Chapter 11 Orbital Motion and the Hydrogen Atom

1Chapter 11
Orbital Motion and the Hydrogen Atom

1. The net work done on a planet in one revolution around the sun in an elliptical orbit is

a. half the difference between its minor and major axis times its mass.

b. zero.

c. half the difference between its minor and major axis times its weight.

d. half the difference between its minor and major axis times the average force on the planet.

e. the force on the planet times the length of the ellipse.
2. The speed of a planet in an elliptical orbit about the sun has the greatest magnitude when the planet is

a. nearest the sun.

b. nearest the Earth.

c. farthest from the sun.

d. farthest from the Earth.

e. between the Earth and the moon.

3. The centripetal acceleration of a planet in an elliptical orbit about the sun is greatest when the planet is

a. nearest the sun.

b. nearest the Earth.

c. farthest from the sun.

d. farthest from the Earth.

e. between the Earth and the moon.

4. The period of revolution of a planet about the sun is

a. greater when the radius is smaller.

b. greater when the radius is greater.

c. greater when the mass is greater.

d. independent of the radius.

e. greater when the mass is smaller.

5. Mercury, the planet closest to the sun, has the

a. greatest period of revolution.

b. smallest angular velocity.

c. smallest tangential velocity.

d. greatest centripetal acceleration.

e. smallest centripetal acceleration.

6. A mass weighs 16 N at the surface of a planet of 3000 km radius. What is the mass’s weight when it is in orbit 3000 km above the surface of the planet?

a. zero

b. 4

c. 8

d. 16

e. 32

7. A planet has the same mass as the Earth. It also has a radius twice the Earth’s radius. If the Earth’s acceleration due to gravity is g, what is the acceleration due to gravity on the planet’s surface?

a. 1/4 g

b. 1/2 g

c. g

d. 2 g

e. 4 g

8. A planet has the same mass as the Earth. It also has a radius half the Earth’s radius. If the Earth’s acceleration due to gravity is g, what is the acceleration due to gravity on the planet’s surface?

a. 1/4 g

b. 1/2 g

c. g

d. 2 g

e. 4 g

9. A planet has the same mass as the Earth. It also has a radius one-third the Earth’s radius. If the Earth’s acceleration due to gravity is g, what is the acceleration due to gravity on the planet’s surface?

a. 1/9 g

b. 1/3 g

c. g

d. 3 g

e. 9 g

10. A planet has the same mass as the Earth. It also has a radius 3 times the Earth’s radius. If the Earth’s acceleration due to gravity is g, what is the acceleration due to gravity on the planet’s surface?

a. 1/9 g

b. 1/3 g

c. g

d. 3 g

e. 9 g

11. Two rockets are ready to blast off and leave the Earth’s gravitational field. The ratio of their masses is 2:1. The ratio of their escape velocities is:

a. 1:1.

b. 2:1.

c. 3:1.

d. 4:1.

e. 9:1.
12. What is the ratio of g at the Earth’s surface to g at one Earth’s radius from the surface?

a. 1:1

b. 2:1

c. 3:1

d. 4:1

e. 9:1
13. An Earth satellite in an orbit of radius is moved ⁴
27. What is the ground state energy of a Bohr hydrogen atom in eV?

a. -4.53

b. -6.8

c. -9.07

d. -13.6

e. -27.2
28. The Rydberg constant is 1.097 x 10⁷ m^-1. What is the wavelength in nm of a photon caused by a hydrogen transition from energy state 4 to energy state 3?

a. 1730

b. 1870

c. 1923

d. 1492

e. 1957
29. The Rydberg constant is 1.10 x 10⁷ m^-1. What is the frequency in s^-1 of a photon caused by a hydrogen transition from energy state 4 to energy state 3?

a. 8.00 x 10¹³

b. 3.21 x 10¹⁴

c. 1.60 x 10¹⁴

d. 2.23 x 10¹⁴

e. 1.79 x 10¹⁴

30. If Planck’s constant is 6.63 x 10^-34 Js, what is the angular momentum of an electron in its second Bohr orbit in kg m²/s?

a. 1.05 x 10^-34

b. 2.11 x 10^-34

c. 3.05 x 10^-34

d. 2.05 x 10^-34

e. 1.92 x 10^-34

31. What is the energy in J of a 132 nm photon if Planck’s constant is 6.63 x 10^-34 Js?

a. 9.11 x 10^-19

b. 8.97 x 10^-19

c. 3.79 x 10^-18

d. 1.21 x 10^-18

e. 1.51 x 10^-18

32. The moon has a mass of 7.36 x 10²² kg. The period and radius of its orbit about Earth are and respectively. What is its orbital angular momentum about the Earth in kg m²/s?

