IIT-Atomic structure test Paper, Chemistry, Entrance Test Prepration JEE Notes | EduRev

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JEE : IIT-Atomic structure test Paper, Chemistry, Entrance Test Prepration JEE Notes | EduRev

 Page 1


1
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
 IIT-JAM CHEMISTRY-(CY) 2016
TEST : ATOMIC STRUCTURE
Time : 00:50 Hour                          Date : 04-07-2015
                           M.M. : 60
Instructions:
• Part-A contains 10 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c)
and (d), for its answer, out of which ONLY ONE is correct. For each correct answer you will be
awarded 3 marks. For each incorrect answered 1 mark will be deducted.
• Part-B contains 05 Multiple Select Questions(MSQ). Each question has 4 choices (a), (b), (c)
and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct
answer you will be awarded 2 marks, there is no negative marking in this section.
• Part-C contains 10 Numerical Answer Type (NAT) questions which contain 2 Marks for each,  and
there is no negative marking.
PART- A
1. A particle is moving in one dimensional box between x = a and x = b. The potential energy is such that
the particle can not be outside these limits and the wave function in between is 
A
x
? ?
. The average value
of x is:
(a) 
ab
b a ?
(b) 
ab b
n
b a a ?
?
(c) 
ab b
n
b a a ?
?
(d) 
ab a
n
b a b ?
?
2. An electron is confined in a 1-D box of 1 nm long. How many energy levels are there with energy less than
10 eV is:
(a) 5 (b) 10 (c) 15 (d) 16
3. Identify which of the following operators is not hermitian ?
(a) 
d
i dx
?
(b) 
2
2
d
i
dx
(c) 
2
2
d
dx
(d) 
2
x
4. TThe angle between the angular momentum l = 2 and the z-axis for m
l
 = 2 is:
(a) 35.3 (b) 65.9 (c) 114.1 (d) 144.7
5. A hydrogenic orbital with radial function of the form ? ?
a
r exp ß r ? and ? –part as ? ? exp 3i ? ? corresponds
to
(a) n 4,l 3, m 3 ? ? ? (b) n 4,l 3,m 3 ? ? ? ?
(c) n 4, l >3, m 3 ? ? (d) n > 4, l = 3, m 3 ? ?
6. A particle is in a one-dimensional box with a potential V
0
 inside the box and infinite outside. An energy state
corresponding to n = 0 (n : quantum number) is not allowed because
(a) the total energy becomes zero
(b) the average momentum becomes zero
(c) the wave function becomes zero everywhere
(d) the potential 
0
V 0 ?
Page 2


1
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
 IIT-JAM CHEMISTRY-(CY) 2016
TEST : ATOMIC STRUCTURE
Time : 00:50 Hour                          Date : 04-07-2015
                           M.M. : 60
Instructions:
• Part-A contains 10 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c)
and (d), for its answer, out of which ONLY ONE is correct. For each correct answer you will be
awarded 3 marks. For each incorrect answered 1 mark will be deducted.
• Part-B contains 05 Multiple Select Questions(MSQ). Each question has 4 choices (a), (b), (c)
and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct
answer you will be awarded 2 marks, there is no negative marking in this section.
• Part-C contains 10 Numerical Answer Type (NAT) questions which contain 2 Marks for each,  and
there is no negative marking.
PART- A
1. A particle is moving in one dimensional box between x = a and x = b. The potential energy is such that
the particle can not be outside these limits and the wave function in between is 
A
x
? ?
. The average value
of x is:
(a) 
ab
b a ?
(b) 
ab b
n
b a a ?
?
(c) 
ab b
n
b a a ?
?
(d) 
ab a
n
b a b ?
?
2. An electron is confined in a 1-D box of 1 nm long. How many energy levels are there with energy less than
10 eV is:
(a) 5 (b) 10 (c) 15 (d) 16
3. Identify which of the following operators is not hermitian ?
(a) 
d
i dx
?
