Chapter Review
Concept Items
10.1 Postulates of Special Relativity
 The longitudinal nature of light waves implies this.
 Light shows the phenomenon of diffraction.
 The speed of light is the maximum possible speed.
 All other wave energy needs a medium to travel.
Describe the relative motion of Earth and the sun:
 if Earth is taken as the inertial frame of reference and
 if the sun is taken as the inertial frame of reference.

 Earth is at rest and the sun orbits Earth.
 The sun is at rest and Earth orbits the sun.

 The sun is at rest and Earth orbits the sun.
 Earth is at rest and the sun orbits Earth.

 The sun is at rest and Earth orbits the sun.
 The sun is at rest and Earth orbits the sun.

 Earth is at rest and the sun orbits Earth.
 Earth is at rest and the sun orbits Earth.

10.2 Consequences of Special Relativity
 The particle’s momentum will rapidly decrease.
 The particle’s momentum will rapidly increase.
 The particle’s momentum will remain constant.
 The particle’s momentum will approach zero.
 Both of them will be the same age.
 This is a paradox and hence the ages cannot be compared.
 The age of the twin who traveled will be less than the age of her twin.
 The age of the twin who traveled will be greater than the age of her twin.
A comet reaches its greatest speed as it travels near the sun. True or false— Relativistic effects make the comet’s tail look longer to an observer on Earth.
 True
 False
Critical Thinking Items
10.1 Postulates of Special Relativity
Explain how the two postulates of Einstein’s theory of special relativity, when taken together, could lead to a situation that seems to contradict the mechanics and laws of motion as described by Newton.
 In Newtonian mechanics, velocities are multiplicative but the speed of a moving light source cannot be multiplied to the speed of light because, according to special relativity, the speed of light is the maximum speed possible.
 In Newtonian mechanics, velocities are additive but the speed of a moving light source cannot be added to the speed of light because the speed of light is the maximum speed possible.
 An object that is at rest in one frame of reference may appear to be in motion in another frame of reference, while in Newtonian mechanics such a situation is not possible.
 The postulates of Einstein’s theory of special relativity do not contradict any situation that Newtonian mechanics explains.
 $18\times {10}^{6}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
 $18\times {10}^{8}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
 $1.08\times {10}^{11}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
 $1.08\times {10}^{8}\phantom{\rule{thinmathspace}{0ex}}\text{km}$
In 2003, Earth and Mars were the closest they had been in 50,000 years. The two planets were aligned so that Earth was between Mars and the sun. At that time it took light from the sun 500 s to reach Earth and 687 s to get to Mars. What was the distance from Mars to Earth?
 5.6×10^{7} km
 5.6×10^{10} km
 6.2×10^{6} km
 6.2×10^{12} km

 Light travels as a longitudinal wave.
 Light travels through a medium that fills up the empty space in the universe.

 Light travels as a transverse wave.
 Light travels through a medium that fills up the empty space in the universe.

 Light travels at the maximum possible speed in the universe.
 Light travels through a medium that fills up the empty space in the universe.

 Light travels at the maximum possible speed in the universe.
 Light does not require any material medium to travel.
Use the postulates of the special relativity theory to explain why the speed of light emitted from a fastmoving light source cannot exceed 3.00×10^{8} m/s.
 The speed of light is maximum in the frame of reference of the moving object.
 The speed of light is minimum in the frame of reference of the moving object.
 The speed of light is the same in all frames of reference, including in the rest frame of its source.
 Light always travels in a vacuum with a speed less than 3.00×10^{8} m/s, regardless of the speed of the source.
10.2 Consequences of Special Relativity
Halley’s Comet comes near Earth every 75 years as it travels around its 22 billion km orbit at a speed of up to 700, 000 m/s. If it were possible to put a clock on the comet and read it each time the comet passed, which part of special relativity theory could be tested? What would be the expected result? Explain.
 It would test time dilation. The clock would appear to be slightly slower.
 It would test time dilation. The clock would appear to be slightly faster.
 It would test length contraction. The length of the orbit would appear to be shortened from Earth’s frame of reference.
 It would test length contraction. The length of the orbit would appear to be shortened from the comet’s frame of reference.
The nucleus of the isotope fluorine18 (^{18} F) has mass defect of 2.44×10^{28} kg. What is the binding energy of ^{18}F?
 2.2×10^{11} J
 7.3×10^{20} J
 2.2×10^{20} J
 2.4×10^{28} J
Problems
10.2 Consequences of Special Relativity
Deuterium (2 H) is an isotope of hydrogen that has one proton and one neutron in its nucleus. The binding energy of deuterium is 3.56×10^{13} J. What is the mass defect of deuterium?
 3.20×10^{4} kg
 1.68×10^{6} kg
 1.19×10^{21} kg
 3.96×10^{30} kg
The sun orbits the center of the galaxy at a speed of 2.3×10^{5} m/s. The diameter of the sun is 1.391684×109 m. An observer is in a frame of reference that is stationary with respect to the center of the galaxy. True or false—The sun is moving fast enough for the observer to notice length contraction of the sun’s diameter.
 True
 False
Consider the nuclear fission reaction $n+{}_{92}{}^{235}U\to {}_{56}{}^{144}Ba+{}_{36}{}^{89}Kr+3n+E$. If a neutron has a rest mass of 1.009u, ${}_{92}{}^{235}U$ has a rest mass of 235.044u, ${}_{56}{}^{144}Ba$ has rest mass of 143.923u, and ${}_{36}{}^{89}Kr$ has a rest mass of 88.918u, what is the value of E in joules?
 $1.8\times {10}^{11}$J
 $2.8\times {10}^{11}$J
 $1.8\times {10}^{10}$J
 $3.3\times {10}^{10}$J
Consider the nuclear fusion reaction ${}_{1}{}^{2}H+{}_{1}{}^{3}H\to {}_{2}{}^{4}He+n+E$. If ${}_{1}{}^{2}H$ has a rest mass of 2.014u, ${}_{1}{}^{3}H$ has a rest mass of 3.016u, ${}_{2}{}^{4}He$ has a rest mass of 4.003u, and a neutron has a rest mass of 1.009u, what is the value of E in joules?
 $2.7\times {10}^{14}$J
 $2.7\times {10}^{13}$J
 $2.7\times {10}^{12}$J
 $2.7\times {10}^{11}$J
Performance Task
10.2 Consequences of Special Relativity
People are fascinated by the possibility of traveling across the universe to discover intelligent life on other planets. To do this, we would have to travel enormous distances. Suppose we could somehow travel at up to 90 percent of the speed of light. The closest star is Alpha Centauri, which is 4.37 light years away. (A light year is the distance light travels in one year.)
 How long, from the point of view of people on Earth, would it take a space ship to travel to Alpha Centauri and back at 0.9c?
 How much would the astronauts on the spaceship have aged by the time they got back to Earth?
 Discuss the problems related to travel to stars that are 20 or 30 light years away. Assume travel speeds near the speed of light.