184 JEE-Chemistry ALLEN

EXERCISE # J-MAINS
1. If the kinetic energy of an electron is increased four times, the wavelength of the de-Broglie wave associated
with it would become :- [JEE-Main(online) 2012]
(1) Two times (2) Half (3) One fourth (4) Four times
AS0171
2. If the radius of first orbit of H atom is a0, the de-Broglie wavelength of an electron in the third orbit
is :- [JEE-Main(online) 2012]
(1) 6 p a0 (2) 8 p a0 (3) 2 p a0 (4) 4 p a0
AS0172
3. The wave number of the first emission line in the Balmer series of H-Spectrum is :
(R = Rydberg constant) : [JEE-Main(online) 2013]
3 9 5 7
(1) R (2) R (3) R (4) R
4 400 36 6
AS0173
4. The de Broglie wavelength of a car of mass 1000 kg and velocity 36 km/hr is :
(h = 6.63 × l0–34 Js) [JEE-Main(online) 2013]
(1) 6.626 × l0 m
–31
(2) 6.626 × 10 m
–34

(3) 6.626 × 10 m–38

(4) 6.626 × 10–30 m
AS0174
5. For which of the following particles will it be most difficult to experimentally verify the
de-Broglie relationship? [JEE-Main(online) 2014]
(1) a dust particle (2) an electron (3) a proton (4) an a-particle.
AS0175
6. If the binding energy of the electron in a hydrogen atom is 13.6 eV, the energy required to remove
the electron from the first excited state of Li++ is : [JEE-Main(online) 2014]
(1) 13.6 eV (2) 30.6 eV (3) 122.4 eV (4) 3.4 eV
AS0176
7. Based on the equation [JEE-Main(online) 2014]
æ 1 1 ö
DE = -2.0 ´10-18 J ç 2 - 2 ÷
è n 2 n1 ø
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the wavelength of the light that must be absorbed to excite hydrogen electron from level n = 1 to level
n = 2 will be (h = 6.625 × 10–34 Js, C = 3 × 108 ms–1) [JEE-Main(online) 2014]
(1) 2.650 × 10 m –7 (2) 1.325 × 10 m
–7

(3) 1.325 × 10 m –10 (4) 5.300 × 10–10 m

AS0177
8. If l0 and l be the threshold wavelength and wavelength of incident light, the velocity of photoelectron
ejected from the metal surface is [JEE-Main(online) 2014]

2hc æ l 0 - l ö 2h æ 1 1 ö 2h 2hc
(1) ç
m è ll 0 ø
÷ (2) ç - ÷
m è l0 l ø
(3) ( l0 - l ) (4) ( l0 - l )
m m

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 ALLEN Atomic Structure 185
AS0178
9. Ionization energy of gaseous Na atoms is 495.5 kjmol–1. The lowest possible frequency of light that ionizes
a sodium atom is
(h = 6.626 × 10–34 Js, NA = 6.022 × 1023 mol–1) [JEE-Main(online) 2014]
(1) 3.15 × 1015 s–1 (2) 4.76 × 1014 s–1 (3) 1.24 × 1015 s–1 (4) 7.50 × 104 s–1
AS0179
10. Which of the following is the energy of a possible excited state of hydrogen?
[JEE-Main(offline) 2015]
(1) –3.4 eV (2) +6.8 eV (3) +13.6 eV (4) –6.8 eV
AS0180
3
11. At temperature T, the average kinetic energy of any particle is kT- The de Broglie wavelength
2
follows the order : [JEE-Main(online) 2015]
(1) Visible photon > Thermal electron > Thermal neutron
(2)Thermal proton > Thermal electron > Visible photon
(3)Visible photon > Thermal neutron > Thermal electron
(4) Thermal proton > Visible photon > Thermal electron
AS0181
12. A stream of electrons from a heated filament was passed between two charged plates kept at a potential
difference V volts. If e and m are charge and mass of an electron respectively, then the value of h/
l (where l is wavelength associated with electron wave) is given by :[JEE-Main(online) 2016]

(1) 2meV (2) meV (3) 2meV (4) meV

AS0182
13. The radius of the second Bohr orbit for hydrogen atom is : [JEE-Main(offline) 2017]
(Plank's const. h = 6.6262 × 10–34 Js ; mass of electron = 9.1091 × 10–31 kg ; charge of electron
e = 1.60210 × 10–19 C ; permittivity of vaccum
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Î0 = 8.854185 × 10–12 kg–1 m–3 A2)

(1) 1.65Å (2) 4.76Å (3) 0.529Å (4) 2.12Å

AS0183
14. If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in
Paschen series of He+ is : [JEE-Main(online) 2017]

36A 9A 36A 5A
(1) (2) (3) (4)
5 5 7 9

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186 JEE-Chemistry ALLEN
AS0184
15. The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 211.6 pm.
This transition is associated with:- [JEE-Main(online) 2017]
(1) Brackett series (2) Balmer series (3) Lyman series (4) Paschen series
AS0185
16. The de-Broglie's wavelength of electron present in first Bohr orbit of 'H' atom is :-
[JEE-Main(online) 2018]
0.529
(1) Å (2) 2p × 0.529Å (3) 0.529Å (4) 4×0.529Å
2p
AS0186
17. Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by
applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is :
(1) 5 eV (2) 4 eV (3) 5.5 eV (4) 4.5 eV[JEE-Main(online) 2018]
AS0187
18. Which of the following statements is false ? [JEE-Main(online) 2018]
(1) Photon has momentum as well as wavelength.
(2) Splitting of spectral lines in electrical field is called Stark effect.
(3) Frequency of emitted radiation from a black body goes from a lower wavelength to higher
wavelength as the temperature increases.
(4) Rydberg constant has unit of energy.
AS0188
19. If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light
having wavelength l, then for 1.5 p momentum of the photoelectron, the wavelength of the light should
be: [JEE-Main(online) 2019]
(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)
1 3 2 4
(1) l (2) l (3) l (4) l
2 4 3 9
AS0189
20. The quantum number of four electrons are given below - [JEE-Main(online) 2019]
I. n = 4, l = 2, ml = –2, ms = – ½
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II. n = 3, l = 2, ml = 1, ms = + ½
III. n = 4, l = 1, ml = 0, ms = + ½
IV. n = 3, l = 1, ml = 1, ms = – ½
The correct order of their increasing energies will be -
(1) IV < III < II < I (2) IV < II < III < I (3) I < II < III < IV (4) I < III < II < IV
AS0190
21. For any given series of spectral lines of atomic hydrogen, let Dn = n max – nmin be the difference in

maximum and minimum frequencies in cm–1. The ratio Dn Lyman / Dn Balmer is :

(1) 27 : 5 (2) 4 : 1 [JEE-Main(online) 2019]
(3) 5 : 4 (4) 9 : 4

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 ALLEN Atomic Structure 187
AS0191
22. The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9.
The spectral series are: [JEE-Main(online) 2019]
(1) Paschen and P fund (2) Lyman and Paschen
(3) Brackett and Piund (4) Balmer and Brackett
AS0192
2
23. The graph betweeen |y| and r(radial distance) is shown below. This represents :-

2
|y|

r
(1) 3s orbital (2) 1s orbital [JEE-Main(online) 2019]
(3) 2p orbital (4) 2s orbital
AS0193
24. Among the following, the energy of 2s orbital is lowest in : [JEE-Main(online) 2019]
(1) K (2) Na (3) Li (4) H
AS0194
25. The electrons are more likely to be found : [JEE-Main(online) 2019]

(1) in the region a and b (2) in the region a and c

(3) only in the region c (4) only in the region a
AS0195
26. What is the work function of the metal if the light of wavelength 4000 Å generates photoelectrons of
velocity 6 × 105 ms–1 form it ? [JEE-Main(online) 2019]
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(Mass of electron = 9 × 10 kg
–31