(b) 
2
2
d
i
dx
(c) 
2
2
d
dx
(d) 
2
x
4. TThe angle between the angular momentum l = 2 and the z-axis for m
l
 = 2 is:
(a) 35.3 (b) 65.9 (c) 114.1 (d) 144.7
5. A hydrogenic orbital with radial function of the form ? ?
a
r exp ß r ? and ? –part as ? ? exp 3i ? ? corresponds
to
(a) n 4,l 3, m 3 ? ? ? (b) n 4,l 3,m 3 ? ? ? ?
(c) n 4, l >3, m 3 ? ? (d) n > 4, l = 3, m 3 ? ?
6. A particle is in a one-dimensional box with a potential V
0
 inside the box and infinite outside. An energy state
corresponding to n = 0 (n : quantum number) is not allowed because
(a) the total energy becomes zero
(b) the average momentum becomes zero
(c) the wave function becomes zero everywhere
(d) the potential 
0
V 0 ?
2
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
7. An eigenstate of energy satisfie 
n n n
H E ? ? ? . In the presence of an extra constant potential V
0
(a) both E
n
 and 
n
? will change (b) both E
n
 and average kinetic energy will change
(c) only E
n
 will change, but not 
n
? (d) only 
n
? will change, but not E
n
.
8. Compare the difference of energies of the first excited and ground states of a particle confined in (i) a 1-d box
? ?
1
? , (ii) a 2-d square box ? ?
2
? and (iii) a 3-d cubic box ? ?
3
? . Assume the length of each of the boxes is the
same. The correct relation between the energy differences 
1 2
, ? ? and 
3
? for the three states is
(a) 
1 2 3
? ? ? ? ? (b) 
1 2 3
? ? ? ? ? (c) 
3 2 1
? ? ? ? ? (d) 
3 1 2
? ? ? ? ?
9. The correct statement about both the average value of position ? ?
x and momentum ? ?
p of a 1-d har-
monic oscillator wavefunction is
(a) 0 x ? and 0 p ? (b) 0 x ? but 0 p ?
(c) 0 x ? and 0 p ? (d) 0 x ? but 0 p ?
10. The value of the commutator ? ? , ,
x
x x p ? ?
? ?
 is
(a) 
i x ?
(b) 
i ? ?
(c) 
i ?
(d) 0
PART- B
11. Analyse the function given , 
2 /3
, ,
sin cos cos
?
?
? n m
e
?
? ? ? ? ?
The correct statement is
(a) Angular node corresponding to this function = 3 and radial node corresonding to this function = 0
(b) The z-component of angular momentum corresponding to the above function is 
2
h
?
(c) Total angular momentum corresponding to this function 
2
2
3
2
h
?
 and energy corresponding to this function is
– 0.055 a.u.
(d) Average value of r corresponding to above function is 12a
0
.
12. Consider the statement. The correct statements are
(a) In the Bohr atom the angular momentum always had a non-zero value. While in the modern theory the
angular momentum is zero in S state only
(b) In Schrodinger model n has nothing directly to do with angular momentum, while on Bohr model n was
measure first of the angular momentum of the system.
(c) If a hydrogen atom in the ground 1s state absorb radiation, then it must be finally in 2s state.
(d) The virial theorem corresonding to H-atom is 2×total energy = – <potential energy)
13. The incorrect statement  is
(a) The degeneracy corresponding to Li
++
 species having energy 
2
0 0
72
?
?
e
a ?
 is 9
(b) The degeneracy corresponding to rotating a particle of mass ‘m’ having energy 
2
2 2
5
2
h
mr ?
 is 7
(c) The energy corresponding to particle confined to move in 2D square box having energy 
2
2
25
4 ?
h
 is 2
(d) The negative value of energy eigenvalue 
2
2
13.6
? ?
?
?
? ?
? ?
? ?
z
E
n
 corresponds to scattering states in which there is
not enough energy for the electron to escape from the nucleus
Page 3


1
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
 IIT-JAM CHEMISTRY-(CY) 2016
TEST : ATOMIC STRUCTURE
Time : 00:50 Hour                          Date : 04-07-2015
                           M.M. : 60
Instructions:
• Part-A contains 10 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c)
and (d), for its answer, out of which ONLY ONE is correct. For each correct answer you will be
awarded 3 marks. For each incorrect answered 1 mark will be deducted.
