Question 1

A spaceship A observes enemy spaceship E escaping with a velocity of $$0.48c$$ relative to A. A missile M is fired from ship A with a velocity of $$0.72c$$ relative to A, both in the same direction. What is the velocity of the missile M as observed by the crew on ship E? Use the relativistic velocity addition formula.

Accepted Answer

$$0.37c$$

Question 2

A tank holds a $$1.44\ \mathrm{m}$$ thick layer of oil (index $$n_1 = 1.40$) floating on a 0.96$$\ \mathrm{m}$$ thick layer of brine (index n_2$ = 1.52). A $$ray from the bottom center of the tank reaches the brine-oil interface at the critical angle. What is the distance from the axis to this point?

Accepted Answer

$$2.3\ \mathrm{m}$$

Question 3

Light of wavelength $$425.0\ \mathrm{nm} in $$air falls at normal incidence on an oil film ($$n = 1.40) of $$thickness $$850.0\ \mathrm{nm}$$ floating on water ($$n = 1.33). $$What is the minimum distance you should increase the oil film so that reflected light is canceled?

Accepted Answer

$$60.7\ \mathrm{nm}$$

Question 4

A thin beam of laser light of wavelength $$514\ \mathrm{nm}$$ passes through a diffraction grating with $$3952$$ lines/cm. If the experiment is performed under water ($$n = 1.33$$), what is the total number of bright spots observed on the screen?

Accepted Answer

$$13$$

Question 5

A spaceship approaches Earth at $$0.50c. A $$passenger measures his heartbeat as $$70$$ beats per minute. What is his heartbeat rate according to an observer at rest on Earth?

Accepted Answer

$$61$$ beats/min

Question 6

Two space stations are $$6.0 	imes 10^7$\ \mathrm{m}$$ apart (in their rest frame). A spaceship travels from one to the other at $$0.90c. $$How long does the trip take according to an observer on the spaceship? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$97\ \mathrm{ms}$$

Question 7

A relativistic proton has a momentum of $$1.00 	imes 10$$^{-19}$$\ \mathrm{kg\cdot m/s}$$ and a rest energy of $$0.150\ \mathrm{nJ}. $$What is the speed of the proton in the lab? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$m_{\mathrm{proton}} = 1.67 	imes 10$$^{-27}$$\ \mathrm{kg})$$

Accepted Answer

$$0.196c$$

Question 8

A relativistic proton has a momentum of $$1.0 	imes 10$$^{-17}$$\ \mathrm{kg\cdot m/s}$$ and a rest energy of $$0.15\ \mathrm{nJ}. $$What is the kinetic energy of this proton? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$m_{\mathrm{proton}} = 1.67 	imes 10$$^{-27}$$\ \mathrm{kg})$$

Accepted Answer

$$3.0\ \mathrm{pJ}$$

Question 9

A stopping potential of $$0.50\ \mathrm{V} is $$required when a phototube is illuminated with light of wavelength $$590\ \mathrm{nm}. If $$the stopping potential is $$2.30\ \mathrm{V}$$ for a different wavelength, what is the wavelength of the new light? ($$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$e = -1.60 	imes 10$$^{-19}$$\ \mathrm{C}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J})$$

Accepted Answer

$$320\ \mathrm{nm}$$

Question 10

A photon of wavelength $$18.0\ \mathrm{pm} is $$scattered through an angle of $$120^\circ by a $$stationary electron. What is the wavelength of the scattered photon? ($$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$, $$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$21.6\ \mathrm{pm}$$

Question 11

A hydrogen atom makes a downward transition from $$n = 20 to$$ $$n = 5. $$What is the wavelength of the emitted photon? The ground state energy is $$-13.6\ \mathrm{eV}$$. ($$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J\cdot s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$2.43\ \mu\mathrm{m}$$

Question 12

A nonrelativistic electron has a kinetic energy of $$5.4\ \mathrm{eV}. $$What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? ($$m_e = 9.11 	imes 10$$^{-31}$$\ \mathrm{kg}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s}$$, $$1\ \mathrm{eV} = 1.60 	imes 10$$^{-19}$$\ \mathrm{J})$$

Accepted Answer

$$2.4\ \mathrm{keV}$$

Question 13

Which of the following best describes the phenomenon of total internal reflection?

Accepted Answer

It occurs when light passes from a medium with a higher index of refraction to a lower one at an angle greater than the critical angle.

Question 14

Which equation correctly expresses the relativistic addition of velocities $$u$$ and $$v$$?

Accepted Answer

$$u' = \frac{u + v}{1 + \frac{uv}{c^2$}}$$

Question 15

In the photoelectric effect, what happens to the kinetic energy of emitted electrons if the frequency of incident light is increased, keeping the intensity constant?

Accepted Answer

It increases.

Question 16

Which of the following is a consequence of time dilation in special relativity?

Accepted Answer

Moving clocks run slower than stationary ones.

Relativistic Velocity Addition: Spaceship and Missile Scenario

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