...",,,,-.-- --_._,.""'_......

--------

114 I G.R. B. GHI=MISTRy' FOR COMPETITIONS

1. Match the following: (c) Paschen series (r) Absorptionspectrum

[A] ( d) Brackett series (s) Ultraviolet region
(i) Aufbau principle (a)' Line spectrum in visible region
(ii) de Broglie
" ' '

(b) Orientation of an eI(:ctron in an

[D] Match the List-lwith
, 'orbital List-ll
(iii) Angular momentum (c) Photon'
(a) K-shelL (P) Electrons in elliptical
, (iv) Hund's rule (d) A ,hl(,,!v) " orbit
: (v) ,:n . (i)'tiedrofu6
(b) L-shell (q) Electrons in circular orbit
(vi) Planck's law (f) mvr
(c) Hydrogen atom, (r) Shell of lowes,! energy
[B] ",
(i) , Thomson (d) Boron atom in groun,d (s) B04(s atomic model
(a)' Exclusion principle
state
(ii) Pauli (b) Radioactivity
(iii) Becquerel' , ' , (c) "Atomiemodel [E] Match the ions of List-I with the properties
(iv) (d) Cathode rays Liit-I List-ll
(v) 'Bohr (e) Neutron
(a) Mn 2 + (p) Diamagnetic
(vi) Chadwick (f) Isotopes
[C] (b) V 2+ (q) Paramagnetic
(i) Cathode rays (a) Helium nuclei (c) Zn 2+ (r) Coloured compounds , .
(ii) Dumb-bell ,(b) Uncertainty principle (d) Ti4+ (s) Magnetic moment = 2.82 BM
(iii) Alpha particles (c) Electromagnetic radiation
[F] Match the List-I with List-II:
(iv) Moseley (d) p -orbital
(v) Heisenberg (e) Atomic number List.;.I List-ll
(vi) (f) Electrons (a) Mg2+ (P) Zero spin multiplicity
2. Matrix Matching Problems (For lIT Aspirants):
(b) Fe 2+ (q) Spin multiplicity = 3
[A] Match the Colurnn-I and Column-II:
(c) C0 3 + (r) Total spin = 0 ,
Column-I ColulIID-D
(d) Ca 2+ (s) Total spin :::: 2
(a) X-rays (P) Davisson and Germer
, experiment , [G] Match the prope.rties of List-I with the formulae in List-II:
(b)' Atomic number (q) Crystal structure List-I ' . List'-ll
determination , determination
(a) Angular momentum of ' (P)
(c) Dual nature of matter (r) Moseley's law electron 2n
(d) Dual nature of radiation (s) Bragg's law (b) Orbital, angular (q) lro
[B] Match the Columil-I and Column-II: momentum
(c) Wavelength of matter (r) nhl2n
Column'" Co)uDID-ll wave
(a) Lyman series (P) Visible region (d) Quantised. value( s) (s) hlp
(b) Balmer series (q) 'UVregion [H] Match the orbitals of List-I with the nodal properties of
"'0·
(c) Pfund ,series (r) IR region List-II:. '
(d) Light emitted by, sodium (s) Line emission spectrum List-I·, List-n
lamp
(a) 2s (P) , Angular node = 1
[C] Match the List-I with List-II in hydrogen atom spectrum:
(b) Is //I" (q) Radial node 0
List-I List-II (c) 2p (r) Radial node = 1
t.:
(a) Lyman series (P) Visible region , (d) 3p (s) Angular node = 0
, (6) Balmer series (q) Infrared region
 I
ATOMIC STRUCTURE
"r 115
[1] Match the dectronic transitions of List-I with spectral [M] Match the List-I with List-II:
properties List-1I:
, List-I List-ll
List-I List-ll
(a) Radius of nth orbital (P) Inversely pj-opOltional to Z
(a) 3 (P) 10 lines in the spectrum
(b) Energy of nth shell (q) Integral mul!ip!e' of h/21t
(b) (q) Spectral lines in visible
region
(c) Angular momentum of (r) Proportional to n 2
electron
(c) n= (r) 6 lines in the spectrum
(d) Velo<.;ity of electron in nth (s) Inversely proportional to
(d) 2 (s) Spectral lines in infrared orbit 'n'
region
[N] Match the entries in Column-! with the correctly related
[1] Match the List-1 with List-II: inColulnn-II:
List:.t List·ll Column.l
,"