• Part-B contains 05 Multiple Select Questions(MSQ). Each question has 4 choices (a), (b), (c)
and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct
answer you will be awarded 2 marks, there is no negative marking in this section.
• Part-C contains 10 Numerical Answer Type (NAT) questions which contain 2 Marks for each,  and
there is no negative marking.
PART- A
1. A particle is moving in one dimensional box between x = a and x = b. The potential energy is such that
the particle can not be outside these limits and the wave function in between is 
A
x
? ?
. The average value
of x is:
(a) 
ab
b a ?
(b) 
ab b
n
b a a ?
?
(c) 
ab b
n
b a a ?
?
(d) 
ab a
n
b a b ?
?
2. An electron is confined in a 1-D box of 1 nm long. How many energy levels are there with energy less than
10 eV is:
(a) 5 (b) 10 (c) 15 (d) 16
3. Identify which of the following operators is not hermitian ?
(a) 
d
i dx
?
(b) 
2
2
d
i
dx
(c) 
2
2
d
dx
(d) 
2
x
4. TThe angle between the angular momentum l = 2 and the z-axis for m
l
 = 2 is:
(a) 35.3 (b) 65.9 (c) 114.1 (d) 144.7
5. A hydrogenic orbital with radial function of the form ? ?
a
r exp ß r ? and ? –part as ? ? exp 3i ? ? corresponds
to
(a) n 4,l 3, m 3 ? ? ? (b) n 4,l 3,m 3 ? ? ? ?
(c) n 4, l >3, m 3 ? ? (d) n > 4, l = 3, m 3 ? ?
6. A particle is in a one-dimensional box with a potential V
0
 inside the box and infinite outside. An energy state
corresponding to n = 0 (n : quantum number) is not allowed because
(a) the total energy becomes zero
(b) the average momentum becomes zero
(c) the wave function becomes zero everywhere
(d) the potential 
0
V 0 ?
2
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
7. An eigenstate of energy satisfie 
n n n
H E ? ? ? . In the presence of an extra constant potential V
0
(a) both E
n
 and 
n
? will change (b) both E
n
 and average kinetic energy will change
(c) only E
n
 will change, but not 
n
? (d) only 
n
? will change, but not E
n
.
8. Compare the difference of energies of the first excited and ground states of a particle confined in (i) a 1-d box
? ?
1
? , (ii) a 2-d square box ? ?
2
? and (iii) a 3-d cubic box ? ?
3
? . Assume the length of each of the boxes is the
same. The correct relation between the energy differences 
1 2
, ? ? and 
3
? for the three states is
(a) 
1 2 3
? ? ? ? ? (b) 
1 2 3
? ? ? ? ? (c) 
3 2 1
? ? ? ? ? (d) 
3 1 2
? ? ? ? ?
9. The correct statement about both the average value of position ? ?
x and momentum ? ?
p of a 1-d har-
monic oscillator wavefunction is
(a) 0 x ? and 0 p ? (b) 0 x ? but 0 p ?
(c) 0 x ? and 0 p ? (d) 0 x ? but 0 p ?
10. The value of the commutator ? ? , ,
x
x x p ? ?
? ?
 is
(a) 
i x ?
(b) 
i ? ?
(c) 
i ?
(d) 0
PART- B
11. Analyse the function given , 
2 /3
, ,
sin cos cos
?
?
? n m
e
?
? ? ? ? ?
The correct statement is
(a) Angular node corresponding to this function = 3 and radial node corresonding to this function = 0
(b) The z-component of angular momentum corresponding to the above function is 
2
h
?
(c) Total angular momentum corresponding to this function 
2
2
3
2
h
?
 and energy corresponding to this function is
– 0.055 a.u.
(d) Average value of r corresponding to above function is 12a
0
.
12. Consider the statement. The correct statements are
(a) In the Bohr atom the angular momentum always had a non-zero value. While in the modern theory the
angular momentum is zero in S state only
(b) In Schrodinger model n has nothing directly to do with angular momentum, while on Bohr model n was
measure first of the angular momentum of the system.
