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 4.4P
To determine
(a)
The proof that
To determine
(b)
The proof for
To determine
(c)
The evaluation for
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1.11 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.
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?
=
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 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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- In his original paper, de Broglie suggested that E = hv and p = h/λ, which hold for electromagnetic waves, are also valid for moving particles. Use these relationships to show that the group velocity ug of a de Broglie wave group is given by dE/dp, and with the help of Eq. (1.24), verify that vg = v for a particle of velocity v.arrow_forwardConsider 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/marrow_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
- 6.133 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_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_forwardThe root mean square speed of the hydrogen molecules at temperature t °C is given by 3x8.31 x (t+273) m 2 x 10-3 Calculate the de Broglie wavelength (in nanometers) of the hydrogen molecules at temperature 24 °C. The mass of the hydrogen molecule is 2 x 1.66 x 10-27 kg. Use two decimals in your answer.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_forwardCalculate the standard uncertainty in z if z=Xsinθ using the angle (45.00 ± 0.74) degrees and the value X = (23.60 ± 0.51) z = ___±___arrow_forwardLet a⪯b⪯c⪯da⪯b⪯c⪯d be the variable ordering.ϕ=ϕ= a&b&d&!c|a&c&d|d&!b&!c|!dβ=β= a&b&c|!c a) Convert the formula ϕϕ to Shannon normal form. b) Convert the formula ββ to Shannon normal form. c) ψψ is obtained by replacing all occurences of the variable b by formula ββ in formula ϕϕ.Compute the ROBDD of ψψ by the Compose algorithm, and convert the result to Shannon normal form.arrow_forward
- The radiant energy density (ρν) for the blackbody radiation is given by (see image below) where ρν dν is the energy per unit volume in the frequency range between ν and ν + dν.a) To exemplify and using ν = 3.5 x 1014 s-1, calculate density (concentration) spectral radiant excitation (in J m-2) as a function of frequency for the blackbody, a T=5776 K (the temperature of the sun).b)Plot the graph of spectral density versus frequency.arrow_forwardSuppose someone is running a fever of 102.0° F (average being 98.6° F). How much more power (in Watts) does this person radiate than when this person is at normal human body temperature, assuming the fever causes no swelling or edema, or emaciation? Remember that for thermal radiators, intensity I = sigma T^4; where sigma is the Stefan-Boltzmann constant and T is temperature in Kelvins.arrow_forward(a) Prove the "vertical angle hypothesis" (I. 15): opposing angles are congruent if two lines cut each other. (Hint: You'll need to use postulate 4 about right angles in this case.) ) (b) Complete the proof of the Exterior Angle Theorem using section (a): illustrate why beta < alphaarrow_forward
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