(a) Radius of eleGtron orbit (P) Principal quantum (a) Orbital angular momentum (P) Principal quantum
number of the electron in a hydrogen- number
(b) Energy of electron (q)-Azimutbalquantum. like at.Qmi,G orl:>ita,l
number (b) A hydrogen-like one electron (q) Azimuthal quarttum
(c) Energy of subshell (r) Magnetic quantum wave function obeying Pauli number
number principle

(d) , Orientation of the atomic (s) Spin quantum number (c) Shape, size and ori,entation (r) Magnetic quantum
of hydrogen-like atomic , number
orbitals
orbitals
[K] M.atch the List-I with List-II: (d) Probability density of (s) Electron spin quantum
List-I List-ll electron at the nucleus in number
hydrogen-like atom
(a) ElectrolJ. cannot exist in (P) de Broglie wave
[0] Match the List-lWith List-II: . ,(lIT 2006)
the nucleus
(b) Microscopic particles in (q) Electromagnetic wave List-I List-ll
, motion are associated with' (a) Wave nature of radiation (1') Photoelectric'
(c) No medium is required for (r) Uncertainty principle effect
propagation (b) Photon nature of radiation , (q) Compton effect
(d) Concept of orbit was (s) Transverse wave (c) , I,nteraction of a photon with an (r) Diffraction
replaced by orbital electron, such that quantum energy
is slightly equal to or greater than
[L] According to Bohr theory: (lIT 2006)
the binding ,energy of electron, is,
En == Total energy more likely to result in:
K /I = Kinetic energy
VII = Potential energy l.:.d) Interaction of a photon with an (s) Interference
,
electron, such that photon energy is
r" Radius of nth orbit
much greater than the binding
Match the following:
energy of electron, is more likely to
Column-I 'Column-ll result in:

(a) VnlKn ?' (p) 0 [P] Match the Column-! with Column-II:
(b) lfradius of nth orbit oc Enx; x = ? (q) Column-I Column-ll
(c) Angular momentum in lowest orbital (r) - 2 (a) Orbital angular (P) (s + l)h/2n
momentum of an electron
(d) 1 ocZY ; y=? (s) 1
r" (b) Angular momentwn of (q) (n + 2) BM
electron
(c) Spin angular mQ,mentum (r) nh/2n
of electron
(d) Magnetic 'moment of atom (s) h/2n
1181 G.R.B. PHYSICAL CHEMISTRY FOR COMPETITIONS