Velocity of light = 3 × 108 ms–1

Planck's constant = 6.626 × 10–34 Js
Charge of electron = 1.6 × 10–19 JeV–1)
(1) 0.9 eV (2) 4.0 eV (3) 2.1 eV (4) 3.1 eV
AS0196
27. If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5
pa0(a0 is Bohr radius), then the value of n/z is : [JEE-Main(online) 2019]
(1) 1.0 (2) 0.75 (3) 0.40 (4) 1.50

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188 JEE-Chemistry ALLEN

AS0197
28. The upper stratosphere consisting of the ozone layer protects us from the sun's radiation that falls in the
wavelength region of : [JEE-Main(online) 2019]
(1) 600-750 nm (2) 0.8-1.5 nm (3) 400-550 nm (4) 200-315 nm
AS0198
29. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral
line of H-atom is suitable for this purpose ? [JEE-Main(online) 2019]
[RH = 1 × 105 cm–1, h = 6.6 × 10–34 Js, c = 3 × 108 ms–1]
(1) Paschen, 5 ® 3 (2) Paschen, ¥ ® 3 (3) Lyman, ¥ ® 1 (4) Balmer, ¥ ® 2
AS0199
30. The de Broglie wavelength (l) associated with a photoelectron varies with the frequency (v) of the
incident radiation as, [v0 is thershold frequency] : [JEE-Main(online) 2019]
1 1
1 1 1
1
(1) lµ 3 (2) lµ (3) lµ (4) lµ (v - v )
(v - v0 )2 (v - v0 )4 0
(v - v0 ) 2
AS0200
31. The ground state energy of hydrogen atom is –13.6 eV. The energy of second excited state He+ ion
in eV is : [JEE-Main(online) 2019]
(1) –6.04 (2) –27.2 (3) –54.4 (4) –3.4
AS0201
32. Which of the graphs shown below does not represent the relationship between incident light and the
electron ejected form metal surface ? [JEE-Main(online) 2019]

(1) (2)
number K.E. of
of e–s e– s

0 0
Frequency of Intensity of
light
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light

(3) (4)
K.E. of K.E. of
e– s e– s

0 0
Frequency of energy of
light light

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 ALLEN Atomic Structure 189
AS0202
33. Which of the following combination of statements is true regarding the interpretation of the atomic
orbitals ? [JEE-Main(online) 2019]
(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron
in the orbital of lower angular momentum.
(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional
to the azimuthal quantum number.
h
(c) According to wave mechanics, the ground state angular momentum is equal to .
2p
(d) The plot of y Vs r for various azimuthal quantum numbers, shows peak shifting towards higher
r value.
(1) (b), (c) (2) (a), (d) (3) (a), (b) (4) (a), (c)
AS0203
34. For emission line of atomic hydrogen from ni = 8 to nf = n the plot of wave number (v) against
æ 1 ö
ç 2 ÷ will be (The Rydberg constant, RH is in wave number unit).
èn ø
(1) Linear with slope - RH [JEE-Main(online) 2019]
(2) Linear with intercept - RH
(3) Non linear
(4) Linear with slope RH
AS0204
1
35. The number of orbitals associated with quantum numbers n = 5, ms = + is :
2
[JEE-Main(online) 2020]
(1) 11 (2) 25 (3) 15 (4) 50
AS0205
ì1 1ü
36. For the Balmer series in the spectrum of H atom, n = R H í 2 - 2 ý , the correct statements among
î n1 n 2 þ
(I) and (IV) are : [JEE-Main(online) 2020]
(I) As wavelength decreases, the lines in the series converge
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(II) The integer n1 is equal to 2

(III) The lines of longest wavelength corresponds to n2 = 3
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines
(1) (II), (III), (IV) (2) (I), (II), (III) (3) (I), (III), (IV) (4) (I), (II), (IV)
AS0206
37. The radius of the second Bohr orbit, in terms of the Bohr radius, a0, in Li2+ is :
[JEE-Main(online) 2020]
4a 0 2a 0 2a 0 4a 0
(1) (2) (3) (4)
9 9 3 3
AS0207
38. The de Broglie wavelength of an electron in the 4th Bohr orbit is : [JEE-Main(online) 2020]

