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Chapter 38. Modern Physics and the Atom
Relativity
38-1. A spaceship travels past an observer at a speed of 0.85c. A person aboard the space craft observes that it requires 6.0 s for him to walk the length of his cabin. What time would the observer record for the same event? [ Proper time to = 6 s, relative time t = ? ]
[pic] [pic] t = 11.4 s

38-2. A rocket A moves past a Lab B ata speed of 0.9c. A technician in the lab records 3.50 s for the time of an event which occurs on the rocket. What is the time as reckoned by a person aboard the rocket? [ Proper time t0 = ?, relative time t = 3.50 s ]
[pic]
[pic] to = 1.52 s

38-3. A blinking light on a spacecraft moves past an observer at 0.75c. The observer records that the light blinks at a frequency of 2.0 Hz.What is the actual frequency of the blinking light? (It’s important to distinguish relative time from relative frequency.)
Relative frequency is 2.0 blinks per second, which is relative time of 0.5 s/blink
Relative time t = 0.50 s; proper time to = ?; [pic]
[pic] to = 0.331 s/blink
[pic] fo = 3.02 Hz
38-4. A particle on a table has a diameter of 2 mm when at rest. What must bethe speed of an observer who measures the diameter as 1.69 mm? ( Proper length Lo = 2 mm. )
[pic]
[pic] v = 0.535c

38-5. A blue meter stick is aboard ship A and a red meterstick is aboard ship B. If ship A moves past B at 0.85c, what will be the length of each meterstick as reckoned by a person aboard ship A? (We must be careful to distinguish proper length from relative length.)Observer A sees blue stick as proper length Lo and red stick as relative length L.
LB = 1.00 m; [pic] Lr = 52.7 cm

38-6. Three meter sticks travel past an observer at speeds of 0.1c, 0.6c, and 0.9c. What lengths would be recorded by the observer? (Proper lengths Lo are each 1.00 m)
[pic] Lr = 99.5 cm;
[pic] Lr = 80.0 cm
[pic] Lr = 43.6 cm

38-7. What mass is required torun about 1 million 100-W light bulbs for 1 year?
Eo = moc2 = (1 x 106)(100 W)(86,400 s/d)(356 d/yr) = 3.154 x 1015 J/yr
[pic] mo = 35.0 g

38-8. Elementary particles called mu-mesons rain down through the atmosphere at 2.97 x 108 m/s. At rest the mu-meson would decay on average 2 (s after it came into existence. What is the lifetime of these particles from the viewpoint of an observeron earth?
[pic] [pic] t = 101 (s

The Photoelectric Effect
38-9. The first photoelectrons are emitted from a copper surface when the wavelength of incident radiation is 282 nm. What is the threshold frequency for copper? What is the work function for a copper surface?
[pic] fo = 1.06 x 1015 Hz;
W = hfo = (6.63 x 10-34 J/Hz)(1.06 x 1015 Hz); W = 7.028 x 10-19 J
[pic] W = 4.40eV

38-10. If the photoelectric work function of a material is 4.0 eV, what is the minimum frequency of light required to eject photoelectrons? What is the threshold frequency?
[pic]
[pic] f0 = 9.65 x 1014 Hz


38-11. The energy E of a photon in joules is found from the product hf. Often we are given the wavelength of light and need to find its energy in electron volts. Show that[pic]
such that if λ is in nanometers, E will be the energy in electron volts.
[pic]
[pic]; Ελ = 1240 eV(nm
When λ is in nm , E will be in J: [pic]
38-12. Use the equation derived in Problem 38-13 to verify that light of wavelength 490 nm has an energy of 2.53 eV. Also show that a photon whose energy is 2.10 eV has a wavelength of 590 nm.
[pic] E = 2.53 J; [pic]λ = 590 nm
*38-13. The threshold frequency for a certain metal is 2.5 x 1014 Hz. What is the work function? If light of wavelength 400 nm shines on this surface, what is the kinetic energy of ejected photoelectrons?
W = hfo = (6.63 x 10-34 J/Hz)(2.5 x 1014 Hz); W = 1.66 x 10-19 J
[pic] W = 1.04 eV
[pic]; Ek = 3.31 x 10-19 J
[pic] Ek = 2.07 eV
*38-14. When light of...