(c) If a hydrogen atom in the ground 1s state absorb radiation, then it must be finally in 2s state.
(d) The virial theorem corresonding to H-atom is 2×total energy = – <potential energy)
13. The incorrect statement  is
(a) The degeneracy corresponding to Li
++
 species having energy 
2
0 0
72
?
?
e
a ?
 is 9
(b) The degeneracy corresponding to rotating a particle of mass ‘m’ having energy 
2
2 2
5
2
h
mr ?
 is 7
(c) The energy corresponding to particle confined to move in 2D square box having energy 
2
2
25
4 ?
h
 is 2
(d) The negative value of energy eigenvalue 
2
2
13.6
? ?
?
?
? ?
? ?
? ?
z
E
n
 corresponds to scattering states in which there is
not enough energy for the electron to escape from the nucleus
3
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
14.
? ?
/3
6 cos
Zr
N r Z r e ? ?
?
? ? , is a proposed  hydrogenic wavefunction, where Z = atomic number, r =
radial distance from the nucleus, 
?
 = azimuthal angle, N is a constant.  The CORRECT statement about ?
is
(a)  0 ? ? in the xy-plane
(b) two radial nodes are presenet in ?
(c) one angular node is present in ?
(d) the size of the orbital decreases with increase in atomic number
15. Among the following statements, which statements  TRUE for a Hermitian operator are :
(a) The eigen values are real
(b) the eigen functions are orthogonal
(c) The represent observables
(d) The scalar product of two different eigen function is equal to one
PART- C
16. The wavelength associated with an electron moving with a velocity of 
3
10 msec
?
 ___________(–10
–7
 m).
17. The degenracy of the energy level 
2
2
12h
8ml
 of a particle in a three dimensional cube of the length ‘a’ is ________
18. In the units of 
2
2
h
8ml
, the energy difference between levels corresponding to 3 to 2 node eigen functions for a
particle of mass m in a one dimensional box of length ‘
?
’ is _________
19. For unnormalized wave-function, 
? ?
2
0 0 0
2r r r
r, , sin cos exp
a a a
? ?
? ? ? ?
? ? ? ? ? ? ? ? ? ?
? ? ? ?
? ?
? ? ? ?
? ?
, the number of radial
node(s) is_____________________
20. The wavelength of an electron accelerated through a potential of 100 kV is _______________________(Å)
21. The probability of finding the particle in one dimensional box of length L in the region between 
L
4
 and 
3L
4
 for
quantum number n = 2 is ____________________ %
22. The ground state translational energy of a particle in one-dimensional box of 300pm length is about 4 eV.
Suppose that the same particle is moving in a three-dimensional cubic box of 100 pm on the side. The ground
state energy of the particle in the three-dimensional box is ______________ (eV).
23. A cubic box of edge-length 1.2 nm contains 10 electrons. Applying the simple particle in a box theory, the value
of E ? for the first excited state of this system is ____________(10
–20 
J)
24. For a particle of mass m confined in a box of length L, assume ?x = L. Assume further that 
1
2 2
p(min) p ? ? .
Use the uncertainity principle to obtain an estimate of the energy of the particle. The value will be ________
2
2
mL
? ?
? ?
? ?
?
.
25. The ground state energy of hydrogen atom is –13.598 eV. The expectation values of kinetic energy, T is
__________ (in units of eV).
Page 4


1
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
 IIT-JAM CHEMISTRY-(CY) 2016
TEST : ATOMIC STRUCTURE
Time : 00:50 Hour                          Date : 04-07-2015
                           M.M. : 60
Instructions:
• Part-A contains 10 Multiple Choice Questions (MCQ). Each question has 4 choices (a), (b), (c)
and (d), for its answer, out of which ONLY ONE is correct. For each correct answer you will be
awarded 3 marks. For each incorrect answered 1 mark will be deducted.
• Part-B contains 05 Multiple Select Questions(MSQ). Each question has 4 choices (a), (b), (c)
and (d) for its answer, out of which ONE or MORE than ONE is/are correct. For each correct
answer you will be awarded 2 marks, there is no negative marking in this section.
