Core Syllabus Module

Atomic Structure

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Chapter Elite-20 Challenge Zone

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JEE Advanced 2020

LEVELJEE Advanced

The figure below is the plot of potential energy versus internuclear distance ( $d$ ) of H $_{2}$ molecule in the electronic ground state. What is the value of the net potential energy $E_{0}$ (as indicated in the figure) in kJ mol $^{- 1}$ , for $d = d_{0}$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart. [Use Avogadro constant as $6.023 \times 1 0^{23} mol^{- 1}$ .]

JEE Advanced 2017

LEVELJEE Advanced

Comprehension Passage

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

a_{0}

is Bohr radius.

Column-1 (I) 1s orbital (II) 2s orbital (III) 2 p_{z} orbital (IV) 3 d_{z^{2}} orbital Column-2 (i) Ψ_{n, l, m_{l}} \propto (\frac{Z}{a _{0}})^{\frac{3}{2}} e^{- (\frac{Z r}{a _{0}})} (ii) One radial node (iii) Ψ_{n, l, m_{l}} \propto (\frac{Z}{a _{0}})^{\frac{5}{2}} r e^{- (\frac{Z r}{2 a _{0}})} cos θ (iv) xy - plane is a nodal plane Column-3 (P) [See Graph in Image] (Q) Probability density at nucleus \propto \frac{1}{a _{0}^{3}} (R) Probability density is maximum at nucleus (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

Question 1:

For the given orbital in column 1, the only CORRECT combination for any hydrogen - like species is :

For $He^{+}$ ion, the only INCORRECT combination is

For hydrogen atom, the only CORRECT combination is

$X^{a +}$ and $Y^{b +}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n = 1$ and $n = 2$ of $X^{a +}$ is $λ$ . The wavelength of light absorbed during the transition between the states with principal quantum numbers $n = 2$ and $n = 4$ of $Y^{b +}$ is $9 λ$ . The lowest possible value of $(a + b)$ is _____.

JEE Advanced 2026

LEVELJEE Advanced

The 2s and the 2p orbital energies of hydrogen atom are $E_{2 s} (H)$ and $E_{2 p} (H)$ , respectively. The 2s and the 2p orbital energies of lithium atom are $E_{2 s} (Li)$ and $E_{2 p} (Li)$ , respectively. The correct option (s) about the orbital energies is (are)

* Multiple Correct Options

(A)

E_{2 s} (Li) < E_{2 p} (Li)

(B)

E_{2 s} (H) = E_{2 p} (H)

(C)

E_{2 p} (H) < E_{2 s} (Li)

(D)

E_{2 s} (H) > E_{2 s} (Li)

JEE Main 2021

LEVELJEE Advanced

When light of wavelength $248 nm$ falls on a metal of threshold energy $3.0 eV$ , the de-Broglie wavelength of emitted electrons is ...... $\overset{˚}{A}$ . [Round off to the nearest integer] [Use: $3 = 1.73$ , $h = 6.63 \times 1 0^{- 34} Js$ , $m_{e} = 9.1 \times 1 0^{- 31} kg$ , $c = 3.0 \times 1 0^{8} ms^{- 1}$ , $1 eV = 1.6 \times 1 0^{- 19} J$ ]

JEE Main 2020

LEVELJEE Advanced

Consider the hypothetical situation where the azimuthal quantum number, $l$ takes values $0, 1, 2, \dots n + 1$ , where $n$ is the principle quantum number. Then, the element with atomic number

(A)

8 is the first noble gas

(B)

13 has a half-filled valence subshell

(C)

9 is the first alkali metal

(D)

6 has a 2p-valence subshell

JEE Main 2019

LEVELJEE Advanced

Which of the following combination of statements is true regarding the interpretation of the atomic orbitals? I. An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum. II. For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number. III. According to wave mechanics, the ground state angular momentum is equal to $\frac{h}{2 π}$ . IV. The plot of $ψ$ vs $r$ for various azimuthal quantum numbers, shows peak shifting towards higher $r$ value.

What is the work function of the metal, if the light of wavelength $4000 \overset{˚}{A}$ generates photoelectron of velocity $6 \times 1 0^{5} ms^{- 1}$ from it? (Mass of electron $= 9 \times 1 0^{- 31} kg$ Velocity of light $= 3 \times 1 0^{8} ms^{- 1}$ Planck's constant $= 6.626 \times 1 0^{- 34} Js$ Charge of electron $= 1.6 \times 1 0^{- 19} JeV^{- 1}$ )

(A)

4.0 eV

(B)

2.1 eV

(C)

0.9 eV

(D)

3.1 eV

JEE Main 2021

LEVELJEE Advanced

An accelerated electron has a speed of $5 \times 1 0^{6} ms^{- 1}$ with an uncertainty of $0.02%$ . The uncertainty in finding its location while in motion is $x \times 1 0^{- 9} m$ . The value of $x$ is ......... . (Nearest integer) [Use mass of electron $= 9.1 \times 1 0^{- 31} kg$ , $h = 6.63 \times 1 0^{- 34} Js$ , $π = 3.14$ ]