28. The wavelength of the first member of the Balmer series of 33. The velocity of an electron in certain Bohr orbit of H-atom
hydrogen is 6563 x IO-IO m. Calculate the wavelength of its bears the ratio I : 275 to the velocity of light. (a) What is the'
second member. quantum number 'n' of the orbit? (b) Calculate the wave
number of the radiation when the electron jumps from (n + I)
[Hint: :1 [;2 -),
== RH and :2 RH [;2 412 J state to ground state.
[Ans. v 9.75 x 104 em-I]
5 16 20
==-x v I 3 X 1010 8
1..1 36 3 27 [Hint: (a) - = orv == == 1.09 X 10 em
c 275 275
nh nh
1..2 == 20 x 6563 X 10- 10,:" 4861 X 10.- 10 m] . v == - - ==
27 21tmr 21tm X 0.529 x I
29. According to Bohr theory, the electronic energy of hydrogen h
or 11=
atom in the nth Bohr orbit is given by, 21tm X 0.529 x XV
2176 x 10- 19 6.625 X 10-27
Ell == J
2 X 3.14 x 9.1 x
Calculate theiongest wavelength of light that will be needed
=2
to remove an electron from the 2nd orbit of Li 2 + ion. .
(b) Thus, II + 1 = 2 + 1 3. The electron jumps from 3rd orbit to
[Ans. 4.059 x 10-8 m] 1st orbit.]
30. Calculate the frequency, energy.. and .wavelengili<of the
radiation corresponding to spectral. line of lowest frequency in
34. Find out the wavelength of the next line in the series having
Lyman series in the spectra of hydrogen atom. Also c'alculate lines of spectrum of H-atom of wavelengths 6565 A, 4863 A,
4342 A and 4103 A.
. the energy of the corresponding line in the spectra of Li 2+.
(lIT 1991) [Ans. 3972 A]
7
[Ans. I.. == 121'; X 10- m;v = 2.47 x lOIS cycle , [Hint: All these lines are in visible region and thus, belong to
Balmer series, Next line is, therefore, from 7th orbit.]
E 16.36 X 10- 19 j, ELi 2+ EH 9 x i6.36 X 10- 19 J
147.27 X 10-19 J]
35. Which jump is responsible for the wave number of emitted
radiations equal to Q.7490 x 106 m- I in Lyman series of
31. Calculate the ratio of the veIocity oflight and the velocity of
electron in the 2nd orbit. of a hydrogen atom. (Given hydrogen spectrum? (R 1.09678 x 107 m- 1 )
h = 6.624 X 10-27 erg-sec;m . 9.108 x 10- 28 g; [ADs. 3]
r 2.11 X 10-8 cm) 36. Calculate the ionisation energy of the hydrogen atom. How
[Ans. 273.2] . much energy will be required to ionise 1 mole of hydrogen
32. What hydrogen-like ion has the wavelength difference atoms? Given, that the Rydberg constant is 10974 X 107 m- I .
betWeen the first lines of and Lyman series equal to [Ans. IE per hydrogen atom = 2.182 x 10-1.8 J
59.3 nm (RH = 109678 em-I)? IE per mole = 1314 kJ mol-I]
[Hint: Wavelength df 1st line in Balmer series, 37. Calculate the ionisation energy of (a) one Li 2 + ion and (b) one
r =Z 2RH
I..B
[l.. _l..J
22 32
2. R Z2
36 H
mqJe ofLi2+ ion. (Given, R == 10974 X 10-7 m- I )
[Ans. (a) 19.638 x 10- 18 J (b) 1.118 X 104 kJ mol-I]
t.. _ 36 38. A series of lines in the spectrum of atomic hydrogen lies at
or
B - 5R Z 656.46 nm, 4i6.27 nm, 439.17 nm and 410.29 nm. What is the
. H
wavelength of the next line in this series? What is the
Wavelength of 1st line in Lyman series is, ionisation energy of the atom when it is in the lower state of
J....
I..L Z2R
B 12 l..l
22.
transition?
[Ans. I..nexl 397.15 nm; IE = 3.40 e':l
4 39. A certain line of the Lyman series of hydrogen and a certain
or AL == ----;:-2
. 3xRH Z line of the Balmer series of He + ion have nearly the same
wavelength. To what transition do they belong? Small
Differencel..B - I..L = 59.3 X 10-7 == - differences between their Rydberg constant may be neglected.
5RHZ 3RH Z
[Ans. Hydrogen Helium
1
RHZ2
[36
5" '3
4J 2 1
3 __ 1
4 __ 2
6 __ 2
88 4 __ 1 8 __ 2]
z 2 == 7 . 9.0
59.3 x 10- x 109678 x 15 40.. What element has a hydrogen-like spectrum whose lines have
.. , or Z='3 wavelengths four times shorter than those of atomic hydrogen?
[ADS. He+]
Hydrogenclike species is Li 2+.]
 ATOMIC STRUCTURE 119

41. What lines of atomic hydrogen absorption spectrum fall 53. CalCulate the momentum of the particle which has de Broglie
within the wavelength ranges from 945 to 130 nm? . wavelength I A (10- 10 m)and h = 6;6 x 10-34 J- se<;.
[Ans. 97.3; 102.6; 121.6 nm] [Ans. 6.6 x 10-24 kgm sec-I]
42. The binding energy of an electron in the ground state of an
54. The uncertainty of a particle in momentum is 3.3 x 10-2
atom is eq:ualto 24.6 eV Find the energy required to remove
both the electrons from the atom. . ,kg ms-I. Calculate the uncertainty in its positiQ'Q.
[Ans. 79 eV] (h = 6.6 x 10-34 J- sec)
43. What is the ratio of the speeds of an electron in the first and [Ans. 3.1 x 10- 14 m]
second orbits of a hydrogen atom?
55. Calculate the product of uncertainties of displacement and
[Ans. 2; 1] .
velocity ofa moving electron having a mass 9,1 x 10-28 g.
44. Find out the number of waves made by a Bohr electron in one
complete revolution in its third orbit. (lIT 1994) [Ans. 5.77 x 10-5 m2 S-I]
[Ans. 3] [Hint: ·Ilv
45. The wave number of first line in Balmer series of hydrogen is .
15200 cm -I. What is the wave number of first line in Balmer 56. (a) A transition metal cation x 3 + has magnetic morrient .,[35
series ofBe 3+? BM. What is the atomic number of x 3+?
[Ans. 2.43 x 105 cm- I ] (b) Select the coloured ion and the ion having maximum
46. Calculate the speed of an electron in thegroJln(istate of
hydrogen atom. What ·fraction of the speed of light is this
1111 1111 11 1 D
value? How long does it take for the electron to complete one magnetic moment (i) Fe +, (ii) Cu +, (iU) Sc 3+ and
2

