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 4.3P
To determine
(a)
The proof for
To determine
(b)
The expression for Planck's constant in terms of frequency and its sketch at a fixed temperature.
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In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 225 nm is used and 1.5 V is needed for light of
wavelength 207 nm.
From these data determine Planck's constant. (Enter your answer, in eV s, to at least four significant figures.)
4.2367e-15 X ev s
From these data determine the work function (in eV) of the metal.
4.6
X ev
The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon:
8AsiVsphere
Msphere = 2h
13
ст-а?
The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the
bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure
constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon
(+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are
exactly eight atoms per unit cell in the sphere.
Compute the relative uncertainty of myphere- To find the uncertainty of l, use the function y = x“, for which the uncertainty
is propagated using %e, = a(%e,).
relative uncertainty of msphere:
%
The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice (
mdefects = 3.8…
(b)
What is the de Broglie wavelength (in m) of a neutron moving at a speed of 2.49 ✕ 108 m/s?
Note that the neutron is moving very close to the speed of light in this case. Therefore, we cannot use the non-relativistic approximation for momentum. What is the relativistic relationship between momentum and speed? What is the gamma factor? m
(1.59E-15 is not the correct answer)
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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- 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_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_forwardThe energy emitted by a black body's surface per unit area at a particul ar wavelength can be calcul ated using Planck's Radiation Law, which can be written as follows, 2nhc? E(2, T) = 25. (ehc/kT -1) where his Planck's constant 6.626 x 10-27 erg.s, c is the speed oflight, kis the Boltzmann constant = 1.38 x 10-18 erg/K, Tis the temperature in Kelvins and A is the wavelength in um. If E is given in erg/um?, what are the units of the constant 2n, given that the equation is valid and therefore dimensionally homogenous? If the speed of light is 3.00x10$ m/s, what value and unit should be used for c in this equation to maintain dimensional homogeneity? Note: erg is a unit of energy equal to 10-7 Joules and the whole expression (ehc/AkT – 1) ends up dimensionless. -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_forwardFor 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?arrow_forwardRadiation has been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature, at what wavelength does the Planck distribution peak? In what part of the elec- tromagnetic spectrum is this wavelength?arrow_forward
- 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.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 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_forward
- Determine 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_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(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.arrow_forward
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