JEE Main 2021

LEVELJEE Advanced

A metal surface is exposed to $500 nm$ radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 1 0^{14} Hz$ . The velocity of ejected electron is ......... $\times 1 0^{5} ms^{- 1}$ . (Nearest integer) [Use $h = 6.63 \times 1 0^{- 34} Js$ , $m_{e} = 9.0 \times 1 0^{- 31} kg$ ]

JEE Advanced 2016

LEVELJEE Main

P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness, dr, at a distance r from the nucleus. The volume of this shell is $4 π r^{2} dr$ . The qualitative sketch of the dependence of P on r is -

Consider a helium (He) atom that absorbs a photon of wavelength $330 nm$ . The change in the velocity (in $cm s^{- 1}$ ) of He atom after the photon absorption is ______. (Assume: Momentum is conserved when photon is absorbed. [Use: Planck constant $= 6.6 \times 1 0^{- 34} J s$ , Avogadro number $= 6 \times 1 0^{23} mol^{- 1}$ , Molar mass of He $= 4 g mol^{- 1}$ ]

JEE Advanced 2019

LEVELJEE Main

The ground state energy of hydrogen atom is $- 13.6 eV$ . Consider an electronic state $Ψ$ of $He^{+}$ whose energy, azimuthal quantum number and magnetic quantum number are $- 3.4 eV$ , $2$ and $0$ respectively. Which of the following statement(s) is(are) true for the state $Ψ$ ?

* Multiple Correct Options

(A)

It has

2

angular nodes

(B)

It has

3

radial nodes

(C)

It is a

4 d

state

(D)

The nuclear charge experienced by the electron in this state is less than

2 e

, where

e

is the magnitude of the electronic charge.

JEE Advanced 2023

LEVELJEE Main

For $He^{+}$ , a transition takes place from the orbit of radius $105.8 pm$ to the orbit of radius $26.45 pm$ . The wavelength (in nm) of the emitted photon during the transition is ______. [Use: Bohr radius, $a = 52.9 pm$ Rydberg constant, $R_{H} = 2.2 \times 1 0^{- 18} J$ Planck's constant, $h = 6.6 \times 1 0^{- 34} J s$ Speed of light, $c = 3 \times 1 0^{8} m s^{- 1}$ ]

JEE Advanced 2015

LEVELJEE Main

Not considering the electronic spin the degeneracy of the second excited state ( $n = 3$ ) of H-atom is 9, where the degeneracy of the second excited state of $H^{-}$ is

JEE Main 2021

LEVELJEE Main

According to Bohr's atomic theory, I. kinetic energy of electron is $\propto \frac{Z ^{2}}{n ^{2}}$ II. the product of velocity ( $v$ ) of electron and principal quantum number ( $n$ ), ' $v n$ ' $\propto Z^{2}$ . III. frequency of revolution of electron in an orbit is $\propto \frac{Z ^{3}}{n ^{3}}$ IV. coulombic force of attraction on the electron is $\propto \frac{Z ^{3}}{n ^{4}}$ Choose the most appropriate answer from the options given below.

If the de-Broglie wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 π a_{0}$ ( $a_{0}$ is Bohr radius), then the value of $n / Z$ is

For any given series of spectral lines of atomic hydrogen, let $Δ \overset{ν}{ˉ} = \overset{ν}{ˉ}_{m a x} - \overset{ν}{ˉ}_{m i n}$ be the difference in maximum and minimum frequencies in $cm^{- 1}$ . The ratio $Δ \overset{ν}{ˉ}_{Lyman} /Δ \overset{ν}{ˉ}_{Balmer}$ is

A source of monochromatic radiation of wavelength $400 nm$ provides $1000 J$ of energy in $10$ seconds. When this radiation falls on the surface of sodium, $x \times 1 0^{20}$ electrons are ejected per second. Assume that wavelength $400 nm$ is sufficient for ejection of electron from the surface of sodium metal. The value of $x$ is ...... . (Nearest integer) $(h = 6.626 \times 1 0^{- 34} Js)$

JEE Main 2021

LEVELJEE Main

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $\frac{h ^{2}}{x m a _{0}^{2}}$ . The value of $10 x$ is ……… . ( $a_{0}$ is radius of Bohr's orbit) (Nearest integer) [Given, $π = 3.14$ ]

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Preliminary Models

Bohr's Model

Wave Particle Duality

Quantum Mechanical Model

Chapter Elite-20 Challenge Zone

Comprehension Passage

For the given orbital in column 1, the only CORRECT combination for any hydrogen - like species is :

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For He+ ion, the only INCORRECT combination is

For hydrogen atom, the only CORRECT combination is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Not considering the electronic spin the degeneracy of the second excited state (n=3) of H-atom is 9, where the degeneracy of the second excited state of H− is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If the de-Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5πa0​ (a0​ is Bohr radius), then the value of n/Z is

For $He^{+}$ ion, the only INCORRECT combination is

Not considering the electronic spin the degeneracy of the second excited state ( $n = 3$ ) of H-atom is 9, where the degeneracy of the second excited state of $H^{-}$ is

If the de-Broglie wavelength of the electron in $n^{th}$ Bohr orbit in a hydrogenic atom is equal to $1.5 π a_{0}$ ( $a_{0}$ is Bohr radius), then the value of $n / Z$ is