Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 36, Problem 20P
(a)
To determine
The proof that the de Broglie wavelengthis
(b)
To determine
The temperature needed to create a Bose condensate in
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What is the de Broglie wavelength of a nitrogen molecule in air at 300 K? Assume that the molecule is moving with the root-meansquare speed of molecules at this temperature. (Atomic mass of nitrogen = 14.0076 u)
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.
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.
Chapter 36 Solutions
Physics for Scientists and Engineers
Ch. 36 - Prob. 1PCh. 36 - Prob. 2PCh. 36 - Prob. 3PCh. 36 - Prob. 4PCh. 36 - Prob. 5PCh. 36 - Prob. 6PCh. 36 - Prob. 7PCh. 36 - Prob. 8PCh. 36 - Prob. 9PCh. 36 - Prob. 10P
Ch. 36 - Prob. 11PCh. 36 - Prob. 12PCh. 36 - Prob. 13PCh. 36 - Prob. 14PCh. 36 - Prob. 15PCh. 36 - Prob. 16PCh. 36 - Prob. 17PCh. 36 - Prob. 18PCh. 36 - Prob. 19PCh. 36 - Prob. 20PCh. 36 - Prob. 21PCh. 36 - Prob. 22PCh. 36 - Prob. 23PCh. 36 - Prob. 24PCh. 36 - Prob. 25PCh. 36 - Prob. 26PCh. 36 - Prob. 27PCh. 36 - Prob. 28PCh. 36 - Prob. 29PCh. 36 - Prob. 30PCh. 36 - Prob. 31PCh. 36 - Prob. 32PCh. 36 - Prob. 33PCh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75P
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- (b) How do you find the expression for the total number of different and distinguishable ways in which n number of particles can be distributed among the various energy levels in the case of Bose-Einstein distribution law? How it differs from the Maxwell- Boltzmann and Fermi-Dirac distribution laws? Justify the reasons of those differences.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_forwardPlank's spectral energy density distribution is given as a function of frequency (v) and Temperature (T), 8Th 3 u (v) = C3 hv ект - 1] c is the speed of light constant, h is the Plank constant, and k is the Boltzmann constant. v at umax determines the color of the radiating blackbody. Find v at umax in the form of a multiple of T.arrow_forward
- Compute λD and ND for the following cases: (a) A glow discharge, with n = 1016 m-3, KT, = 2 eV. (b) The earth's ionosphere, with n = 1012 m-3, KT, = 0.1 eV. (c) A ϴ-pinch, with n = 1023 rn-3, KT, = 800 eVarrow_forward1) The temperature of the absorber plate of a flat plate collector is 102 degrees * C and an be accepted as a black body. What percent of the radiant energy comes from this ate in the long wavelength band gap of 8 um to 11 um?arrow_forwardThe sun can be treated as a blackbody at 5780 K. Using EES (or other) software, calculate and plot the spectral blackbody emissive power Ebl of the sun versus wavelength in the range of 0.01 µm to 1000 µm. Discuss the results.arrow_forward
- The partition function of an ensemble at a temperature T is N Z = (2 cosh kgT where kg is the Boltzmann constant. The heat capacity of this ensemble at T = is X Nkg, where the value of X is %3D kB (up to two decimal places).arrow_forward-. (a) Find the de Broglie wavelength of a nitrogen molecule in air at room temperature (293 K). (b) The density of air at room temperature and atmospheric pressure is 1.292 kg/m³. Find the average distance between air molecules at this temperature and compare with the de Broglie wavelength. What do you conclude about the importance of quantum effects in air at room temper- ature? (c) Estimate the temperature at which quantum effects might become important.arrow_forwardFind the typical de Broglie wavelength associated with a He atom in helium gas at room temperature (27 °C) and 1 atm pressure; and compare it with the mean separation between two atoms under these conditions.arrow_forward
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