Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 3, Problem 19Q
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The use of Planck’s
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1. Temperature of the Cosmic Microwave Background radiation (CMB) is
T= 2.725 K.
a) Assuming it has a Planck energy distribution, use Wien's Displacement
Law to find the maximum wavelength of the CMB (in metres).
b) What is the radiation energy density, u (measured in J/m³) of the CMB?
c) Maximum intensity of the CMB occurs at frequency vmax = 160 GHz.
Calculate energy (in Joules, J) of one photon at this frequency.
d) Using the results of (2) and (3), find the number of CMB photons per m3,
Nph •
As2.
A planet orbits a red dwarf star of radius r0 at a distance of 120r0. In-
telligent beings on this planet observe that the radiation from their star
arriving at the top of their atmosphere is 1100W/m2. Assume the star’s
radiation follows Planck’s law for black body radiation. a) What is the
temperature of the star’s surface, within 10K accuracy? b) What is the
color of the star’s light? This would correspond to the frequency at which
the function B(ν, T) is maximal.
The Sun radiates almost like a perfect blackbody at a temperature of T= 5800 K.
a) Show, using the Stefan-Boltzmann law, that the rate at which it radiates energy is - 4x1026 W.
b) If you were at Earth's orbit, in space, how many Sun photons would reach you per second? Assume you have a mass of 70 kg, are spherical and full
of water. You may need to find your cross sectional area and assume all Sun photons move in the same direction.
Chapter 3 Solutions
Modern Physics for Scientists and Engineers
Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8QCh. 3 - Prob. 9QCh. 3 - In the experiment of Example 3.2, how could you...
Ch. 3 - Prob. 11QCh. 3 - Prob. 12QCh. 3 - Prob. 13QCh. 3 - Prob. 14QCh. 3 - Prob. 15QCh. 3 - Prob. 16QCh. 3 - Prob. 17QCh. 3 - Prob. 18QCh. 3 - Prob. 19QCh. 3 - Prob. 20QCh. 3 - Prob. 21QCh. 3 - Prob. 22QCh. 3 - Prob. 23QCh. 3 - Prob. 24QCh. 3 - Prob. 25QCh. 3 - Prob. 26QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Across what potential difference does an electron...Ch. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Calculate max for blackbody radiation for (a)...Ch. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - White dwarf stars have been observed with a...Ch. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 52PCh. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Prob. 55PCh. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - Prob. 62PCh. 3 - Prob. 63PCh. 3 - Prob. 64PCh. 3 - Prob. 65PCh. 3 - Prob. 66PCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - The Fermi Gamma-ray Space Telescope, launched in...Ch. 3 - Prob. 70P
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- Which of the following statements about a black body are true? Select one or more: a.The spectrum of the cosmic background radiation corresponds with great accuracy to the radiation of a black body at a temperature of 2.7 K. b.A black body absorbs all the radiation that hits it, and emits no radiation at all. c.According to Planck's radiation law (black body distribution), the wavelength corresponding to the maximum energy density of the radiation decreases (and the frequency increases) as the temperature increases. d.A black body reflects all the radiation that hits it, and absorbs no radiation at all.arrow_forwardWhich of the following statements about a black body are true? Select one or more: a. The spectrum of the cosmic background radiation corresponds with great accuracy to the radiation of a black body at a temperature of 2.7 K. b. A black body absorbs all the radiation that hits it, and emits no radiation at all. C. According to Planck's radiation law (black body distribution), the wavelength corresponding to the maximum energy density of the radiation decreases (and the frequency increases) as the temperature increases. d. A black body reflects all the radiation that hits it, and absorbs no radiation at all.arrow_forwardWhen stars like the Sun die, they lose their outer layers and expose their very hot cores. These exposed cores are called white dwarf stars. A certain white dwarf star has a peak emission wavelength of 0.546 nm. Approximating the star as a blackbody, what is its surface temperature? Wien's Displacement constant is b = 2.898 x 10-3 K m. The Stefan-Boltzmann constant is ? = 5.670 x 10-8 W/m2K4.arrow_forward
- 1. Wien’s Law states that the peak wavelength of photons emitted by an object is inversely proportional to the object’s absolute temperature. For a 4,000 K body, the peak photon wavelength is 1000 nm. What is the peak wavelength of photons emitted by an object with a surface temperature of 212 F? 2. An object with a temperature of 5,000 K emits an electromagnetic (EM) flux of 50 nanowatts. Apply the blackbody radiation law to calculate approximate EM flux emitted by this body if its temperature is changed to 18,000 F.arrow_forwardWhat will be the energy associated with a blue photon (in electronvolts, eV), if the frequency of the blue light is 650 THz (Terahertz (THz); 1 Tera = 1012)? [Hint: Use Planck's equation: E - hf to calculate the photon energy! h- Planck's constant – 6.63 x 10-34 Js = 4.14 x1015 eVs] A. 6.5 eV B. 6.5×10-3 eV C. 2.7 eV D. 2.7×10-27eV E. 2.7x107 eVarrow_forward4. The sun approximates an ideal blackbody radiator at a temperature of 5825K. (a) By Wien’s Law, what is the peak wavelength of this distribution? (b) What is the energy of a blackbody photon at this wavelength? (c) Is this photon in the visible band of the electromagnetic spectrum and why or why not? (d) The Cosmic Microwave Background has a nearly perfect blackbody spectrum with a temperature of 2.73K. What is the peak blackbody wavelength?arrow_forward
- Asaparrow_forward) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?arrow_forwardCalculate the wavelength of a photon that has energy 2.83 × 10−19 Joules. Give your answer in units of nano metres. Hint: Planck’s constant h = 6.625 × 10−34 J s.arrow_forward
- QUESTION1: Stefan-Boltzman law can be used to estimate H emitted from a surface where H = AeoT, where H = surface area (m2) in units of watts, e = diffusivity characterizing the spreading properties of the surface, o = a universal constant called the Stefan-Boltzman constant. (-5.67x108 W m?K4) and T = absolute temperature (K). a) Determine the error of the radiation H of a steel sphere surface with radius = 0.15 + 0.02 m, e 0.90+ 0.05 and T = 550 ± 25 K. Compare your results with the exact error. Calculations b) radius = 0.15 0.01 m, e 0.90 +0.025 Repeat for T = 550 12.5 K. and Interpret your results.arrow_forwardThe Planck radiation law* (1 Point) is a theoretical relationship between electromagnetic radiation and wavelength for a blackbody, which postulates that electromagnetic radiation can be emitted continuously. is a theoretical relationship between electromagnetic radiation and wavelength for a blackbody, which postulates that electromagnetic radiation is different than light. is a theoretical relationship between electromagnetic radiation and wavelength for a blackbody, which is identical to the Rayleigh-Jeans law. is a theoretical relationship between electromagnetic radiation and wavelength for a blackbody, which postulates that electromagnetic radiation comes in packets.arrow_forwardA east.cengagenow.com/ilrn/takeAssignment/takeCovalentActivity.do?locator=assignment-take AM radio stations broadcast at frequencies between 530 kHz and 1700 kHz. (1 kHz = 10° /s.) For a station broadcasting at 1.17 × 10³ kHz, what is the energy of this radio wave? Note that Planck's constant is 6.63 x 10-34 J.s, and the speed of light is 3.00 x 10 m/s. Energy = Submit Answer Try Another Version 6 item attempts remaining Previous Next P Type here to search 12:03 PM 12/8/2021arrow_forward
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