• Part-C contains 10 Numerical Answer Type (NAT) questions which contain 2 Marks for each,  and
there is no negative marking.
PART- A
1. A particle is moving in one dimensional box between x = a and x = b. The potential energy is such that
the particle can not be outside these limits and the wave function in between is 
A
x
? ?
. The average value
of x is:
(a) 
ab
b a ?
(b) 
ab b
n
b a a ?
?
(c) 
ab b
n
b a a ?
?
(d) 
ab a
n
b a b ?
?
2. An electron is confined in a 1-D box of 1 nm long. How many energy levels are there with energy less than
10 eV is:
(a) 5 (b) 10 (c) 15 (d) 16
3. Identify which of the following operators is not hermitian ?
(a) 
d
i dx
?
(b) 
2
2
d
i
dx
(c) 
2
2
d
dx
(d) 
2
x
4. TThe angle between the angular momentum l = 2 and the z-axis for m
l
 = 2 is:
(a) 35.3 (b) 65.9 (c) 114.1 (d) 144.7
5. A hydrogenic orbital with radial function of the form ? ?
a
r exp ß r ? and ? –part as ? ? exp 3i ? ? corresponds
to
(a) n 4,l 3, m 3 ? ? ? (b) n 4,l 3,m 3 ? ? ? ?
(c) n 4, l >3, m 3 ? ? (d) n > 4, l = 3, m 3 ? ?
6. A particle is in a one-dimensional box with a potential V
0
 inside the box and infinite outside. An energy state
corresponding to n = 0 (n : quantum number) is not allowed because
(a) the total energy becomes zero
(b) the average momentum becomes zero
(c) the wave function becomes zero everywhere
(d) the potential 
0
V 0 ?
2
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
7. An eigenstate of energy satisfie 
n n n
H E ? ? ? . In the presence of an extra constant potential V
0
(a) both E
n
 and 
n
? will change (b) both E
n
 and average kinetic energy will change
(c) only E
n
 will change, but not 
n
? (d) only 
n
? will change, but not E
n
.
8. Compare the difference of energies of the first excited and ground states of a particle confined in (i) a 1-d box
? ?
1
? , (ii) a 2-d square box ? ?
2
? and (iii) a 3-d cubic box ? ?
3
? . Assume the length of each of the boxes is the
same. The correct relation between the energy differences 
1 2
, ? ? and 
3
? for the three states is
(a) 
1 2 3
? ? ? ? ? (b) 
1 2 3
? ? ? ? ? (c) 
3 2 1
? ? ? ? ? (d) 
3 1 2
? ? ? ? ?
9. The correct statement about both the average value of position ? ?
x and momentum ? ?
p of a 1-d har-
monic oscillator wavefunction is
(a) 0 x ? and 0 p ? (b) 0 x ? but 0 p ?
(c) 0 x ? and 0 p ? (d) 0 x ? but 0 p ?
10. The value of the commutator ? ? , ,
x
x x p ? ?
? ?
 is
(a) 
i x ?
(b) 
i ? ?
(c) 
i ?
(d) 0
PART- B
11. Analyse the function given , 
2 /3
, ,
sin cos cos
?
?
? n m
e
?
? ? ? ? ?
The correct statement is
(a) Angular node corresponding to this function = 3 and radial node corresonding to this function = 0
(b) The z-component of angular momentum corresponding to the above function is 
2
h
?
(c) Total angular momentum corresponding to this function 
2
2
3
2
h
?
 and energy corresponding to this function is
– 0.055 a.u.
(d) Average value of r corresponding to above function is 12a
0
.
12. Consider the statement. The correct statements are
(a) In the Bohr atom the angular momentum always had a non-zero value. While in the modern theory the
angular momentum is zero in S state only
(b) In Schrodinger model n has nothing directly to do with angular momentum, while on Bohr model n was
measure first of the angular momentum of the system.
(c) If a hydrogen atom in the ground 1s state absorb radiation, then it must be finally in 2s state.
(d) The virial theorem corresonding to H-atom is 2×total energy = – <potential energy)
13. The incorrect statement  is
(a) The degeneracy corresponding to Li
++
 species having energy 
2
0 0
72
?
