Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 3, Problem 15E
To determine
To Derive: The Stefan- Boltzmann law.
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A neutron of mass 1.675 × 10-27 kg has a de Broglie wavelength of 7.8x10-12 m. What is the kinetic energy (in eV) of this non-relativistic neutron? Please give your answer with two decimal places.
1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s.
A blackbody (a hollow sphere whose inside is black) emits radiation when it is heated. The emittance (Mλ, W/m3), which is the power per unit area per wavelength, at a given temperature (T, K) and wavelength (λ, m) is given by the Planck distribution, where h is Planck's constant, c is the speed of light, and k is Boltzmann's constant.
Determine the temperature in degrees Celsius at which a blackbody will emit light of wavelength 3.57 μm with an Mλ of 5.31×1010 W/m3.
The power per unit area emitted can be determined by integrating Mλ between two wavelengths, λ1 and λ2. However, for narrow wavelength ranges (Δλ), the power emitted can be simply calculated as the product of Mλ and Δλ.
power emitted=MλΔλ
Using the conditions from the first part of the question, determine the power emitted per square meter (W/m2) between the wavelengths 3.56 μm and 3.58 μm.
In an experiment on the photoelectric effect, a metal is illuminated by visible light of different
wavelengths. A photoelectron has a maximum kinetic energy of 0.9 eV when red light of
wavelength 640 nm is used. With blue light of wavelength 420 nm, the maximum kinetic energy
of the photoelectron is 1.9 eV. Use this information to calculate an experimental value
for the Planck constant h.
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Chapter 3 Solutions
Modern Physics
Ch. 3 - Prob. 1CQCh. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Prob. 7CQCh. 3 - A ball rebounds elastically from the floor. What...Ch. 3 - Prob. 9CQCh. 3 - Prob. 10CQ
Ch. 3 - Prob. 11ECh. 3 - Prob. 12ECh. 3 - Prob. 13ECh. 3 - Prob. 14ECh. 3 - Prob. 15ECh. 3 - Prob. 16ECh. 3 - Prob. 17ECh. 3 - What is the stopping potential when 250 nm...Ch. 3 - Prob. 19ECh. 3 - Prob. 20ECh. 3 - Prob. 21ECh. 3 - Prob. 22ECh. 3 - Prob. 23ECh. 3 - Prob. 24ECh. 3 - Prob. 25ECh. 3 - Prob. 26ECh. 3 - Prob. 27ECh. 3 - Prob. 28ECh. 3 - Prob. 29ECh. 3 - Prob. 30ECh. 3 - Prob. 31ECh. 3 - Prob. 32ECh. 3 - Prob. 33ECh. 3 - Prob. 34ECh. 3 - Prob. 35ECh. 3 - Prob. 36ECh. 3 - Verify that the Chapter 2 formula KE=mc2 applies...Ch. 3 - Prob. 38ECh. 3 - Prob. 39ECh. 3 - Prob. 40ECh. 3 - Prob. 41ECh. 3 - Prob. 42ECh. 3 - Prob. 43ECh. 3 - Prob. 44ECh. 3 - Prob. 45ECh. 3 - Prob. 46ECh. 3 - Prob. 47CECh. 3 - Prob. 49CECh. 3 - Prob. 50CECh. 3 - Prob. 51CECh. 3 - Prob. 52CECh. 3 - Prob. 53CECh. 3 - Prob. 54CECh. 3 - Prob. 55CE
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- A photon in a laboratory experiment has an energy of 4.2 eV. What is the frequency of this photon? Planck’s constant is 6.63 × 10−34 J · s. Answer in units of Hz.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_forwardThe unit surface of a black body at 37 °C radiates a number of electromagnetic waves with a certain wavelength. If the Wien constant is 2.898 x 10^-3 m.k, then the wavelength at which the blackbody radiation density per unit length has a maximum value isarrow_forward
- A) Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one six hundredth of the speed of light (c/600). Enter at least 4 significant figures. (I got the answer 949.4 pm but it is wrong, please help) B) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 230.1 pm.arrow_forwardProblem-1: An asteroid is hurtling toward earth at 150,000“. The temperature of the asteroid is about 100 K, meaning that its peak emission is 2 = 29 µm. The speed of light is c = 3E[8]. a) What is the wavelength of light that we receive from the asteroid? (Answer: 2.89855E[-05] m)arrow_forwardThe intensity of blackbody radiation peaks at a wavelength of 613 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/m?) of the radiation source at this temperature. W/m2arrow_forward
- 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? =arrow_forwardCalculate the de Broglie wavelength of proton, if it is moving with speed of 2 × 105 m/s. Mass of proton (m) = 1.67 x 10-27 kg. Planck's × constant = 6.625 × 10-34 Js.arrow_forwardA certain shade of blue has a frequency of 7.33×1014 Hz. What is the energy ? of exactly one photon of this light? Planck's constant ℎ=6.626×10−34 J⋅s.arrow_forward
- Describe a typical nuclear fusion process with a neat sketch. Calculate the de Broglie wavelength of an electron having a mass of 9.11 x 10-31 kg with a Kinetic energy of 90 eV. The value of the Planck's constant is equal to 6.63 * 10-34 Js and 1 eV is equal to 1.602 x 10-19 J. How Raman scattering occurs?arrow_forwardA dust particle of 1.0 μm diameter and 10−15 kg mass is confined within a narrow box of 10.0 μm length. Planck’s constant is 6.626 × 10−34 J ∙ s. What is the range of possible velocities for this particle? What is the range of possible velocities for an electron confined to a region roughly the size of a hydrogen atom?arrow_forwardPrior 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_forward
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