EBK PHYSICS FOR SCIENTISTS & ENGINEERS
5th Edition
ISBN: 9780134296074
Author: GIANCOLI
Publisher: VST
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Chapter 37, Problem 7P
(a)
To determine
Planck’s
(b)
To determine
The value of the
(c)
To determine
To know about
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(b)
(i) Calculate the de Broglie wavelength of an electron having a mass
of 9.11 x 1031 kg and a charge of 1.602 x 10-19 J with a Kinetic
energy of 135 eV. The value of the Planck's constant is equal to
6.63 * 10-34 Js.
(ii) Assume that an electron is moving along the x-axis with a speed
of 3.66 x 106 m/s and with a precision of 0.50%. Calculate the
minimum uncertainty (as allowed by the uncertainty principle in
quantum theory) with which the position of the electron along the
X-axis simultaneously can be measured with the speed?
Planck's radiation law can be written
ux
=
8лhc 1
25 eßhc/2-1
Show that the wavelength corresponding to the maximum energy density of the
radiation fulfills the condition
λmax T
=
.
constant
What is this constant? (This result is known as Wien's transition law.) Tip: you can
solve the constant approximation by e.g. iterating an equation of the form
Xn = 5 (1-e¯Xn-1)
with a suitable initial value x1.
(b) Calculate the de Broglie wavelength of an electron having a mass of 9.11
x 10-31 kg and a charge of 1.602 x 10-19 J with a Kinetic energy of 110 eV.
The value of the Planck’s constant is equal to 6.63 * 10-34 Js.
Chapter 37 Solutions
EBK PHYSICS FOR SCIENTISTS & ENGINEERS
Ch. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4QCh. 37 - Prob. 5QCh. 37 - Prob. 6QCh. 37 - Prob. 7QCh. 37 - Prob. 8QCh. 37 - Prob. 9QCh. 37 - Prob. 10Q
Ch. 37 - Prob. 11QCh. 37 - Prob. 12QCh. 37 - Prob. 13QCh. 37 - Prob. 14QCh. 37 - Prob. 15QCh. 37 - Prob. 16QCh. 37 - Prob. 17QCh. 37 - Prob. 18QCh. 37 - Prob. 19QCh. 37 - Prob. 20QCh. 37 - Prob. 1PCh. 37 - Prob. 3PCh. 37 - Prob. 7PCh. 37 - Prob. 9PCh. 37 - Prob. 13PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 32PCh. 37 - Prob. 34PCh. 37 - Prob. 37PCh. 37 - Prob. 45PCh. 37 - Prob. 52PCh. 37 - Prob. 76GPCh. 37 - Prob. 77GP
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- Show that Planck’s constant has the dimensions of angular momentum.arrow_forwardShow that Wien’s displacement law results from Planck’s radiation law. (Him: substitute x=hckT and write Planck’s law in the form I(x,T)=Ax5(ex1) , where A=2( kT)5(h4c3). Now, for fixed T, find the position of the maximum in I(x,T) by solving for x in the equation dI(x,T)dx=0.arrow_forward(b) A sodium vapor lamp is placed at the center of a large sphere that absorbs all the light reaching it. The rate at which the lamp emits energy is 80 W; assume that the emission is entirely at a wavelength of 380 nm. Evaluate the rate at which the photon is absorbed by the lamp. Take, Planck Constant h = 6.63 x 10-34 J.S Speed of light c = 3.00 x 108m/sarrow_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_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_forward8πhy3 dv (a) Express the Planck radiation formula, Edv = c3 ehv/kT-1' terms of λ (and dλ), namely Edλ. (b) Solved=0 for λ = Amax in to determine the value of maxT in m-K, where max is the wavelength at which the blackbody spectrum has its maximum value at a given temperature T.arrow_forward
- Planck's principal assumption was that the energies of the electronic oscillators can have only the values &n=nhv and that Aε = hv. (a) Further assume that the number of oscillators with the energy En, Nn, is proportional to e-En/kT at the temperature T, namely Nn xe-En/kT, where N is the total number of oscillators. Show N that the average energy per oscillator is ɛ̃ = formula, Edv = formula as v → 0. ΣNnEn N c3 ehv/kT-1' = (b) As v→ 0, then Aɛ → 0 and & is essentially continuous. Hence, we should expect the non-classical Planck distribution to go over to the classical Rayleigh-Jeans distribution at low frequencies, where Ac→ 0. Show that the Planck radiation 8πhy3 dv reduces to the Rayleigh-Jeans hv ehv/kT-1arrow_forwardNotation: (i) A vector is denoted by a bold letter, e.g., E(1) is a time-dependent vector. (ii) A unit vector is identified by a ^ sign, e.g., â, is a unit vector along the z-axis. Physical constants: Planck's constant, h = 6.626 × 10-34 m² kg s-I Boltzmann's constant, k = 1.38 × 10-23 m² kg s-² K-' Speed of light in vacuum, c = 3 × 10% m s-! Permittivity of vacuum, & = 8.854 × 10-12 F/m Permeability of vacuum, flo=4r × 10-’ H/m Electron charge, q = 1.602 ×10-19 C EEE/ELEC2347/ page 2 of 6 1. (a) As shown in Fig. la, the object and the screen is separated by l = 100cm. When we put a convex lens in the middle point between the object and the screen, a clear image is formed on the screen. What is the focal length of the lens? You may use either ABCD matrix or other methods. 100cm Fig. laarrow_forward(b) A/ The work function of a certain metal is o = 4.15 eV. Determine the minimum frequency of light for which photoelectrons are emitted from the metal. (Planck's constant is: h = 4.1357x10^-15 eV s.) (c) B/ Determine the corresponding wavelength of light. (Possibly useful constant: hc = 1240 eVnm.) Correction: the work function is = 5.30 eV; (a) C/ Calculate the kinetic energy of the emitted electrons if the frequency of the photons is doubled.arrow_forward
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