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190 JEE-Chemistry ALLEN
EXERCISE # J-ADVANCED
Paragraph for questions 1 to 3
The hydrogen-like species Li2+ is in a spherically symmetric state S1 with one radial node. Upon
absorbing light the ion undergoes transition to a state S2. The state S2 has one radial node and its
energy is equal to the ground state energy of the hydrogen atom. [JEE 2010]
1. The state S1 is :-
(A) 1s (B) 2s (C) 2p (D) 3s
AS0209
2. Energy of the state S1 in units of the hydrogen atom ground state energy is :-
(A) 0.75 (B) 1.50 (C) 2.25 (D) 4.50
AS0210
3. The orbital angular momentum quantum number of the state S2 is :-
(A) 0 (B) 1 (C) 2 (D) 3
AS0211
4. The maximum number of electrons that can have principal quantum number, n=3, and spin quantum
number, ms = – 1/2, is [JEE 2011]
AS0212
5. The work function (f) of some metals is listed below. The number of metals which will show
photoelectric effect when light of 300 nm wavelength falls on the metal is : :- [JEE 2011]

Metal Li Na K Mg Cu Ag Fe Pt W
f(eV) 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75
AS0213
6. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr radius]
[JEE 2012]
2 2 2 2
h h h h
(A) 4p 2 ma 2 (B) 16p 2 ma 2 (C) 32p 2 ma 2 (D) 32p 2 ma 2
0 0 0 0
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AS0214
7. The atomic masses of He and Ne are 4 and 20 a.m.u. respectively. The value of the de Broglie
wavelength of He gas at –73 ºC is "M" times that of the de Broglie wavelength of Ne at 727
ºC. M is. [JEE 2013]
AS0215
8. In an atom, the total number of electrons having quantum numbers n = 4, |m l| = 1 and

1
ms = – is [JEE 2014]
2

AS0216
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 ALLEN Atomic Structure 191

9. P is the probability of finding the 1s electron of hydrogen atom in a spherical shell of infinitesimal thickness,
2
dr, at a distance r from the nucleus. The volume of this shell is 4pr dr. The qualitative sketch of the
dependence of P on r is - [JEE 2016]

p p

(A) (B)
0 r 0 r

p p

(C) (D)
0 r 0 r
AS0217
Answer Q.10, Q.11 and Q.12 by appropriately matching the information given in the three
columns of the following table. [JEE 2017]
Column-1 Column-2 Column-3

3 æ Zr ö
æ Z ö 2 -ç a ÷
(I) 1s orbital (i) y n, l ,m1 µç ÷ e è eø (P)
è a0 ø
a

(II) 2s orbital (ii) One radial node (Q) Probability density at

1
nucleus µ
a 30
5 æ Zr ö
æ Z ö 2 -ç 2a ÷
(III) 2pz orbital (iii) y n, l ,m1 µ ç ÷ re è 0 ø cos q (R) Probability density is
è a0 ø
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maximum at nucleus

(IV) 3dz2 orbital (iv) xy - plane is a nodal plane (S) Energy needed to excite
electron from n = 2 state to
27
n = 4 state is times the
32
energy needed to excite
electron from n = 2 state to
n = 6 state

