Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Question
Chapter 38, Problem 5P
To determine
The precision for measuring the electron speed.
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Students have asked these similar questions
(I) A proton is traveling with a speed of
(8.660 ± 0.012) × 10° m/s. With what maximum precision
can its position be ascertained? [Hint: Ap = m Av.]
(I) Suppose the wave function for an electron at time t = 0 is given by (x,0) = /2/L sin(57x/L).
Which one of the following is the wave function at time t?
(a) p(x, t) =
Vž sin(57x/L) cos(Est/h)
(b) p(x, t) =
Vž sin(57x/L)e-iEst/h
(c) Both (a) and (b) above are appropriate ways to write the wave function.
(d) None of the above.
(II) The wave function for an electron at timet =0 is given by (x,0) = /? sin(57x/L). Which one of
the following is true about the probability density, |p(x, t)², after time t?
(a) [h(x, t)* = { sin²(57x/L) cos²(Est/h).
(b) |Þ(x, t)P = Z sin?(57x/L)e¬i2Est/h.
(c) |Þ(x,t)[² = } sin (57x/L) which is time-independent.
(d) None of the above.
4
(c) A proton confined in a one dimensional box emits a 2.0 MeV gamma-ray photon in a quantum jump
from n = 2 to n = 1. What is the length of the box? The mass of a proton is 1.67 x 1027 kg.
Chapter 38 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
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- (ii) A beam of electrons is incident on a barrier 5 eV high and 0.5 nm wide. Find the energy they should have if 1% of them are to get through the barrier.arrow_forward(i) Is an electron a particle? Is it a wave? Explain your answer citing relevant experimental evidence. Calculate the De-Broglie wavelength of an electron having a kinetic energy of 1000eV. Compare the result with wavelength of X-rays having the same energy.arrow_forwardIf a proton has an uncertainty in its velocity of 5.90 × 10⁻⁴ m/s, what is the uncertainty (in meters) in its position?arrow_forward
- (10) i) Use the quantum mechanical kinetic energy operator T, = to find the kinetic energy of the first 2m dx? excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE = p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you obtained in part ii) is correct.arrow_forward(II) Show that the energy E (in electron volts) of a photon whose wavelength is A (nm) is given by 1.240 x 10° eV·nm E = λ (nm) Use at least 4 significant figures for values of h, c, e (see inside front cover).arrow_forward(3) In order to study the atomic nucleus, we would like to observe the diffraction of particles whose de Broglie wavelength is about the same size as the nuclear diameter, about 14 fm for a heavy nucleus such as lead. What kinetic energy should we use if the diffracted particles are (a) electrons? (b) Neutrons? (c) Alpha particles (m = 4 u)?arrow_forward
- If the speed of a proton is measured to be 2.9 × 105 m/s with a precision of 0.70% then what is the maximum precision with which its position could be measured, Ax? How does this uncertainty compare to the size of the proton?arrow_forward(i) Compare stimulated and spontaneous emission. What is the significance of Einstein's coefficients? (ii) Calculate the frequency difference between resonant longitudinal 20th mode and 21th mode, if the cavity length is 20 cm.arrow_forwardAn unknown moving ion is confined in a OD nanomaterial in which all three dimensions are equals to 5 nm. Estimate with what accuracy its velocity and energy can be measured (given mass of the ion is 4.8×10 26 kg)?arrow_forward
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