Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 3, Problem 6P
To determine
Validate the dimensions of the expressions calculate the values.
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4. In Section 1.3 we used dimensional analysis to show that the size of a
hydrogen atom can be understood by assuming that the electron in the
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of relativity, dimensional analysis gives an atomic size which is four orders
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Consider a relativistic, classical theory of an electron moving in the
Coulomb potential of a proton. Such a theory only involves three physical
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it is possible to construct a length from these three physical constants, but
show that it too small to characterize the size of the atom.
Imagine an alternate universe where the value of the Planck constant is
×6.62607·10−36Js
.
In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics?
object
quantum or classical?
A turtle with a mass of 560. g, 29. cm long, moving at 2.4 cm/s.
classical
quantum
An iceberg with a mass of 3.8 x 108 kg, 80. m wide, moving at 0.75 km/h.
classical
quantum
A mosquito with a mass of 1.2 mg, 11.4 mm long, moving at 2.5 m/s.
quantum
classical
A buckyball with a mass of 1.2 x 10-21 g, 0.7 nm wide, moving at 40. m/s.
classical
quantum
A person weighing 77 kg jogs at 1.5 m/s.
a) Calculate the momentum and wavelength of this person.
b) What is the uncertainty in determining his position at any given instant if we can measure his momentum to +- 0.05%?
c) Predict the changes that would take place in this problem if the Planck constant were 1 J s.
Chapter 3 Solutions
Modern Physics
Ch. 3.2 - Calculate the quantum number, n, for this pendulum...Ch. 3.2 - An object of mass m on a spring of stiffness k...Ch. 3 - Prob. 1QCh. 3 - Prob. 2QCh. 3 - Prob. 3QCh. 3 - Prob. 4QCh. 3 - Prob. 5QCh. 3 - Prob. 6QCh. 3 - Prob. 7QCh. 3 - Prob. 8Q
Ch. 3 - Prob. 9QCh. 3 - Prob. 10QCh. 3 - Prob. 11QCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - As a single crystal is rotated in an x-ray...Ch. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48P
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- Imagine another universe in which the value of Planck’s constant is 0.0663 J . s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 m apart, and one throws a 0.25 kg ball directly toward the other with a speed of 6.0 m/s. (a) What is the uncertainty in the ball’s horizontal momentum, in a direction perpendicular to that in which it is being thrown, if the student throwing the ball knows that it is located within a cube with volume 125 cm3 at the time she throws it? (b) By what horizontal distance could the ball miss the second student?arrow_forwardIn his classic 1940 book Mr. Tompkins in Wonderland, physicist George Gamow imagined a trip to a "quantum jungle" where the value of Planck's constant h was 1.0 J*s instead of its real value of 6.63 x 10-34 J*s. Imagine that while exploring in this quantum jungle, you disturb a community of bats residing in a ruined temple. Imagine that a "beam" of identical bats (each with a mass of 0.5 kilograms) flies at 6 meters per second through two temple doors 3 meters apart and into a flat, large courtyard beyond. If you are 30 meters from the doors, where could you stand in the courtyard to avoid being struck by any bats? (Hint: the answer is 1.6 meters, 4.9 meters, etc, to either side of the center line perpendicular to the doors)arrow_forwardImagine an alternate universe where the value of the Planck constant is 6.62607 x 10* J-s. In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? object quantum or classical? O classical An alpha particle with a mass of 6.6 x 10-27 kg, 8.0 x 10 15 m wide, moving at 18. km/s. O quantum O classical A mosquito with a mass of 2.0 mg, 10.8 mm long, moving at 2.1 m/s. O quantum O classical An iceberg with a mass of 3.6 x 108 kg, 200. m wide, moving at 0.44 km/h. O quantum O classical A turtle with a mass of 900. g, 30. cm long, moving at 2.3 cm/s. O quantumarrow_forward
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- 3. The equation 1.45 in our textbook says that the de Broglie wavelength as a function of temperature is given by 1 Assuming the accepted accuracy for h, R, and m are very high, what is the V3MRT maximum uncertainty in the de Broglie wavelength if AT is the uncertainty in temperature?arrow_forwardIn an advanced laboratory class a student performs the photoelectric experiment. Ultraviolet light is shone on a particular metal and the stopping potential is measured at the same time. It is found that 3.47 V is needed to stop all the electrons when the wavelength of the light is 270 nm, and 4.98 V for a wavelength of 213 nm. What is the work function of the metal? What is Planck's constant based on this measurement?arrow_forwardHow much time is needed to measure the kinetic energy of an electron whose speed is 10 m/s with an uncertainty of no more than 0.1 percent? Howarrow_forward
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