revolution around the nucleus? How many times does the

electron travel around the nucleus in one second? 2
(b)Fe + 11111 11 11 11 I·
[Ans. 2.186 x Hf ms-J ; 7.29 X 10-3 ]
47. An electron, in a hydrogen atom, in its ground state absorbs
1.5 times as much energy as the minimum required for its
escape 13.6 eV) from the atom. Calculate the value of A
for the emitted electron. (iy) Mn 2 +
6 2
[Hint: (a) 26, 3d 4s
[Ans. 4.69 A]
48. The radius of the fourth orbit of hydrogen is 0.85 nm. Fe3i; 3d 5 4sO
Calculate the velocity of an electron in this orbit
(me 9.1 x 10-31 kg).
Il =In(n + 2) =..J5X7 = 55
Both these ions will be coloured and magnetic moment of Fe2 +
[Ans. 5.44 x 105 m sec-I]
will be greater.]
49. A beam of electrons accelerated with 4.64 V was passed 57. A photon of wavelength 4000 A strikes a metal surface, the
through a tube having mercury vapours. As a result of work function of the metal being 2.13 eV Calculate (i) energy
absorption, electronic changes occurred with mercury atoms 9f the photon in eV; (ii) kinetic energy of. the emitted
and light was emitted. If the full energy of single electron was photoelectron and (iii) velocity of the photoelectron.
converted into light, what was the wave number of emitted
[Ans.E = 3.10 eV; KE= 0.97 eV; Velocity = 5.85 x 105 Ins-I]
light?
[Hint: I eV = 1602 X 10-19 J]
[Ans. : 3.75 x 104 em- I I
so. An electron jumps from an outer orbit to an inner orbit with
58. Calculate the ratio between the wavelengths of an electron and
the energy difference of 3.0 eV. What will be the wavelength a proton, if the proton is moving at half the velocity of the
of the line and in what region does the emission take. place? electron (mass of the proton = 167 x 10-27 kg; mass of the
[Ans. A 4140A; visible region] electron = 9.11 x 10-28 g).
[Hint: leV 1.6 X 10- 12 erg] [Ans. 9.2455 x 10-2 m]
h
51 •. The first ionisation energy of a certain atom took place with an [Hint: Applyde. Broglie equation, A
absorption of radiation of frequency 1.5 x 1018 cycle per
second. Calculate its ionisation energy in calorie per gram atom. Wavelength of electron
[Ans. 1.43 x 108 cal l
[Hint: 1 calorie 4.18 x 107 erg Wavelength of proton
Apply E = h x v x Avogadro's number]
52. Find the wavelength associated' with an electron which has 59. A moving electron has 2.8 x 10-25 J of kinetic energy.
mass 9.1 x 10-28 g and 'is moving with a velocity of lOS cm Calculate its wavelength.
sec-I. (Given h 6.625 x 10- 27
erg-sec) (Mass of electron = 9.1 x 10-3,1 kg)