a. 4.93 x 10³⁴

b. 2.24 x 10³⁴

c. 2.89 x 10³⁴

d. 1.72 x 10³⁴

e. 3.13 x 10³⁴

33. The moon has a mass of 7.36 x 10²² kg. The period and radius of its orbit about Earth are and respectively. What is the magnitude in of its linear momentum at any point of the orbit?

a. 6.94 x 10²⁵

b. 7.03 x 10²⁵

c. 7.44 x 10²⁵

d. 7.53 x 10²⁵

e. 7.92 x 10²⁵

34. Planet "Zero” has a mass of 5.0 x 10²³ kg and a radius of 2.0 x 10⁶ m. A space probe is launched vertically from the surface of Zero with an initial speed of 4.0 km/s. What is the speed of the probe in km/s when it is 3.0 x 10⁶ m from Zero’s center. (G = 6.67 x 10^-11 Nm²/kg² )

a. 3.0

b. 2.2

c. 1.6

d. 3.7

e. 5.9
35. Planet "Zero” has a mass of 4.0 x 10²³ kg and a radius of 2.0 x 10⁶ m. With what kinetic energy in J should a 10 kg space probe be launched from the surface of Zero just to reach a maximum distance of from the center of that planet? (G = 6.67 x 10^-11 Nm²/kg² )

a. 6.7 x 10⁷

b. 8.0 x 10⁷

c. 9.3 x 10⁷

d. 5.3 x 10⁷

e. 1.3 x 10⁸
36. What is the escape speed in km/s from a planet of mass M and radius R if M = 3.2 x 10²³ kg and

R = 2.4 x 10⁶ m? (G = 6.67 x 10^-11 Nm²/kg² )

a. 5.5

b. 4.2

c. 5.2

d. 4.8

e. 3.7
37. A projectile is launched vertically with an initial speed of 3.0 km/s from the surface of a planet

(radius = 1.5 x 10⁶ m). The projectile rises to a maximum height of 3.0 x 10⁶ m above the surface of the planet. What is the mass of the planet in kg if G = 6.67 x 10^-11 Nm²/kg²?

a. 1.0 x 10²³

b. 2.0 x 10²³

c. 1.5 x 10²³

d. 2.4 x 10²³

e. 3.0 x 10²⁴

38. A satellite of mass m circles a planet of mass M and radius R in an orbit at a height 2R above the surface of the planet. What minimum energy is required to change the orbit to one for which the height of the satellite is 3R above the surface of the planet?

a.

b.

c.

d.

e.

39. An electron in a hydrogen atom makes a transition from the n = 4 to n = 3 energy state. The energy of the emitted photon in eV is

a. 0.54

b. 0.66

c. 0.85

d. 1.51

e. 10.2
40. An electron in a hydrogen atom makes a transition from the n = 3 to n = 1 energy state. The wavelength of the emitted photon in nm is

a. 1006

b. 209

c. 306

d. 103

e. 821
41. A hydrogen atom is in its first excited state (n = 2). The linear momentum of the electron in kg m/s is

a. 3 x 10^-24

b. 2 x 10^-24

c. 1 x 10^-24

d. 4 x 10^-24

e. 3 x 10^-15

42. How fast in m/s is the electron moving in the first Bohr orbit?

a. 3.3 x 10⁶

b. 2.2 x 10⁶

c. 4.4 x 10⁶

d. 5.5 x 10⁶

e. 5.5 x 10¹⁵

43. A satellite circles planet "Roton” every 2.8 h in an orbit having a radius of 1.2 x 10⁷ m. If the radius of Roton is 5.0 x 10⁶ m, what is the magnitude of the free-fall acceleration on the surface of Roton in m/s²?

a. 31

b. 27

c. 34

d. 40

e. 19
44. The period of a satellite circling planet "Nutron” is observed to be 84 s when it is in a circular orbit with a radius of 8.0 x 10⁶ m. What is the mass of planet Nutron in kg?

