Concept explainers
The classical Doppler shift for light. A light source recedes from an observer with a speed v that is small compared with c. (a) Show that in this case, Equation 1.15 reduces to
(b) Also show that in this case
(Hint: Differentiate λf = c to show that Δλ/λ = –Δf/f) (c) Spectroscopic measurements of an absorption line normally found at λ = 397 nm reveal a redshift of 20 nm for light coming from a galaxy in Ursa Major. What is the recessional speed of this galaxy?
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Chapter 1 Solutions
Modern Physics
- A galaxy G is moving away radially with speed with respect to an observer O. The relation between X, the wavelength of light emitted at G, and λo, the wavelength observed at O, is 入。 λ = λe λε 1+B 1- B' = where ẞ v/c (c is the speed of light). For ẞ < 1 find a power series expansion of the above formula up to and including terms of order ẞ³.arrow_forwardEarth's neighboring galaxy, the Andromeda Galaxy, is a distance of 2.54 x 10' light-years from Earth. If the lifetime of a human is taken to be 75.0 years, a spaceship would need to achieve some minimum speed vmin to deliver a living human being to this galaxy. How close to the speed of light would this minimum speed be? Express your answer as the difference between umin and the speed of light c. C- Umin = m/sarrow_forwardElectrons are accelerated through a potential difference of 850 kVkV , so that their kinetic energy is 8.5×105 eVeV . A) What is the ratio of the speed vv of an electron having this energy to the speed of light, ccc? Express your answer as a multiple of speed of light cc. B) What would the speed be if it were computed from the principles of classical mechanics? Express your answer in meters per second.arrow_forward
- i have no clue where to start with this question.arrow_forwardAlbert Einstein is pondering how to write his (soonto-be-famous) equation. He knows that energy E is a function of mass m and the speed of light c, but he doesn't know the functional relationship (E = m2c? E = mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluid mechanics class, you help Albert come up with his equation. Use the step-by-step method of repeating variables to generate a dimensionless relationship between these parameters, showing all of your work. Compare this to Einstein's famous equation—does dimensional analysis give you the correct form of the equation?arrow_forwardHW Q.3arrow_forward
- Answer part D and E.arrow_forwardOf 1.5, 3, 5, and 10 give the maximum apparent speeds. 2. Consider a relativistic jet with an angle of 70 degrees relative to the line of sight (i.e. it is almost, but not quite perpendicular to the line of sight). Let its value of gamma for the motion be 3. (a) Will it appear superluminal? (b) Will it appear to be brighter or fainter than it would in its own rest frame? 3. State whether the following reactions are possible under special relativity. If not, explainarrow_forwardA particle has γ=2,865. a) Calculate c-v in m/s. If your calculator gives problems, you might want to solve the appropriate equation for c-v or c(1 - v/c) and use an approximation. b) In the previous problem, in a race to the moon, by 3/4ths the distance, light is one or ten meters ahead of the particle. We routinely approximate mass as zero, gamma as infinite, and speed as the speed of light. ("Massless particles" -- gamma and m have to be eliminated from the expressions. Light is a true massless particle.) If a massless particle has momentum 2,910 MeV/c, calculate its energy in MeV.arrow_forward
- Mass of a proton: 1.007825 u; Mass of a neutron: 1.008665 u 1 The lifetime of a free neutron is 887 s. If a neutron moves with a speed 2.9 × 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be? What is this an example of? 2. (a) What is the rest energy (in joules) of a subatomic particle whose (rest) mass is 6.7 x 10-3¹ kg? (b) How many MeV's of energy is this? 3. The rest energy of a particular subatomic particle is 1200 MeV. If this particle is traveling at 90% the speed of light, what is its total relativistic energy?arrow_forwardEarth's neighboring galaxy, the Andromeda Galaxy, is a distance of 2.54 × 107 light-years from Earth. If the lifetime of a human is taken to be 85.0 years, a spaceship would need to achieve some minimum speed Umin to deliver a living human being to this galaxy. How close to the speed of light would this minimum speed be? Express your answer as the difference between Umin and the speed of light c. 8.96 ×10¹3 C- Umin m/s Incorrectarrow_forwardYou are in the magic school bus alone. For some reason, you decide to shine a laser straight up. The bus is at a height h = 3.50 m, excluding the wheels, and is travelling at a speed v = 0.800c. Now, your crush is on a car at rest, watching as the bus goes right past.(a) What is the time it takes for the light in your perspective to bounce from the laser to the top of the bus, then to the floor, and back to the laser? (b) Do this same calculation, but for your crush’s perspective. Hint: Light travels at the same speed from any perspective. (c) What is the ratio of the time from your crush’s view and that of your view?arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning