Deck 27: Quantum Physics Blackbody Radiation and Plancks Hypothesis: Part A

Question 1

The astronaut whose heart rate on Earth is 60 beats/min increases his velocity to v = 0.60c.Now what is his heart rate as measured by an Earth observer?

A) 100 beats/min
B) 75 beats/min
C) 36 beats/min
D) 48 beats/min

Answer 1

48 beats/min

Question 2

If astronauts could travel at v = 0.90c,we on Earth would say it takes (4.2/0.90)= 4.7 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

A) 2.0 years
B) 2.4 years
C) 1.4 years
D) 3.0 years

Answer 2

2.0 years

Question 3

A muon formed high in the Earth's atmosphere travels at a speed 0.990c for a distance of 6.40 km before it decays.What is the muon's lifetime as measured in its reference frame?

A) 4.65 × 10−⁶ s
B) 1.55 × 10−⁵ s
C) 2.18 × 10−⁶ s
D) 3.04 × 10−⁶ s

Answer 3

3.04 × 10−⁶ s

Question 4

A space probe has a 24.7-m length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.860c?

A) 25.2 m
B) 6.43 m
C) 9.19 m
D) 12.6 m

Question 5

A ground observer measures the period of a pendulum moving as a part of an inertial frame of reference to be 2.30 s as the inertial frame moves by at a velocity of 0.800c.What would the observed period be of the same pendulum if its inertial frame were at rest with respect to the observer?

A) 3.03 s
B) 1.38 s
C) 1.84 s
D) 4.25 s

Question 6

The observed relativistic length of a super rocket moving by the observer at 0.57c will be what factor times that of the measured rocket length if it were at rest?

A) 0.82
B) 0.45
C) 1.4
D) 0.71

Question 7

A spaceship is moving away from an observer at relativistic speed.Its length at rest is 100 m,but the observer measures its length as 67 m.A time interval of 100 s on the spaceship would be measured by the observer to be which of the following?

A) 200 s
B) 150 s
C) 50 s
D) 100 s

Question 8

An astronaut is traveling at a high rate of speed from the Earth to a distant star system.Observers here on Earth note the relativistic effect that the astronaut's clocks run slow.What relativistic effect,if any,does the astronaut observe?

A) Her pulse rate slows.
B) The distance from the Earth to the star system has decreased.
C) Her clocks run faster.
D) There is no relativistic effect to be observed by the astronaut since she is the one doing the moving.

Question 9

A rocket ship is 74.0 m in length when measured before leaving the launching pad.What would its velocity be if a ground observer measured its length as 60.0 m while it is in flight? (c = 3.00 × 10⁸ m/s)

A) 1.76 × 10⁸ m/s
B) 0.980 × 10⁸ m/s
C) 1.98 × 10⁸ m/s
D) 1.15 × 10⁸ m/s

Question 10

A muon formed high in Earth's atmosphere travels at a speed 0.9900c for a distance (as we see it)of 9200 m before it decays.How far does the muon travel as measured in its frame?

A) 2596 m
B) 1298 m
C) 4554 m
D) 649 m

Question 11

An astronaut at rest has a heart rate of 65 beats/min.What will her heart rate be as measured by an earth observer when the astronaut's spaceship goes by the earth at a speed of 0.80c?

A) 108 beats/min
B) 39 beats/min
C) 81 beats/min
D) 52 beats/min

Question 12

A knight on horseback holds a 10-m lance.The horse can run at 0.78c.(It wins most of its races!)How long will the lance appear to a person that is standing still on the ground as the horse runs past?

A) 7.1 m
B) 15 m
C) 10 m
D) 6.3 m

Question 13

Muons at speed 0.9994c are sent round and round a circular storage ring of radius 1500 m.If a muon at rest decays into other particles after an average T = 2.2 × 10−⁶ s,how many trips around the storage ring do we expect the 0.9994c muons to make before they decay?