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192 JEE-Chemistry ALLEN
10. For the given orbital in column 1, the only CORRECT combination for any hydrogen - like species
is :
(A) (IV) (iv) (R) (B) (II) (ii) (P) (C) (III) (iii) (P) (D) (I) (ii) (S)
AS0218
+
11. For He ion, the only INCORRECT combination is
(A) (II) (ii) (Q) (B) (I) (i) (S) (C) (I) (i) (R) (D) (I) (iii) (R)
AS0219
12. For hydrogen atom, the only CORRECT combination is
(A) (I) (iv) (R) (B) (I) (i) (P) (C) (II) (i) (Q) (D) (I) (i) (S)
AS0220
13. The ground state energy of hydrogen atom is –13.6 eV. Consider an electronic state Y 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 Y? [JEE 2019]
(1) It has 2 angular nodes
(2) It has 3 radial nodes
(3) It is a 4d state
(4) The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude
of the electronic charge.
AS0221
14. Answer the following by appropriately matching the lists based on the information given in
the paragraph [JEE 2019]
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus.
In the following List-I contains some quantities for the nth orbit of the atom and List-II contains
options showing how they depend on n.
List-I List-II
(I) Radius of the nth orbit (P) µ n–2
(II) Angular momentum of the electron in the nth orbit (Q) µ n–1
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(III) Kinetic energy of the electron in the nth orbit (R) µ n0

(IV) Potential energy of the electron in the nth orbit (S) µ n1
(T) µ n2
(U) µ n1/2
Which of the following options has the correct combination considering List-I and List-II?
(1) (II), (R) (2) (I), (P) (3) (I), (T) (4) (II), (Q)
AS0222

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 ALLEN Atomic Structure 193

15. Answer the following by appropriately matching the lists based on the information given in
the paragraph [JEE 2019]
Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus.
In the following List-I contains some quantities for the nth orbit of the atom and List-II contains
options showing how they depend on n.
List-I List-II
th –2
(I) Radius of the n orbit (P) µ n
(II) Angular momentum of the electron in the nth orbit (Q) µ n–1
th 0
(III) Kinetic energy of the electron in the n orbit (R) µ n
th 1
(IV) Potential energy of the electron in the n orbit (S) µ n
(T) µ n2
(U) µ n1/2
Which of the following options has the correct combination considering List-I and List-II?
(1) (III), (S) (2) (IV), (Q) (3) (IV), (U) (4) (III), (P)
AS0223
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194 JEE-Chemistry ALLEN

ANSWER KEY
EXERCISE # S-I
1. Ans.(1 : 1) 2. Ans.(4 : 9)
3. Ans. n < a < p < e 4. Ans.6.0 × 10–19 unit.
5. Ans.1.6 × 10–19 Coulomb. 6. Ans.8 × 10–15 : 1
7. Ans.2.3 × 1017 kg/m3 8. Ans.1 : 2
9. Ans.1.28 × 10–14 m. 10. Ans.1.44 × 107 m/s
11. Ans.1500 Å 12. Ans.150 KHz
13. Ans.1 : 5 14. Ans.7.5 × 1012 Hz
15. Ans.4.96 × 10–19 Joule 16. Ans.1.0 × 105
17. Ans.10 22 18. Ans.0.5
19. Ans.6200 Å 20. Ans.3 × 1022
21. Ans.(2 × 1015 Hz , 1.5 × 10–7 m) 22. Ans. (1)
23. Ans.50 % 24. Ans.3.06 V
25. Ans. 0.41375 eV 26. Ans.(0.2645) Å
27. Ans.(x = 4) 28. Ans.5.44 × 105 m/s
29. Ans. 2 30 Ans.8×106
31. Ans. 6530×1012Hz 32. Ans. – 1.36 × 10–19 Joules
33. h/p 34. Ans.(2)
35. Ans. 1.18 × 107 36. Ans.(– 217.9 × 10–20 J)
37 Ans. 340 ev , – 680 eV 38 Ans.(6)
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39. Ans.6563 Å ; 1216 Å ; 1026 Å 40. Ans.10.2 eV , z = 2

x 36x
41. Ans.113.74 Å 42. Ans. (i) ; (ii)
4 7

43 Ans.(3) 44 Ans. (4)

45 Ans.3.09 × 108 cm/sec 46. Ans(3)
47. Ans (8) 48. Ans.(4)
49. Ans.3.68 × 10–65 m 50 Ans.10 pm
51. Ans.0.0826 volts 52. Ans.1.05×10–13 m