Modern Physics For Scientists And Engineers
2nd Edition
ISBN: 9781938787751
Author: Taylor, John R. (john Robert), Zafiratos, Chris D., Dubson, Michael Andrew
Publisher: University Science Books,
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Chapter 4, Problem 4.32P
To determine
Plot the graph ofPlanck distribution function (i.e the spectral distribution of the
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Chapter 4 Solutions
Modern Physics For Scientists And Engineers
Ch. 4 - Prob. 4.1PCh. 4 - Prob. 4.2PCh. 4 - Prob. 4.3PCh. 4 - Prob. 4.4PCh. 4 - Prob. 4.5PCh. 4 - Prob. 4.6PCh. 4 - Prob. 4.7PCh. 4 - Prob. 4.8PCh. 4 - Prob. 4.9PCh. 4 - Prob. 4.10P
Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - Prob. 4.16PCh. 4 - Prob. 4.17PCh. 4 - Prob. 4.18PCh. 4 - Prob. 4.19PCh. 4 - Prob. 4.20PCh. 4 - Prob. 4.21PCh. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - Prob. 4.24PCh. 4 - Prob. 4.25PCh. 4 - Prob. 4.26PCh. 4 - Prob. 4.27PCh. 4 - Prob. 4.28PCh. 4 - Prob. 4.29PCh. 4 - Prob. 4.30PCh. 4 - Prob. 4.31PCh. 4 - Prob. 4.32PCh. 4 - Prob. 4.33P
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- Question #1 a) Plot the energy spectral density p(2) of black-body radiation at T=3000 K and at 7= 5000 K. (These correspond to the apparent temperatures of "warm white" and "cool white" light bulbs.) (Note: Show both curves on a single graph, using a standard plotting software. Report the wave- length in nanometers.) b) For each of these two temperatures, at which wavelength is the radiation intensity maximum? (Note: Report the wavelengths in nanometers. Your answers should be consistent with the curves from part a), of course.)arrow_forward1.11 Calculate the Doppler width of a spectrum line from a neon discharge tube operating at a temperature of 100°C. The value of the Boltzmann constant k is 1.38 x 10-23 joules per degree Kelvin (J/K) and the mass of the neon atom is 3.34 x 10-26 kg. Take A = 600 nm and find the line width in both frequency and wavelength.arrow_forward6.1.5. Radiation has been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature, at what wavelength does the Planck distribution peak? In what part of the electromagnetic spectrum is this wavelength? %3Darrow_forward
- Outline the steps leading to the formula for the number of photons with angular fre- quencies between w and w + dw in blackbody radiation at a temperature T: w? dw V n(w)dw = 2 x 272c3 ehw/kBT Show that n(w) has a peak at a frequency given by w = 1.59kgT/h. Show further that the spectral energy densities ux and uw peak at Amax = hc/(4.97KBT) and wmax = 2.82KBT/ħ, respectively.arrow_forwardWhat is the frequency fmax of the maximum (peak) in the blackbody distribution of a blackbody at 3000 K? Give your answer to 2 significant figures in THz (terahertz). Formulas.pdf (Click here-->)arrow_forward6.133 Blackbody radiation is the term used to describe thedependence of the radiation energy emitted by an objecton wavelength at a certain temperature. Planck proposed the quantum theory to account for the dependence.Shown in the figure is a plot of the radiation energyemitted by our sun versus wavelength. This curve ischaracteristic of objects at about 6000 K, which is thetemperature at the surface of the sun. At a highertemperature, the curve has a similar shape but themaximum will shift to a shorter wavelength. (a) Whatdoes this curve reveal about two consequences ofgreat biological significance on Earth? (b) How areastronomers able to determine the temperature at thesurface of stars in general?arrow_forward
- identify the knowns, unknown(s), appropriate formula(s) then computation 1. a). The wavelength of maximum solar emission is observed to be approximately 0.475μm. What is the surface temperature of the sun (assumed as blackbody)? (b) The temperature of the human body when having a high fever is 40 deg C. The intensity of radiation emitted by the human body is maximum at what wavelength? (c) The Cosmic Microwave Background radiation (CMB) fills the universe. If temperature of the space is 2.7 K, then CMB attains intensity maxima at what wavelength?arrow_forward4, 3. Excited Ground state 1(ground state) state 4. 4.85E-19 J 4.42E-19 J 3.98E-19 J 3. 1. 3.03E-19 J 2. 1. 1 (ground state) Energy Energy paquosqe emitted 2) [30] Energy Levels Above is a schematic of a Hydrogen atom with its first 5 energy levels. On the right is the energy emitted from the transitions (lines pointing down on the diagram). Using the knowledge that energy and wavelength are hc, connected ( E =) you will figure out the wavelength for each of these %3D transitions. %3D E. h = Planck constant = 6.63E-34 J*s c = speed of light = 3E8 m/s 2 = wavelength in meters E = energy in Joules (J) %3D hc %3D E will be in meters! Divide by 10-9 for nm If you need help converting this to a color easier, try this website once you get the wavelength in nm: https://academo.org/demos/wavelength-to- colour-relationship/arrow_forwardA sphere has a radius of 2 80x102 m. This perfectly emitting sphere glows an orange-ish color and is found to have a peak black-body wavelength of 770. nm. Answer the five parts below, using three significant figures as appropriate Part A-What is the temperature, T, of the sphere in Kelvin?arrow_forward
- 2 A.) FOR TWO OBSERVABLES A=x %3D B= LZ, FIND THE UNCERTAINTY RELATIONS TA Jo. AND B.) FOR THE STATE Ynim IN A HYOROGEN ATOM, FIND 8. USE THE DEFINITION OF STANDARD DEVIATION.arrow_forwardTownsend 1.34: Starting from first principles, show that the probability that a photon of wavelength 2 hits a photomultiplier center on a point P in the detection plane that makes an angle Owith the horizontal for a grating composed of three very narrow slits each separated by a distance d is given by Prob = r2(1 +4 cos 4 + 4cos2 ¢),where is the probability that the photon would strike the photomultipliers with a single slit open and 2Td sin 0/ = kd sin0 =arrow_forward*13.1-8 Momentum of a Photon in a Gaussian Beam. (a) What is the probability that the momentum vector of a photon associated with a Gaus- sian beam of waist radius Wo lies within the beam divergence angle 00? Refer to Sec. 3.1 for definitions. (b) Does the relation p = E/c. hold in this case? Explain.arrow_forward
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