A) 2
B) 4
C) 0.2
D) 6

Question 14

An Earth observer sees a spaceship at an altitude of 980 m moving downward toward the Earth at a speed of 0.600c.What is the spaceship's altitude as measured by an observer in the spaceship?

A) 588 m
B) 784 m
C) 1630 m
D) 1270 m

Question 15

A tuning fork has a frequency of 400 Hz and hence a period of 2.50 × 10−³ s.If the tuning fork is in an inertial frame of reference moving by the observer at speed of 0.680c,what is the frequency of the fork as measured by the observer? (Assume that measurements are strictly by optical means and that the speed of sound waves in air is not pertinent here. )

A) 454 Hz
B) 293 Hz
C) 605 Hz
D) 265 Hz

Question 16

A meterstick moving in a direction parallel to its length appears to be only 60.0 cm long to an observer.What is the meterstick's speed relative to the observer? (c = 3.00 × 10⁸ m/s)

A) 1.19 × 10⁸ m/s
B) 2.40 × 10⁸ m/s
C) 2.93 × 10⁸ m/s
D) 2.75 × 10⁸ m/s

Question 17

A mass is bouncing on the end of a spring with a period T when measured by a ground observer.What would the period of oscillation be (as measured by the same observer)if the mass and spring were moving past the ground observer at a speed of 0.600c?

A) 0.440 T
B) 1.25 T
C) 0.600 T
D) 1.67 T

Question 18

What is proper time?

A) Proper time is the time measured by a clock at rest with respect to the observer.
B) Proper time is time based on your actual longitude,not your time zone.
C) Proper time is the time given on your GPS.
D) Proper time means standard time as opposed to daylight savings time.

Question 19

The period of a pendulum is 2.0 s in a stationary inertial frame of reference.What is its period when measured by an observer moving at a speed of 0.80c with respect to the inertial frame of reference?

A) 1.6 s
B) 1.2 s
C) 2.5 s
D) 3.3 s

Question 20

How fast would a rocket have to move past a ground observer if the latter were to observe a 3.0% length shrinkage in the rocket length? (c = 3.00 × 10⁸ m/s)

A) 1.2 × 10⁸ m/s
B) 0.60 × 10⁸ m/s
C) 0.73 × 10⁸ m/s
D) 0.12 × 10⁸ m/s

Question 21

An object moves by an observer at 0.600c.The total energy of the object will be what factor times that of the rest energy?

A) 1.25
B) 0.970
C) 1.15
D) 0.600

Question 22

Doubling the momentum of a particle:

A) does not change its relativistic total energy.
B) quadruples its relativistic total energy.
C) doubles its relativistic total energy.
D) requires less of a speed increase as the speed increases.

Question 23

As measured from the Earth,a spacecraft is moving at speed 0.80c toward another spacecraft moving at speed 0.60c in the same direction,i.e. ,the first spacecraft is catching up with the second spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

A) 0.38c
B) -0.20c
C) -0.38c
D) not given

Question 24

What is the total energy of a proton moving at a speed of 2.10 × 10⁸ m/s? (proton mass is 1.67 × 10−²⁷ kg and c = 3.00 × 10⁸ m/s)

A) 1.11 × 10−²⁷ J
B) 2.10 × 10−¹⁰ J
C) 2.02 × 10−¹⁰ J
D) 2.24 × 10−²⁷ J

Question 25

As measured from the Earth,a spacecraft is moving at speed 0.80c toward a second spacecraft moving at speed 0.60c back toward the first spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

A) 0.81c
B) 0.95c
C) 0.38c
D) 0.20c

Question 26

A particle is moving the +x direction at speed c/2.Another particle is moving in the -x direction at speed c/2 toward the first particle.Which of the following best describes the speed of one particle as seen by an observer moving with the other particle?