a. 6.2 x 10²⁸

b. 5.0 x 10²⁸

c. 5.5 x 10²⁸

d. 4.3 x 10²⁸

e. 3.7 x 10²⁸

45. A 50 kg satellite circles "Cruton” every 5.6 h in an orbit with a radius of 12 x 10⁶ m. What is the magnitude of the gravitational force in N on the satellite by planet Cruton?

a. 63

b. 58

c. 68

d. 73

e. 50
46. A satellite circles planet "Zeron” every 98 minutes. The mass of this planet is known to be 5.0 x 10²⁴ kg. What is the radius of the orbit in m?

a. 7.8 x 10⁶

b. 7.4 x 10⁶

c. 6.6 x 10⁶

d. 8.1 x 10⁶

e. 1.3 x 10⁷
47. Two stars of masses M and 6M are separated by a distance D. Determine the distance in D (measured from M) to a point at which the net gravitational force on a third mass would be zero.

a. 0.41

b. 0.33

c. 0.37

d. 0.29

e. 0.14
48. What is the magnitude of the free-fall acceleration in m/s² at a point that is a distance 2R above the surface of the Earth, where R is the radius of the Earth?

a. 4.8

b. 1.1

c. 3.3

d. 2.5

e. 6.5

49. Three 5.0 kg masses are located at points in the xy plane as shown in the figure. What is the magnitude of the resultant force in N (caused by the other two masses) on the mass at the origin?

a. 2.7 x 10^-8

b. 2.1 x 10^-8

c. 1.8 x 10^-8

d. 2.4 x 10^-8

e. 2.9 x 10^-8

50. Three 5.0 kg masses are located at the corners of an equilateral triangle with sides 0.30 m in length. What is the magnitude in N of the resultant force exerted on one of the masses by the other two masses?

a. 2.8 x 10^-8

b. 3.6 x 10^-8

c. 3.2 x 10^-8

d. 4.0 x 10^-8

e. 1.8 x 10^-8
51. A satellite in an elliptical orbit around the Earth is moving at maximum speed when it is

a. closest to the moon.

b. closest to the Earth.

c. furthest from the Earth.

d. furthest from the moon.

e. between the Earth and the sun.

52. A space station and a weather satellite are orbiting the Earth. The space station is 8 times as far from the Earth’s center as the weather satellite. If the period of revolution of the weather satellite is 24 hours, what is the period of revolution of the space station in hours?

a. 48

b. 96

c. 108

d. 543

e. 672
53. A satellite in an elliptical orbit around the Earth has its greatest centripetal acceleration when it is

a. nearest the moon.

b. nearest the Earth.

c. furthest from the Earth.

d. furthest from the moon.

e. between the Earth and the sun.

54. The Hale-Bopp comet has the sun at a focus of its elliptical path. What is at the other focus?

a. Another star of the same mass as the sun.

b. Nothing.

c. The Earth.

d. The comet passes through the other focus.

e. The comet’s tail stays at the other focus.
55. A synchronous orbit about the Earth is obtained when the period of the orbit is the same as the length of the day. If the length of an Earth day is 24 hours and the radius of the Earth is 6.37 x 10⁶ m, how high above the Earth’s surface in m should a body be placed in order to be in a synchronous orbit?

a. 4.22 x 10⁷

b. 2.77 x 10⁷

c. 8.35 x 10⁷

d. 3.58 x 10⁷

e. 6.78 x 10⁷

56. A perfectly spheroid planet rotates on its axis once every 24 hours Earth time. If you weighed yourself at the equator and a pole of that planet,

a. your weight would be greater at the pole.

b. your mass would be greater at the pole.

c. your weight would be greater at the equator.

d. your mass would be greater at the equator.

e. your mass and weight would be the same at both the equator and the pole.

57. In the limit in which air resistance is ignored

a. all objects fall to Earth at a velocity of 10 m/s.

b. the gravitational force on an object decreases as it approaches the surface of the Earth.

c. the gravitational force on an object increases as it approaches the surface of the Earth.

d. larger and more massive objects fall faster than smaller and less massive ones.

e. both (c) and (d) above are correct.

58. When Carole is outside the space station to repair a satellite

a. her weight is zero.

b. her weight is equal to the gravitational force of the Earth on her.

c. her weight is equal to her weight on the surface of the Earth.

d. her weight is equal to the gravitational force on her minus the product of her mass and her centripetal acceleration

e. her weight cannot be defined because she is “weightless.”

59. A structural model contains

a. a description of the physical components of a system and where they are located relative to one another.

b. a description of the time evolution of the system.

c. a description of the agreement between predictions of the model and actual observations.

d. all of the above.

e. only (a) and (c) above.

60. The area swept out by the radius vector from the sun to a planet is constant because

a. the gravitational force on the planet is constant.

b. the kinetic energy of the planet is constant.

c. the angular momentum of the planet relative to the sun is constant.

d. the linear momentum of the planet relative to the sun is constant.

e. (c) and (d) above are both correct.

61. A comet is in a highly elliptical orbit around the sun. The period of the comet is 90 days. The mean distances from the sun of Mercury, Venus and Earth are , and respectively. This comet might collide with

a. Mercury.

b. Venus.

c. Earth.

d. all of the above.

e. only (a) or (b) above.

62. We know that the same gravitational force that Earth exerts on objects near its surface is also exerted on the moon because we find that

a. .

b. G measured on the moon equals one sixth G measured on the Earth.

c. the gravitational acceleration of the moon equals the centripetal acceleration of the moon (both measured relative to the center of the Earth.)

d. the gravitational acceleration of the moon equals the tangential acceleration of the moon (both measured relative to the center of the Earth.)

e. both (c) and (d) above are correct.

63. As a comet traveling in an elliptic orbit of major axis a moves away from the sun, its gravitational potential energy (in the standard definition)

a. decreases in magnitude.

b. increases in magnitude.

c. becomes more negative.

d. becomes positive.

e. becomes zero.

64. Which statement is not a basic postulate of the Bohr model?

a. The angular momentum of an electron in an orbit is quantized.

b. An electron in an allowed orbit does not radiate.

c. Radiation is emitted when an electron jumps from a more energetic initial state to a less energetic final state.

d. The electron travels in a circular orbit about the proton under the influence of the electrostatic force of attraction.

e. The electric force on the electron balances the gravitational force on the electron.

65. The ionization energy of a hydrogen atom is the energy required to reach

a. the state in which the electron and the proton are separated from each other.

b. the first excited state of the hydrogen atom.

c. the state in which the radius of the electron is .

d. the state with energy equal to .

e. either (a) or (c) above.

66. With the standard definition of the zero of potential energy, the gravitational potential energy of the Earth-Sun system is negative. The physical meaning of this is that

a. the gravitational force is always an attractive force.

b. the Earth is in a bound state about the Sun.

c. the Earth is traveling in a hyperbolic orbit.

d. the Earth’s kinetic energy is equal to the magnitude of the gravitational potential energy of the system.

e. the magnitude of the gravitational potential energy of the system equals the energy the Earth lost in capturing the Moon.

67. A satellite loses energy to friction when traveling through the very thin upper atmosphere. Which statement correctly describes the satellite’s energy changes during this process?

a. Its kinetic energy and its potential energy both decrease in magnitude.

b. Its kinetic energy decreases but its potential energy increases in magnitude.

c. Its kinetic energy increases but its potential energy decreases in magnitude.

d. Its kinetic energy increases and its potential energy increases in magnitude.
68. Sixty-kilogram Roger and 60 kg Mary are standing side by side, 0.50 m apart, both wearing sneakers for which . The ratio of the maximum frictional force on each of them to the gravitational force of attraction each exerts on the other in the approximation where we treat them as point particles is

a.

b.

c.

d.

e.

Chapter 11 Answers
Number Type Answer Number Type Answer

1. C b 36. 2 b

2. C a 37. 3 c

3. C a 38. C a

4. C b 39. 2 b

5. C d 40. 2 d

6. C b 41. 1 c

7. C a 42. 2 b

8. C e 43. 2 b

9. C e 44. 2 d

10. C a 45. 2 b

11. C a 46. 2 c

12. C d 47. 2 d

13. C d 48. 2 b

14. C d 49. 3 b

15. 2 b 50. 3 c

16. 3 d 51. C b

17. 3 e 52. 2 d

18. 3 b 53. C b

19. 3 d 54. C b

20. 1 a 55. 1 d

21. 2 c 56. C a

22. 1 e 57. C c

23. 2 c 58. C b

24. 1 d 59. C d

25. 2 a 60. C c

26. 3 e 61. 2 a

27. 1 d 62. C c

28. 2 b 63. C a

29. 2 c 64. C e

30. 1 b 65. C a

31. 2 e 66. C b

32. 1 c 67. C d

33. 2 d 68. 3 d

34. 3 b

35. 3 a