?
e
a ?
 is 9
(b) The degeneracy corresponding to rotating a particle of mass ‘m’ having energy 
2
2 2
5
2
h
mr ?
 is 7
(c) The energy corresponding to particle confined to move in 2D square box having energy 
2
2
25
4 ?
h
 is 2
(d) The negative value of energy eigenvalue 
2
2
13.6
? ?
?
?
? ?
? ?
? ?
z
E
n
 corresponds to scattering states in which there is
not enough energy for the electron to escape from the nucleus
3
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
14.
? ?
/3
6 cos
Zr
N r Z r e ? ?
?
? ? , is a proposed  hydrogenic wavefunction, where Z = atomic number, r =
radial distance from the nucleus, 
?
 = azimuthal angle, N is a constant.  The CORRECT statement about ?
is
(a)  0 ? ? in the xy-plane
(b) two radial nodes are presenet in ?
(c) one angular node is present in ?
(d) the size of the orbital decreases with increase in atomic number
15. Among the following statements, which statements  TRUE for a Hermitian operator are :
(a) The eigen values are real
(b) the eigen functions are orthogonal
(c) The represent observables
(d) The scalar product of two different eigen function is equal to one
PART- C
16. The wavelength associated with an electron moving with a velocity of 
3
10 msec
?
 ___________(–10
–7
 m).
17. The degenracy of the energy level 
2
2
12h
8ml
 of a particle in a three dimensional cube of the length ‘a’ is ________
18. In the units of 
2
2
h
8ml
, the energy difference between levels corresponding to 3 to 2 node eigen functions for a
particle of mass m in a one dimensional box of length ‘
?
’ is _________
19. For unnormalized wave-function, 
? ?
2
0 0 0
2r r r
r, , sin cos exp
a a a
? ?
? ? ? ?
? ? ? ? ? ? ? ? ? ?
? ? ? ?
? ?
? ? ? ?
? ?
, the number of radial
node(s) is_____________________
20. The wavelength of an electron accelerated through a potential of 100 kV is _______________________(Å)
21. The probability of finding the particle in one dimensional box of length L in the region between 
L
4
 and 
3L
4
 for
quantum number n = 2 is ____________________ %
22. The ground state translational energy of a particle in one-dimensional box of 300pm length is about 4 eV.
Suppose that the same particle is moving in a three-dimensional cubic box of 100 pm on the side. The ground
state energy of the particle in the three-dimensional box is ______________ (eV).
23. A cubic box of edge-length 1.2 nm contains 10 electrons. Applying the simple particle in a box theory, the value
of E ? for the first excited state of this system is ____________(10
–20 
J)
24. For a particle of mass m confined in a box of length L, assume ?x = L. Assume further that 
1
2 2
p(min) p ? ? .
Use the uncertainity principle to obtain an estimate of the energy of the particle. The value will be ________
2
2
mL
? ?
? ?
? ?
?
.
25. The ground state energy of hydrogen atom is –13.598 eV. The expectation values of kinetic energy, T is
__________ (in units of eV).
4
North Delhi: 33-35, First Floor, Mall Road, G.T.B. Nagar (Opp.- Metro Gate No. 3), Delhi-09, Ph: 011-65462244, 65662255
South Delhi: 28-A/11, Jia Sarai, Near-IIT Hauz Khas, New Delhi-16, Ph : 011-26851008, 26861009  www.careerendeavour.in
 IIT-JAM CHEMISTRY-2016
TEST : ATOMIC STRUCTURE
ANSWER KEY
Part - A
1. (c) 2. (a) 3. (b) 4. (a) 5. (d) 6. (c) 7. (c)
8. (b) 9. (c) 10. (d)
Part - B
11. (b,c,d) 12. (a,b) 13. (a,b,c,d) 14. (a,c,d) 15. (a,b,c )
Part - C
16. (7.25) 17. (1) 18. (7) 19.  (1) 20. (0.037) 21. (50)
22. (108) 23. (8.366) 24. (0.125) 25. (13.598 )
Date : 04-07-2015
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