A) c
B) some value less than 3c/4
C) some value more than 3c/4
D) 3c/4

Question 27

A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.800c in an accelerator.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

A) 7.52 × 10−¹¹ J
B) 1.00 × 10−¹⁰ J
C) 9.02 × 10−¹¹ J
D) 3.76 × 10−¹¹ J

Question 28

Our best measurements from Earth indicate that the star system Alpha Centauri is 4.2 light-years away.Suppose some of our astronauts traveled there at a speed v = 0.90c.What would the astronauts measure as the distance to Alpha Centauri?

A) 1.3 lightyears
B) 4.0 lightyears
C) 1.8 lightyears
D) 2.7 lightyears

Question 29

What is the relativistic kinetic energy of an electron moving at a speed of 2.00 × 10⁸ m/s? (electron mass is 9.11 × 10−³¹ kg and c = 3.00 × 10⁸ m/s)

A) 2.80 × 10−¹⁴ J
B) 1.27 × 10−¹⁴ J
C) 11.6 × 10−¹⁴ J
D) 9.47 × 10−¹⁴ J

Question 30

A proton with mass 1.67 × 10−²⁷ kg moves in an accelerator with a speed of 0.600c.What is its total energy? (c = 3.00 × 10⁸ m/s)

A) 3.26 × 10−¹⁰ J
B) 1.88 × 10−¹⁰ J
C) 0.540 × 10−¹⁰ J
D) 2.51 × 10−¹⁰ J

Question 31

As measured from the Earth,a spacecraft is moving at speed c/2 toward a second spacecraft that is not moving.The first spacecraft emits a laser pulse toward the second spacecraft.What is the speed of the laser pulse measured by the second spacecraft as it passes by?

A)

B)

C)

D)

Question 32

A nuclear reaction,which gives off a total of 2.0 × 10¹⁶ J of energy,expends how much mass in the process? (c = 3.00 × 10⁸ m/s)

A) 2.2 kg
B) 180 kg
C) 22 kg
D) 0.22 kg

Question 33

A particle of mass m is moving at speed ​v​ = ​c​/2.What is its momentum?

A)

B)

C)

D)

Question 34

As measured from the Earth,a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction.What would be the speed of the probe as measured from the Earth?

A) 0.70c
B) 0.81c
C) c
D) 0.95c

Question 35

At what speed is the momentum of an object triple that found classically?

A) c/3
B) 0.942 c
C) 0.866c
D) 2c/3

Question 36

A proton with mass 1.67 × 10−²⁷ kg moves with a speed of 0.800c in an accelerator.What is its relativistic momentum? (c = 3.00 × 10⁸ m/s)

A) 2.40 × 10−¹⁹ kg⋅m/s
B) 6.68 × 10−¹⁹ kg⋅m/s
C) 0.530 × 10−¹⁹ kg⋅m/s
D) 3.76 × 10−¹⁹ kg⋅m/s

Question 37

If a proton with mass 1.67 × 10−²⁷ kg moves in an accelerator such that its total energy is two times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

A) 1.00 × 10⁸ m/s
B) 2.83 × 10⁸ m/s
C) 1.41 × 10⁸ m/s
D) 2.60 × 10⁸ m/s

Question 38

Two spaceships are approaching one another,one with speed v​₁ and the other with speed v​₂.Neither speed is 0.Their speed of approach,according to Newtonian mechanics,is ​v​₁ + ​v​₂.Special relativity tells us that the speed of approach

A) is more than the Newtonian value if each speed is more than half the speed of light.
B) is always greater than the Newtonian value.
C) is the same as the Newtonian value if each speed is less than half the speed of light.
D) is always less than the Newtonian value.

