A light source recedes from an observer with a speed νs that is small compared with c. (a) Show that the fractional shift in the measured wavelength is given by the approximate expression
This phenomenon is known as the redshift because the visible light is shifted toward the red. (b) Spectroscopic measurements of light at λ = 397 nm coming from a galaxy in Ursa Major reveal a redshift of 20.0 nm. What is the recessional speed of the galaxy?
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Chapter 39 Solutions
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- In December 2012, researchers announced the discovery of ultramassive black holes, with masses up to 40 billion times themass of the Sun (seen as the bright spot at the center of the galaxy near the center of Fig. P39.78). a. What is the Schwarz-schild radius of a black hole that has a mass 40 billion times that of the Sun? b. Suppose this black hole is 1.3 billion ly from theEarth. What is the angular radius of a galaxy that is 1.7 billion lybehind it, as viewed from the Earth? FIGURE P39.78arrow_forwardSuppose the primed and laboratory observers want to measure the length of a rod that rests on the ground horizontally in the space between the helicopter and the tower (Fig. 39.8B). To derive the length transformation L = L (Eq. 39.5), we had to assume that the positions of the two ends were determined simultaneously. What happens to the length transformation equation if both observers measure the end below the helicopter at one time t1 and the other end at a later time t2?arrow_forwardA box is cubical with sides of proper lengths L1 = L2 = L3, as shown in Figure P26.14, when viewed in its own rest frame. If this block moves parallel to one of its edges with a speed of 0.80c past an observer, (a) what shape does it appear to have to this observer? (b) What is the length of each side as measured by the observer? Figure P26.14arrow_forward
- A rod moving with a speed v along the horizontal direction is observed to have length and to make an angle with respect to the horizontal as shown in Figure P38.17. (a) Show that the length of the rod as measured by an observer at rest with respect to the rod is p = [1( v2/c2) cos2 ]1/2. (b) Show that the angle p that the rod makes with the x axis according to an observer at rest with respect to the rod can be found from tan p = tan . These results show that the rod is observed to be both contracted and rotated. (Take the lower end of the rod to be at the origin of the coordinate system in which the rod is at rest.)arrow_forwardThe light from a heated atomic gas is shifted in frequency because of the random thermal motion of light-emitting atoms toward or away from an observer. Estimate the fractional Doppler shift (f/f0), assuming that light of frequency f0 is emitted in the rest frame of each atom, that the light-emitting atoms are iron atoms in a star at temperature 6000 K, and that the atoms are moving relative to an observer with the mean speed =8kBTm Must we use the relativistic Doppler shift formulas f=f01/c1/c for this calculation? Such thermal Doppler shifts are measurable and are used to determine stellar surface temperatures.arrow_forwardA certain X-ray machine generates X-rays from a beam of electrons accelerated from zero to 99.9999999 per cent the speed of light in a long linear accelerator of length 3.2 km. The electrons are generated in pulses of duration ∆t = 100 fs. The generated x-rays from the target are also short pulses (λ = 0.15 nm). What is the average power of the x-ray beam if it pulses 120 times per second and one x-ray pulse contains about a trillion photons (n = 1012). a) 16.0 W b) 1.6 W c) 0.16 W d) none of these.arrow_forward
- 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_forwardConsider a region where the following electric and magnetic fields are present: E = 12.52 ax + 19.68 ay + 18.72 az volts per meter and B = -12.00 ax + 18.86 ay + 18.27 az teslas. If a 1.38-coulomb charge is moving at a speed of 2.73 meters per second in the -y-direction, determine the magnitude of the Lorentz force in newtons.arrow_forwardA linear particle accelerator using beta particles collides electrons with their anti-matter counterparts, positrons. The accelerated electron hits the stationary positron with a velocity of 98 x 106 m/s, causing the two particles to annihilate.If two gamma photons are created as a result, calculate the energy of each of these two photons, giving your answer in MeV (mega electron volts), accurate to 1 decimal place. Take the mass of the electron to be 5.486 x 10-4 u, or 9.109 x 10-31 kg.Note: Assume that the kinetic energy is also converted into the gamma rays, and is included in the two photons.arrow_forward
- An electron of charge ee of modulus v completes a semicircle of radius R due to a magnetic field of modulus B, placed perpendicular to v. What is the work W done by the Lorentz force? O (a) W = π eVBR/2 J O (b) W = 0J O (C) W=2 TT eVBR J O (d) W = π eVBR Jarrow_forwardQuasars are faint, distant sources of radio waves. (Quasar is short for "quasi-stellar source." They are so named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the frequency of their emitted light toward the red, called the "redshift," we know that quasars are moving very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In this way they determine that quasars are billions of light years from earth. To be visible at this great distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the order of 1040 W, roughly 1014 times greater than the sun or 40 times greater than the most luminous galaxy. At what rate is rest mass being consumed to produce this much radiation?arrow_forwardQuasars are faint, distant sources of radio waves. (Quasar is short for "quasi-stellar source." They are so named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the frequency of their emitted light toward the red, called the "redshift," we know that quasars are moving very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In this way they determine that quasars are billions of light years from earth. To be visible at this great distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the order of 1040 W, roughly 1014 times greater than the sun or 40 times greater than the most luminous galaxy. At what rate is rest mass being consumed to produce this much radiation? Quasar 3C-273arrow_forward
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