Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 3, Problem 5P
(a)
To determine
The general relationship between temperature and
(b)
To determine
The numerical value for the Wien’s constant.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A blackbody is an object with a radiation spectrum that is dependent solely on its tempera-
ture. A blackbody spectrum (or spectral radiancy curve) is described by the Planck Radiation
Law.
(a)
i. Sketch the spectral radiancy curves for blackbodies with temperatures of T = 4000 K
and T = 6000 K, respectively. Describe the main differences between the two
curves in terms of the appropriate physical laws defined as a function of tempera-
ture.
ii. What is the wavelength at peak intensity for each blackbody? State the part of
the electromagnetic spectrum to which each wavelength belongs.
(b) Use the Planck Radiation Law to determine the power radiated per unit area between
the wavelengths A 500 nanometres and λ = 503 nanometres for the T 6000 K
blackbody. What fraction of the blackbody's radiancy lies in this wavelength range?
=
Consider a black body of surface area 22.0 cm² and temperature 5700 K.
(a) How much power does it radiate?
131675.5
W
(b) At what wavelength does it radiate most intensely?
508.421
nm
(c) Find the spectral power per wavelength at this wavelength. Remember that the Planck intensity is "intensity per unit wavelength", with units of W/m³, and "power per unit
wavelength" is equal to that intensity times the surface area, with units of W/m
131.5775
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. W/m
The energy density distribution function in terms of frequency for blackbody radiation is described by the
formula Planck derived, given as: p(v,T) =
c3 exp(hu/kT)-1
Specify what each of the parameters or variables (i.e. {h, c, k, v,T}) are called in this equation.
You may have to look this up, since we did not cover this in the lectures or book.
What is the dimension of h?
Sketch what this distribution function looks like as a function of v. You can do this with information given.
Chapter 3 Solutions
Modern Physics
Ch. 3.2 - Calculate the quantum number, n, for this pendulum...Ch. 3.2 - An object of mass m on a spring of stiffness k...Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8Q
Ch. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 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 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - As a single crystal is rotated in an x-ray...Ch. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Prior to Planck’s derivation of the distribution law for black-body radiation, Wien found empirically a closely related distribution function which is very nearly but not exactly in agreement with the experimental results, namely ρ(λ,T) = (a/λ5)e−b/λkT. This formula shows small deviations from Planck’s at long wavelengths. (a) Find a form of the Planck distribution which is appropriate for short wavelengths (Hint: consider the behaviour of the term ehc/λkT - 1 in this limit). (b) Compare your expression from (a) with Wien’s empirical formula and hence determine the constants a and b. (c) Integrate Wien’s empirical expression for ρ(λ,T) over all wavelengths and show that the result is consistent with the Stefan–Boltzmann law (Hint: to compute the integral use the substitution x = hc/λkT and then refer to the Resource section). (d) Show that Wien’s empirical expression is consistent with Wien’s law.arrow_forwardI need help with problem 4.12 (see picture). This problem involves gamma ray detectors. Problem 4.10: Calculate the amplitude of the voltage pulse produced by collecting a charge equal to that carried by 10^6 electrons on a capacitance of 100pF. (e=1.602x10^-19 C). Thank you.arrow_forwardHow fast should an electron move such that its kinetic energy is equal to the energy of a red photon (λ = 722 nm). For simplicity, express your answer as v x 105 m/s and type in just the value of v. Use three significant figures in your answer.arrow_forward
- Through what potential difference ΔVΔV must electrons be accelerated (from rest) so that they will have the same wavelength as an x-ray of wavelength 0.130 nmnm? Use 6.626×10−34 J⋅sJ⋅s for Planck's constant, 9.109×10−31 kgkg for the mass of an electron, and 1.602×10−19 CC for the charge on an electron. Express your answer using three significant figures. =89.0 V Through what potential difference ΔVΔV must electrons be accelerated so they will have the same energy as the x-ray in Part A? Use 6.626×10−34 J⋅sJ⋅s for Planck's constant, 3.00×108 m/sm/s for the speed of light in a vacuum, and 1.602×10−19 CC for the charge on an electron. Express your answer using three significant figures. Second question is what I need help on! Thanks!arrow_forwardDetermine lm , the wavelength at the peak of the Planck distribution, and the corresponding frequency ƒ, at these temperatures: (a) 3.00 K; (b) 300 K; (c) 3000 K.arrow_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_forward
- When an atom emits a photon in a transition from a state of energy E1 to a state of energy E2, the photon energy is not precisely equal to E1-E2. Conservation of momentum requires that the atom must recoil, and so some energy must go into recoil kinetic energy KR. Show that KR is roughly equal to (E1-E2)2/2Mc2, where M is the mass of the atom. Evaluate this recoil energy for the n=2 to n=1 transition of hydrogen.arrow_forwardElectrons are ejected from a metallic surface with speeds ranging up to 4.1 × 105 m/s when light with a wavelength of 630nm is used. What is the cutoff frequency for this surface? Express your answer in terms of 1014 Hz and round it to the nearest hundredth. For example, if you get 1.234 x 1014 Hz, you type in 1.23. (Hint: you should first calculate the work function of the surface.) Use h=6.626x1034 Js; c=3 x108 m/s. ; me=9.11x10-31kg Js; c=3 x108 m/s. ; me=9.11x1031kgarrow_forwardThe intensity of blackbody radiation peaks at a wavelength of 583 nm. (a) What is the temperature (in K) of the radiation source? (Give your answer to at least 3 significant figures.) K (b) Determine the power radiated per unit area (in W/m2) of the radiation source at this temperature. W/m?arrow_forward
- 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_forwardThe wavelength λmax at which the Planck distribution is a maximum can be found by solving dρ(λ,T)/dT = 0. Differentiate ρ(λ,T) with respect to T and show that the condition for the maximum can be expressed as xex − 5(ex − 1) = 0, where x = hc/λkT. There are no analytical solutions to this equation, but a numerical approach gives x = 4.965 as a solution. Use this result to confirm Wien’s law, that λmaxT is a constant, deduce an expression for the constant, and compare it to the value quoted in the text.arrow_forwardFind the de Broglie wavelength À for an electron moving at a speed of 1.00 × 106 m/s. (Note that this speed is low enough that the classical momentum formula p = mv is still valid.) Recall that the mass of an electron is me = 9.11 × 10-³1 kg, and Planck's constant is h = 6.626 × 10-34 J.s.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON