Download PTU Quantum Mechanics 2018 Question Bank

Download PTU (Punjab Technical University) Quantum Mechanics 2018 Question Bank

QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 1 of 4)



QUANTUM MECHANICS


1. If the mass of a neutron is kg
27
10 66 1
- ? ? , then find the de-Broglie wavelength at
300K. (Given
1 38
10 38 1
- - ? ? = JK k ) (2) {JUN 15 [GNE]}
2. A wavefunction of a particle in a one dimensional box of length L is given as
integer n ; sin
2
) ( =
?
?
?
?
?
?
= ?
L
x n
L
x
?
. Show that this wave function satisfies one
dimensional time independent Schrodinger equation. Given that
2
2 2 2
2mL
n
E
h ?
= and
U = 0. (4) {JUN 15 [GNE]}
3. Define wavefunction. Give its significance and write conditions for a
wavefunction to be well behaved. (4) {JUN 15 [GNE]}
4. Why a particle trapped in a box cannot be at rest? (2) {JUN 15 [PTU]}
5. What is the matter wave associated with a moving particle? Derive expression for
phase and group velocities of such a wave packet. (4) {JUN 15 [PTU]}
6. Give a brief account of need and origin of quantum mechanics. (4) {JUN 15
[PTU]}
7. Derive expression for time independent Schrodinger wave equation. (4) {DEC 14
[GNE]}
8. Derive relation between group velocity and phase velocity. Hence discuss the
cases of normal and anomalous dispersion. Which dispersion is must for group
velocity to be less than velocity of light? (4) {DEC 14 [GNE]}
9. What are essential conditions for a wave function to be well behaved? (2) {DEC
14 [PTU]}
10. Discuss the formation of wave packet and hence prove that particle velocity is
equal to the group velocity. (4) {JUN 14 [GNE]}
11. Calculate the energy Eigen values and Eigen functions for the motion of a particle
in one dimensional box. (4) {JUN 14 [GNE]}
12. Can
2
) ( x x = ? be an acceptable wave function in quantum mechanics? (2) {JUN
14 [GNE]}
13. Calculate the de-Broglie wavelength associated with electrons, which are
accelerated by a voltage of 50kV. (3) {JUN 14 [PTU]}
14. Solve Schrodinger equation for a particle confined to an infinite potential box of
width L in order to derive the expression for energy eigen values. (5) {JUN 14
[PTU]}
15. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wavefunction? (2) {JUN 14 [PTU]}
16. What do you understand by wave particle puzzle? (2) {Dec 2013 [PTU]}
17. Derive time dependent Schrodinger equation and discuss its significance in
today?s context. (4) {Dec 2013 [PTU]}
18. What is de-Broglie hypothesis. (2) {Dec 2013 [PTU]}
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QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 1 of 4)



