q )$
C $( I ) ( iv ) ( R )$
D $( I ) ( i ) ( S )$

Correct answer

D. $( I ) ( i ) ( S )$

Step-by-step solution

We have to select only correct combination hence, the option (iv) is correct.

For 1s orbital : ${ψ}_{n, l, m}\alpha\left(\dfrac{Z}{{a}_{0}}\right)\dfrac{3}{2}e\dfrac{- zr}{{a}_{0}}$

Energy needed to excite an electron : from $n = 2$ to $n = 4$

${\Delta E}_{2 - 4} = 13 .6 {Z}^{2} \times \dfrac{3}{16}eV$

Energy needed to excite an electron : from $n = 2$ to $n = 6$

${\Delta E}_{2 - 6} = 13 .6 {Z}^{2} \times \dfrac{8}{36}$

${\Delta E}_{2 - 4} = \dfrac{27}{32}{E}_{2 - 6}$ (hence, true)

Practice Structure of Atom on Quantrex Academy →

More from Structure of Atom

The 2s and the 2p orbital energies of hydrogen atom are E_ 2s (H) and E_ 2p (H)… JEE Advanced 2026 X^ a+ and Y^ b+ are hydrogen-like species. The wavelength of light absorbed during the… JEE Advanced 2026 Consider two radiations of wavelengths 1. λ_1 = 2000 Å 2. λ_2 = 6000 Å The ratio of the… JEE Main 2026 The Bohr radius of a hydrogen like species is 70.53 pm. The species and the stationary… JEE Main 2026 If shortest wavelength of hydrogen atom in Lyman series is x , then longest wavelength in… JEE Main 2026 Match the LIST-I with LIST-II List-I Orbital List-II Radial nodes and nodal plane A. 2s… JEE Main 2026 Which of the following statement(s) is/are true ? A. If two orbitals have the same value… JEE Main 2026 Arrange the following atomic orbitals of multi electron atoms in order of increasing… JEE Main 2026 Full Structure of Atom list All JEE Advanced PYQs