Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 3, Problem 13E
To determine
To Show: Planck’s formula in terms of wavelength
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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?
=
(a) A vacuum photocell is sequentially illuminated with light of different wavelengths 2. A
voltmeter is used to determine that there is a different voltage between the cathode and the
anode.
V
(iii) Determine a relation for Planck's constant in terms of pairs of voltage measurements at
different wavelengths such that W₁ cancels out.
(iv) Evaluate Planck's constant for the following pair of measurements:
measurement 1 finds = 447 nm and V=635 mV, and
measurement 2 finds = : 502 nm and V=339 mV.
For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2000 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and IP represent the corresponding intensity per unit wavelength according to the Planck expression.What is the ratio Ic/IP for a wavelength of (a) 400 nm (at the blue end of the visible spectrum) and (b) 200 mm (in the far infrared)? (c) Does the classical expression agree with the Planck expression in the shorter wavelength range or the longer wavelength range?
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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- For a black body, the temperature and the wavelength of the emission maximum, Amax, are related by Wein's Law, expressed as: T/°C λmax/nm Values of Amax from a small pinhole in an electrically heated container were determined at a series of temperatures. The results are given below. Deduce the value of Planck's constant. 1000 2181 c = 3.00 x 108 m/s 1500 1600 λmaxT = 2000 1240 k= 1.38 x 10-34 J-S hc 4.965k 2500 1035 3000 878 3500 763arrow_forward(1 A photocathode has a work function of 2.4 eV. The photocathode is illuminated with monochromatic radiation in which the photon energy is 3.5 eV. What is the wavelength of the illuminating radiation? Let1 eV= 1.60 x 10 19 J, the mass of an electron m=9.11 × 10 kg, the speed of light c= 3.00 x 10° m/s, and Planck's constant h=4.136 × 105 eV s. O 380 nm O 300 nm O410 nm 330 nm 350 nmarrow_forwardFor a temperature of 5800 K (the sun's surface temperature), find the wavelength for which the spectral distribution calculated by the Planck and Rayleigh-Jeans results differ by 5%. Hint: To match the required condition consider: IR-J = 1.05 Iarrow_forward
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