QUANTUM MECHANICS


1. If the mass of a neutron is kg
27
10 66 1
- ? ? , then find the de-Broglie wavelength at
300K. (Given
1 38
10 38 1
- - ? ? = JK k ) (2) {JUN 15 [GNE]}
2. A wavefunction of a particle in a one dimensional box of length L is given as
integer n ; sin
2
) ( =
?
?
?
?
?
?
= ?
L
x n
L
x
?
. Show that this wave function satisfies one
dimensional time independent Schrodinger equation. Given that
2
2 2 2
2mL
n
E
h ?
= and
U = 0. (4) {JUN 15 [GNE]}
3. Define wavefunction. Give its significance and write conditions for a
wavefunction to be well behaved. (4) {JUN 15 [GNE]}
4. Why a particle trapped in a box cannot be at rest? (2) {JUN 15 [PTU]}
5. What is the matter wave associated with a moving particle? Derive expression for
phase and group velocities of such a wave packet. (4) {JUN 15 [PTU]}
6. Give a brief account of need and origin of quantum mechanics. (4) {JUN 15
[PTU]}
7. Derive expression for time independent Schrodinger wave equation. (4) {DEC 14
[GNE]}
8. Derive relation between group velocity and phase velocity. Hence discuss the
cases of normal and anomalous dispersion. Which dispersion is must for group
velocity to be less than velocity of light? (4) {DEC 14 [GNE]}
9. What are essential conditions for a wave function to be well behaved? (2) {DEC
14 [PTU]}
10. Discuss the formation of wave packet and hence prove that particle velocity is
equal to the group velocity. (4) {JUN 14 [GNE]}
11. Calculate the energy Eigen values and Eigen functions for the motion of a particle
in one dimensional box. (4) {JUN 14 [GNE]}
12. Can
2
) ( x x = ? be an acceptable wave function in quantum mechanics? (2) {JUN
14 [GNE]}
13. Calculate the de-Broglie wavelength associated with electrons, which are
accelerated by a voltage of 50kV. (3) {JUN 14 [PTU]}
14. Solve Schrodinger equation for a particle confined to an infinite potential box of
width L in order to derive the expression for energy eigen values. (5) {JUN 14
[PTU]}
15. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wavefunction? (2) {JUN 14 [PTU]}
16. What do you understand by wave particle puzzle? (2) {Dec 2013 [PTU]}
17. Derive time dependent Schrodinger equation and discuss its significance in
today?s context. (4) {Dec 2013 [PTU]}
18. What is de-Broglie hypothesis. (2) {Dec 2013 [PTU]}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 2 of 4)

19. An electron is bound in one dimensional box of size . 10 4
10
m
- ? What will be the
minimum energy? (2) {Dec 2013 [PTU]}
20. At time t = 0, a particle is represented by a wave function
?
?
?
?
?
?
?
?
?
? ?
? ?
= ?
elsewhere 0
x a for
a) - (b
x) - (b
A
a x 0 for
a
x
A
) ( b x ; where A, a and b are constants.
(i) Normalize ) 0 , (x ?
(ii) Sketch ) 0 , (x ? as a function of x.
(iii) Where is the particle most likely to be at t = 0 ?
(iv) What is the probability of finding the particle to the left of x = a at t = 0?
(4) {Dec 2013 [PTU]}
21. Calculate the energy eigen values and eigen functions for the motion of a particle
confined in a 1-D box. (4) {Dec 2013 [GNE]}
22. At a certain time, the normalized wave function of the particle moving along the
X-axis is given by:
?
?
?
?
?
< < +
< < +
= ?
elsewhere 0
x 0 for x -
0 x - for
) ( ? ?
? ? x
x . Find the value of ? and the
probability that the particle?s position is between ?
?
= = x x &
2
. (4) {Dec 2013
[GNE]}
23. Differentiate between phase velocity and group velocity. (2) {Jun 2013 [PTU]}
24. Obtain Bohr?s condition of quantization of angular momentum using de Broglie?s
idea of matter waves. (3) {Jun 2013 [PTU]}
25. Write the expression of normalized wave function for a particle confined in a
potential box. (2) {Jun 2013 [GNE]}
26. Find the probability of finding a particle in a region 4L 0 ? to 6L 0 ? trapped in an
infinite potential well of width L. (4) {Jun 2013 [GNE]}
27. Derive an expression for energy of a particle of mass m confined to infinite
potential well of width L. Why such a particle cannot have zero energy? (4) {Jun
2013 [GNE]}
28. What do you understand by wave-particle duality? (2) {Dec 2012 [GNE]}
29. A particle of mass m is confined to move inside an infinite potential well
described by following function:
?
?
?
?
?
> ? +
? ?
< ? +
=
a for x
a x 0 for 0
a for x
V(x)
Calculate the wave function and energy of the particle. (4) {Dec 2012 [GNE]}
30. What do you understand by wave packet? (2) {Dec 2012}
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QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 1 of 4)