[ Ans. A 7.28 x 10- ern] 5

[Ans. 9.2455 'X IO-7 m ]
136 G.R.B. PHYSICAL CHEMISTRY FOR COMPETITIONS

Assertion-Reason TYPE QUESTIONS

Set-1 S.t-2
The questions given below consist of an 'Assertioa' (A) and
the 'ReasGII' (R). Use the following keys for the appropriate The questions given below consist of two statements as 'Assertion'
answer: (A) and 'Reasoa" (R); while answering these choose anyone of
them:
(a) If both (A) and (R) are correct and (R) is the correct reason for
(a) If (A) and (R) are both correct and (R) is the correct reason for
(A).
(A).
(b) If both (A) and (R) are correct but (R) is not the correct
(b) If (A) and (R) are both correct but (R) is not the correct reason
explanation for (A).
for (A).
(c) If (A) is correct but (R) is incorrect.
(c) If (A) is true but (R) is false.
{d} If(A) is incorrect but (R) is correct.
(d) Ifboth (A) and (R) are false.
I. (A) F-atom has less electron affinity than cr atom. 11. (A) A special line will be seen for 2px - 2py transition.
(R) Additional electrons are repelled more effectively by 3 p (R) Energy is released in the form of wave of light when the
electrons in CI atom than by 2p electrons in F-atom. electron dropsfrom2px to -2py orbital. (AHMS 1996}--
2. (A) Nuclide rgAI is less stable than ~Ca. U. (A) Ionization potential of Be (At. No. = 4) is less than B (At.
No. =5).
(R) Nuclide having odd number of protons and neutrons are
generally unstable. . (lIT 1998) (R) The first electron released from Be is of p-orbital but that
from B is of s-orbital. (AIlMS 1997)
3. (A) The first IE of Be is greater than that of B.
13. (A) In Rutherford's gold foil experiment, very few a-particles
(R) 2p-Olbital is lower in energy than 2s.
are deflected back.
4. (A) The electronic configuration of nitrogen atom is
(R) Nucleus present inside the atom is heavy.
represented as:

If rt Iii
14. (A) Limiting line in the Balmer series has a wavelength of
DO
and not as:'
[J[] 364.4mm.
(R) Limiting line is obtained for a jump of electron from
n = 00.
[U 15. (A) Each electron in an atom has two spin quantum numbers.
(R) Spin quantum numbers are obtained by solving
(R) The electronic configuration of the ground state of an Schrodinger wave equation.
atom is the one which has the greatest mUltiplicity. 16. (A) There are two spherical nodes in 3s-orbital.
5. (A) The atomic radii of the elements of oxygen family are (R) There is no planar node in 3s-orbital.
smaller than the atomic radii of corresponding elements of 17. (A) In an atom, the velocity of electron in the higher orbits
the nitrogen family. keeps on decreasing.
(R) The members of oxygen family are all more (It) Velocity of electrons is inversely proportional to radius of
electronegative and thus have lower value of nuclear the orbit.
charge than those of the nitrogen family. II. (A) If the potential difference applied to an electron is made 4
6. (A) For n = 3, I may be 0, I and 2 and may be 0, ±l and 0, ±l times, the de Broglie wavelength associated is halved.
and±2. (R) On. making potential difference 4 times, velocity is
(R) For each value of n, there are 0 to (n - 1) possible values doubled and hence d is halved.
of I; for each value of I, there are 0 to ±l values of m. 19. (A) Angular momentum of Is, 2s, 3s, etc., all have spherical
7. (A) An orbital cannot have more than two electrons. shape.
(R) The Iwo electrons in an orbital create opposite magnetic (R) Is, 2s, 3s,etc., all have spherical shape.
field. 10. (A) The radial probability of Is electron first increases, till it is
I. (A) The configuration ofB-atom cannot be 1s2 2s2 . maximum at 53 A and then decreases to zero.
(R) Hund's rule demands that the configuration should disph~! (R) Bohr radius for the first orbit is 53 A.
maximum multiplicity. 11. (A) On increasing the intensity of incident radiation, the
9. (A) The ionization energy ofN is more than that ofO. number of photoelectrons ejected and their KE increases.
(R) Electronic configuration of N is more stable due to half- (R) Greater the intensity means greater the energy which in
filled 2p-orbitals. tum means greater the frequency of the radiation.
18. (A) p-orbital is dumb-bell shaped. ll. (A) A spectral line will be seen for a 2px 2py transition.
(R) Electron present in p.:orbital can have anyone of the three (R) Energy is released in the form of wave of light when the
values of magnetic quantum number, i.e., 0, +1 or-I. electron drops from 2px to 2py orbital. (VMMC 2007)