Question 39

An electron of mass 9.11 × 10−³¹ kg moves with a speed of 0.800c.What is its momentum? (c = 3.00 × 10⁸ m/s)

A) 3.64 × 10−²² kg⋅m/s
B) 2.05 × 10−²² kg⋅m/s
C) 6.03 × 10−²² kg⋅m/s
D) 1.34 × 10−²² kg⋅m/s

Question 40

An unknown particle in an accelerator moving at a speed of 2.00 × 10⁸ m/s has a measured total energy of 1.22 × 10−⁹ J.What is its mass? (c = 3.00 × 10⁸ m/s)

A) 1.49 × 10−²⁶ kg
B) 0.650 × 10−²⁶ kg
C) 0.810 × 10−²⁶ kg
D) 1.01 × 10−²⁶ kg

Question 41

At what speed must an object be moving in order that it has a kinetic energy 2.50 times its rest energy? (c = 3.00 × 10⁸ m/s)

A) 2.52 × 10⁸ m/s
B) 1.91 × 10⁸ m/s
C) 2.75 × 10⁸ m/s
D) 2.87 × 10⁸ m/s

Question 42

An electron of mass 9.11 × 10−³¹ kg moves with a speed of 0.800c.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

A) 5.47 × 10−¹⁴ J
B) 2.05 × 10−¹⁴ J
C) 3.90 × 10−¹⁴ J
D) 6.22 × 10−¹⁴ J

Question 43

What is the speed of a particle having a kinetic energy equal to its rest energy?

A) The mass of the particle must be given since the answer can only be given in terms of the mass.
B)

C)

D)

Question 44

A proton with mass 1.67 × 10−²⁷ kg moves in an accelerator with speed of 0.900c.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

A) 1.95 × 10−¹⁰ J
B) 1.00 × 10−¹⁰ J
C) 3.70 × 10−¹⁰ J
D) 1.35 × 10−¹⁰ J

Question 45

When a four-megaton nuclear bomb is exploded,approximately 18 × 10¹⁵ J of energy is released.How much mass would this represent in a mass-to-energy conversion? (c = 3.00 × 10⁸ m/s)

A) 0.20 kg
B) 18 kg
C) 1.8× 10³ kg
D) 0.050 kg

Question 46

If the total energy of an electron in an accelerator is five times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

A) 1.98 × 10⁸ m/s
B) 2.94 × 10⁸ m/s
C) 2.32 × 10⁸ m/s
D) 2.90 × 10⁸ m/s

Question 47

A spaceship of mass 10⁶ kg is to be accelerated to 0.60c.How much energy does this require?

A) 2.3 × 10²² J
B) 6.0 × 10²² J
C) 2.5 × 10²³ J
D) 1.5 × 10²³ J

Question 48

The mass of a proton at rest is m.If the proton is moving so fast that its total energy is four times its rest energy,then what is the kinetic energy of the proton?

A) 3mc²
B) mc²
C) 2mc²
D) 4mc²

Question 49

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be triple its rest energy? (m_e = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,and q_e = 1.6 × 10−¹⁹ C)

A) 5.1 × 10⁵ V
B) 1.6 × 10^-19 V
C) 1.0 × 10⁶ V
D) 2.6 × 10⁵ V

Question 50

In an X-ray tube,high-speed electrons are slammed into a lead target,giving off X-rays.If the electrons are accelerated from rest through a potential difference of 100,000 volts,what speed do they have when they strike the target? (q_e = 1.6 × 10−¹⁹ C,m_e = 9.11 × 10−³¹ kg,and c = 3.00 × 10⁸ m/s)

A) 0.17c
B) 0.41c
C) 0.91c
D) 0.55c

Question 51

An electron of mass 9.11 × 10−³¹ kg moves with a speed of 0.800c.What is its total energy? (c = 3.00 × 10⁸ m/s)

A) 13.7 × 10−¹⁴ J
B) 10.2 × 10−¹⁴ J
C) 4.80 × 10−¹⁴ J
D) 7.30 × 10−¹⁴ J

Question 52

A satellite is powered by a small nuclear generator that puts out 20 W.How much matter is converted into energy over the 10 year life span of the generator?

A) 70 µg
B) 53 g
C) 53 kg
D) 53 µg