QUANTUM MECHANICS


1. If the mass of a neutron is kg
27
10 66 1
- ? ? , then find the de-Broglie wavelength at
300K. (Given
1 38
10 38 1
- - ? ? = JK k ) (2) {JUN 15 [GNE]}
2. A wavefunction of a particle in a one dimensional box of length L is given as
integer n ; sin
2
) ( =
?
?
?
?
?
?
= ?
L
x n
L
x
?
. Show that this wave function satisfies one
dimensional time independent Schrodinger equation. Given that
2
2 2 2
2mL
n
E
h ?
= and
U = 0. (4) {JUN 15 [GNE]}
3. Define wavefunction. Give its significance and write conditions for a
wavefunction to be well behaved. (4) {JUN 15 [GNE]}
4. Why a particle trapped in a box cannot be at rest? (2) {JUN 15 [PTU]}
5. What is the matter wave associated with a moving particle? Derive expression for
phase and group velocities of such a wave packet. (4) {JUN 15 [PTU]}
6. Give a brief account of need and origin of quantum mechanics. (4) {JUN 15
[PTU]}
7. Derive expression for time independent Schrodinger wave equation. (4) {DEC 14
[GNE]}
8. Derive relation between group velocity and phase velocity. Hence discuss the
cases of normal and anomalous dispersion. Which dispersion is must for group
velocity to be less than velocity of light? (4) {DEC 14 [GNE]}
9. What are essential conditions for a wave function to be well behaved? (2) {DEC
14 [PTU]}
10. Discuss the formation of wave packet and hence prove that particle velocity is
equal to the group velocity. (4) {JUN 14 [GNE]}
11. Calculate the energy Eigen values and Eigen functions for the motion of a particle
in one dimensional box. (4) {JUN 14 [GNE]}
12. Can
2
) ( x x = ? be an acceptable wave function in quantum mechanics? (2) {JUN
14 [GNE]}
13. Calculate the de-Broglie wavelength associated with electrons, which are
accelerated by a voltage of 50kV. (3) {JUN 14 [PTU]}
14. Solve Schrodinger equation for a particle confined to an infinite potential box of
width L in order to derive the expression for energy eigen values. (5) {JUN 14
[PTU]}
15. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wavefunction? (2) {JUN 14 [PTU]}
16. What do you understand by wave particle puzzle? (2) {Dec 2013 [PTU]}
17. Derive time dependent Schrodinger equation and discuss its significance in
today?s context. (4) {Dec 2013 [PTU]}
18. What is de-Broglie hypothesis. (2) {Dec 2013 [PTU]}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 2 of 4)

19. An electron is bound in one dimensional box of size . 10 4
10
m
- ? What will be the
minimum energy? (2) {Dec 2013 [PTU]}
20. At time t = 0, a particle is represented by a wave function
?
?
?
?
?
?
?
?
?
? ?
? ?
= ?
elsewhere 0
x a for
a) - (b
x) - (b
A
a x 0 for
a
x
A
) ( b x ; where A, a and b are constants.
(i) Normalize ) 0 , (x ?
(ii) Sketch ) 0 , (x ? as a function of x.
(iii) Where is the particle most likely to be at t = 0 ?
(iv) What is the probability of finding the particle to the left of x = a at t = 0?
(4) {Dec 2013 [PTU]}
21. Calculate the energy eigen values and eigen functions for the motion of a particle
confined in a 1-D box. (4) {Dec 2013 [GNE]}
22. At a certain time, the normalized wave function of the particle moving along the
X-axis is given by:
?
?
?
?
?
< < +
< < +
= ?
elsewhere 0
x 0 for x -
0 x - for
) ( ? ?
? ? x
x . Find the value of ? and the
probability that the particle?s position is between ?
?
= = x x &
2
. (4) {Dec 2013
[GNE]}
23. Differentiate between phase velocity and group velocity. (2) {Jun 2013 [PTU]}
24. Obtain Bohr?s condition of quantization of angular momentum using de Broglie?s
idea of matter waves. (3) {Jun 2013 [PTU]}
25. Write the expression of normalized wave function for a particle confined in a
potential box. (2) {Jun 2013 [GNE]}
26. Find the probability of finding a particle in a region 4L 0 ? to 6L 0 ? trapped in an
infinite potential well of width L. (4) {Jun 2013 [GNE]}
27. Derive an expression for energy of a particle of mass m confined to infinite
potential well of width L. Why such a particle cannot have zero energy? (4) {Jun
2013 [GNE]}
28. What do you understand by wave-particle duality? (2) {Dec 2012 [GNE]}
29. A particle of mass m is confined to move inside an infinite potential well
described by following function:
?
?
?
?
?
> ? +
? ?
< ? +
=
a for x
a x 0 for 0
a for x
V(x)
Calculate the wave function and energy of the particle. (4) {Dec 2012 [GNE]}
30. What do you understand by wave packet? (2) {Dec 2012}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 3 of 4)

31. Develop time independent Schrodinger equation and discuss its significance. (5)
{Dec 2012}
32. What are matter waves? (2) {June 2012}
33. Compute the de-Broglie wavelength of a proton of wavelength whose kinetic
energy is equal to the rest energy of an electron. Given that mass of proton is
1840 times the mass of electron. (4) {June 2012}
34. What do you mean by normalization of a wave function? (4) {June 2012}
35. Calculate the wave number of 10keV neutron. (3) {Dec 2011}
36. What is the significance of wave function? (2) {June 2011}
37. Derive an expression for time dependent Schrodinger wave equation. (6) {June
2011}
38. What is the energy of Gamma ray having wavelength of
o
A 1 ? (2) {June 2011}
39. What is de-Broglie?s hypothesis? (2) {Dec 2010}
40. What is Born?s interpretation of wave function? (2) {Dec 2010}
41. What is the difference between phase velocity and group velocity? Show that the
de-Broglie group velocity associated with the wave packet is equal to the velocity
of the particle. (6) {Dec 2010}
42. Why 0 = n state is not allowed for a particle confined to an infinite potential box?
(2) {June 2010}
43. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wave function? (2) {June 2010}
44. Establish time dependent Schrodinger wave equation and further deduce tie
independent equation from it. (4) {June 2010}
45. What are the characteristics of a well behaved wave function? (2) {June 2010}
46. Find the probability of a particle trapped in a box of length L to be found in the
region L to L 55 0 45 0 ? ? for the ground state. (2) {June 2010}
47. Differentiate between phase velocity and group velocity. (2) {Dec 2009}
48. Define wave function and obtain the expression for time dependent Schrodinger
wave equation. (4) {Dec 2009}
49. Define Eigen values and Eigen functions. (2) {June 2009}
50. Define wave function and calculate the expression for Time Independent
Schrodinger wave equation. (4) {June 2009}
51. Distinguish between phase and group velocity. (2) {Dec 2007}
52. If the energy of a particle is zero, then prove using quantum mechanics that it
cannot exist in a one dimensional box. (4) {Dec 2007}
53. What do you mean by matter waves? (2) {May 2007}
54. What is the de Broglie wavelength of an electron, which has been accelerated
from rest through a potential difference of 150V? (3)
55. Explain de Broglie concept of matter waves. (2) {May 2006}
56. Write the Schrodinger equation for particle in a box and solve it to obtain energy
Eigen values and Eigen functions. (6) {May 2006}
57. What voltage must be applied to an electron to produce electrons of
wavelength
o
A 5 0 ? ? Given that Js h
34
10 62 6
- ? ? = , C e
19
10 6 1
- ? ? = &
kg m
31
10 1 9
- ? ? = . (2) {Dec2005}
58. What is the physical significance of wave function? (2) {Dec2005}
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QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 1 of 4)



QUANTUM MECHANICS


1. If the mass of a neutron is kg
27
10 66 1
- ? ? , then find the de-Broglie wavelength at
300K. (Given
1 38
10 38 1
- - ? ? = JK k ) (2) {JUN 15 [GNE]}
2. A wavefunction of a particle in a one dimensional box of length L is given as
integer n ; sin
2
) ( =
?
?
?
?
?
?
= ?
L
x n
L
x
?
. Show that this wave function satisfies one
dimensional time independent Schrodinger equation. Given that
2
2 2 2
2mL
n
E
h ?
= and
U = 0. (4) {JUN 15 [GNE]}
3. Define wavefunction. Give its significance and write conditions for a
wavefunction to be well behaved. (4) {JUN 15 [GNE]}
4. Why a particle trapped in a box cannot be at rest? (2) {JUN 15 [PTU]}
5. What is the matter wave associated with a moving particle? Derive expression for
phase and group velocities of such a wave packet. (4) {JUN 15 [PTU]}
6. Give a brief account of need and origin of quantum mechanics. (4) {JUN 15
[PTU]}
7. Derive expression for time independent Schrodinger wave equation. (4) {DEC 14
[GNE]}
8. Derive relation between group velocity and phase velocity. Hence discuss the
cases of normal and anomalous dispersion. Which dispersion is must for group
velocity to be less than velocity of light? (4) {DEC 14 [GNE]}
9. What are essential conditions for a wave function to be well behaved? (2) {DEC
14 [PTU]}
10. Discuss the formation of wave packet and hence prove that particle velocity is
equal to the group velocity. (4) {JUN 14 [GNE]}
11. Calculate the energy Eigen values and Eigen functions for the motion of a particle
in one dimensional box. (4) {JUN 14 [GNE]}
12. Can
2
) ( x x = ? be an acceptable wave function in quantum mechanics? (2) {JUN
14 [GNE]}
13. Calculate the de-Broglie wavelength associated with electrons, which are
accelerated by a voltage of 50kV. (3) {JUN 14 [PTU]}
14. Solve Schrodinger equation for a particle confined to an infinite potential box of
width L in order to derive the expression for energy eigen values. (5) {JUN 14
[PTU]}
15. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wavefunction? (2) {JUN 14 [PTU]}
16. What do you understand by wave particle puzzle? (2) {Dec 2013 [PTU]}
17. Derive time dependent Schrodinger equation and discuss its significance in
today?s context. (4) {Dec 2013 [PTU]}
18. What is de-Broglie hypothesis. (2) {Dec 2013 [PTU]}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 2 of 4)

19. An electron is bound in one dimensional box of size . 10 4
10
m
- ? What will be the
minimum energy? (2) {Dec 2013 [PTU]}
20. At time t = 0, a particle is represented by a wave function
?
?
?
?
?
?
?
?
?
? ?
? ?
= ?
elsewhere 0
x a for
a) - (b
x) - (b
A
a x 0 for
a
x
A
) ( b x ; where A, a and b are constants.
(i) Normalize ) 0 , (x ?
(ii) Sketch ) 0 , (x ? as a function of x.
(iii) Where is the particle most likely to be at t = 0 ?
(iv) What is the probability of finding the particle to the left of x = a at t = 0?
(4) {Dec 2013 [PTU]}
21. Calculate the energy eigen values and eigen functions for the motion of a particle
confined in a 1-D box. (4) {Dec 2013 [GNE]}
22. At a certain time, the normalized wave function of the particle moving along the
X-axis is given by:
?
?
?
?
?
< < +
< < +
= ?
elsewhere 0
x 0 for x -
0 x - for
) ( ? ?
? ? x
x . Find the value of ? and the
probability that the particle?s position is between ?
?
= = x x &
2
. (4) {Dec 2013
[GNE]}
23. Differentiate between phase velocity and group velocity. (2) {Jun 2013 [PTU]}
24. Obtain Bohr?s condition of quantization of angular momentum using de Broglie?s
idea of matter waves. (3) {Jun 2013 [PTU]}
25. Write the expression of normalized wave function for a particle confined in a
potential box. (2) {Jun 2013 [GNE]}
26. Find the probability of finding a particle in a region 4L 0 ? to 6L 0 ? trapped in an
infinite potential well of width L. (4) {Jun 2013 [GNE]}
27. Derive an expression for energy of a particle of mass m confined to infinite
potential well of width L. Why such a particle cannot have zero energy? (4) {Jun
2013 [GNE]}
28. What do you understand by wave-particle duality? (2) {Dec 2012 [GNE]}
29. A particle of mass m is confined to move inside an infinite potential well
described by following function:
?
?
?
?
?
> ? +
? ?
< ? +
=
a for x
a x 0 for 0
a for x
V(x)
Calculate the wave function and energy of the particle. (4) {Dec 2012 [GNE]}
30. What do you understand by wave packet? (2) {Dec 2012}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 3 of 4)

31. Develop time independent Schrodinger equation and discuss its significance. (5)
{Dec 2012}
32. What are matter waves? (2) {June 2012}
33. Compute the de-Broglie wavelength of a proton of wavelength whose kinetic
energy is equal to the rest energy of an electron. Given that mass of proton is
1840 times the mass of electron. (4) {June 2012}
34. What do you mean by normalization of a wave function? (4) {June 2012}
35. Calculate the wave number of 10keV neutron. (3) {Dec 2011}
36. What is the significance of wave function? (2) {June 2011}
37. Derive an expression for time dependent Schrodinger wave equation. (6) {June
2011}
38. What is the energy of Gamma ray having wavelength of
o
A 1 ? (2) {June 2011}
39. What is de-Broglie?s hypothesis? (2) {Dec 2010}
40. What is Born?s interpretation of wave function? (2) {Dec 2010}
41. What is the difference between phase velocity and group velocity? Show that the
de-Broglie group velocity associated with the wave packet is equal to the velocity
of the particle. (6) {Dec 2010}
42. Why 0 = n state is not allowed for a particle confined to an infinite potential box?
(2) {June 2010}
43. What is the physical significance attached to the conditions of continuity and
single valued nature of an acceptable wave function? (2) {June 2010}
44. Establish time dependent Schrodinger wave equation and further deduce tie
independent equation from it. (4) {June 2010}
45. What are the characteristics of a well behaved wave function? (2) {June 2010}
46. Find the probability of a particle trapped in a box of length L to be found in the
region L to L 55 0 45 0 ? ? for the ground state. (2) {June 2010}
47. Differentiate between phase velocity and group velocity. (2) {Dec 2009}
48. Define wave function and obtain the expression for time dependent Schrodinger
wave equation. (4) {Dec 2009}
49. Define Eigen values and Eigen functions. (2) {June 2009}
50. Define wave function and calculate the expression for Time Independent
Schrodinger wave equation. (4) {June 2009}
51. Distinguish between phase and group velocity. (2) {Dec 2007}
52. If the energy of a particle is zero, then prove using quantum mechanics that it
cannot exist in a one dimensional box. (4) {Dec 2007}
53. What do you mean by matter waves? (2) {May 2007}
54. What is the de Broglie wavelength of an electron, which has been accelerated
from rest through a potential difference of 150V? (3)
55. Explain de Broglie concept of matter waves. (2) {May 2006}
56. Write the Schrodinger equation for particle in a box and solve it to obtain energy
Eigen values and Eigen functions. (6) {May 2006}
57. What voltage must be applied to an electron to produce electrons of
wavelength
o
A 5 0 ? ? Given that Js h
34
10 62 6
- ? ? = , C e
19
10 6 1
- ? ? = &
kg m
31
10 1 9
- ? ? = . (2) {Dec2005}
58. What is the physical significance of wave function? (2) {Dec2005}
QUESTION BANK IN PHYSICS (B.TECH FIRST YEAR)

(Page 4 of 4)

59. What do you understand by Eigenvalues and Eigen functions? (2) {May 2005}
60. What is the need for quantum mechanics? Discuss the Born?s interpretation of
wave function and normalization of the wave function. (2,2) {May 2005}
61. At a certain time, the normalized wave function of the particle moving along the
X-axis is given by:
?
?
?
?
?
< < +
< < +
= ?
elsewhere 0
x 0 for x -
0 x - for
) ( ? ?
? ? x
x . Find the value of ? and the
probability that the particle?s position is between ?
?
= = x x &
2
. (4) {May 2005}
62. Can every physical system be described by the time independent Schrodinger
equation? Comment. (2) {May 2004}
63. Find the ground state energy of an electron confined to a one dimensional rigid
box of length
o
A 1 . (2)
64. What is the utility of normalization of wave function? (2) {Dec2003}
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