Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 35, Problem 20E
To determine
How big would
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Imagine 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?
classical
A raindrop with a mass of 2.0 mg, 6.7 mm wide, moving
at 6.9 m/s.
O quantum
O classical
A turtle with a mass of 530. g, 27. cm long, moving at 2.2
cm/s.
O quantum
O classical
A buckyball with a mass of 1.2 x 1021 g, 0.7 nm wide,
moving at 38. m/s.
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O classical
A human with a mass of 86. kg, 2.5 m high, moving at
3.0 m/s.
O quantum
Imagine an alternate universe where the value of the Planck constant is 6.62607 x 10
36
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?
classical
A raindrop with a mass of 2.0 mg, 6.7 mm wide, moving
at 6.9 m/s.
quantum
A turtle with a mass of 530. g, 27. cm long, moving at 2.2
classical
cm/s.
quantum
classical
A buckyball with a mass of 1.2 x 1021 g, 0.7 nm wide,
moving at 38. m/s.
quantum
classical
A human with a mass of 86. kg, 2.5 m high, moving at
3.0 m/s.
quantum
Imagine an alternate universe where the value of the Planck constant is 6.62607x10−17J·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?
A bacterium with a mass of 9.0 pg, 6.0 µm long, moving at 9.00 µm/s.
A mosquito with a mass of 2.3 mg, 6.0 mm long, moving at 3.0 m/s.
A paper airplane with a mass of 5.9 g, 295. mm long, moving at 3.7 m/s.
A car with a mass of 2000. kg, 4.4 m long, moving at 81.0 km/h.
Chapter 35 Solutions
Essential University Physics (3rd Edition)
Ch. 35.1 - Prob. 35.1GICh. 35.2 - Prob. 35.2GICh. 35.3 - Prob. 35.3GICh. 35.3 - Prob. 35.4GICh. 35.3 - Prob. 35.5GICh. 35.4 - Prob. 35.6GICh. 35 - Prob. 1FTDCh. 35 - Prob. 2FTDCh. 35 - Prob. 3FTDCh. 35 - Prob. 4FTD
Ch. 35 - Prob. 5FTDCh. 35 - Prob. 6FTDCh. 35 - Prob. 7FTDCh. 35 - What did Einstein mean by his re maxi, loosely...Ch. 35 - Prob. 9FTDCh. 35 - Prob. 10FTDCh. 35 - Prob. 12ECh. 35 - Prob. 13ECh. 35 - Prob. 14ECh. 35 - Prob. 15ECh. 35 - Prob. 16ECh. 35 - Prob. 17ECh. 35 - Prob. 18ECh. 35 - Prob. 19ECh. 35 - Prob. 20ECh. 35 - Prob. 21ECh. 35 - Prob. 22ECh. 35 - Prob. 23ECh. 35 - Prob. 24ECh. 35 - Prob. 25ECh. 35 - Prob. 26ECh. 35 - Prob. 27ECh. 35 - Prob. 28ECh. 35 - Prob. 29ECh. 35 - Prob. 30ECh. 35 - Prob. 31ECh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38PCh. 35 - Prob. 39PCh. 35 - Prob. 40PCh. 35 - Prob. 41PCh. 35 - Prob. 42PCh. 35 - Prob. 43PCh. 35 - Prob. 44PCh. 35 - Prob. 45PCh. 35 - Prob. 46PCh. 35 - Prob. 47PCh. 35 - Prob. 48PCh. 35 - Prob. 49PCh. 35 - Prob. 50PCh. 35 - Prob. 51PCh. 35 - Prob. 52PCh. 35 - Prob. 53PCh. 35 - Prob. 54PCh. 35 - Prob. 55PCh. 35 - Prob. 56PCh. 35 - Prob. 57PCh. 35 - Prob. 58PCh. 35 - Prob. 59PCh. 35 - Prob. 60PCh. 35 - Prob. 61PPCh. 35 - Prob. 62PPCh. 35 - Prob. 63PPCh. 35 - Prob. 64PP
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- Given this quantum state: ¥(r,0,0) = R(r)(√₂Y+Y¹-Y₂²), a) measured: |Z|² , find possible outcomes, corresponding probabilities and the average value b) repeat the same but instead with measured say Lz c) If you had first measured Lz to be planck's constant, and then measured |Z|² what can be said about the result of |Z|² ?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
- 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 quantumarrow_forward4. 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 atom is wave-like and non-relativistic. In this problem we show that, if we assume the electron in the atom is a classical electron described by the theory of relativity, dimensional analysis gives an atomic size which is four orders of magnitude too small. Consider a relativistic, classical theory of an electron moving in the Coulomb potential of a proton. Such a theory only involves three physical constants: m, /4mc9, and e, the maximum velocity in relativity. Show that 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.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 1.0J-s instead of its real value of 6.63 × 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 kg) flies at 6 m/s through two temple doors 3 m apart and into a flat, large courtyard beyond. Where could you stand in the courtyard to avoid being struck by any bats?arrow_forward
- : In class we did a problem where we saw that Planck’s law, which is given byI(λ, T) = 2πhc2λ5(ehc/λkbT − 1),at high wavelengths reduces to the classical predictionI(λ, T) = 2πckBTλ4.We did this by using the MacLaurin series for an exponential.1 + x +x22! +x33! +x44! + ...When we did this problem in class, we reasoned that,when the wavelength (λ) is large, the term hc/λkbTis small enough that any term (hc/λkbT)2 or (hc/λkbT)3 or any higher power is neglible. That’s how weshowed that, in the limit of large λ, Planck’s law reduces to the classical prediction. Now assume that wewant to make a slightly better approximation. We still assume that λ is large and therefore (hc/λkbT)3 and(hc/λkbT)4 and all higher powers are negligible, but now we want to work at the level of precision where(hc/λkbT)2is not negligible. What does Planck’s law reduce to in this case?arrow_forwardDetermine 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_forwardIn the LHC, protons are accelerated to a total energy of 7.80 TeV. The mass of proton is 1.673 × 10−27 kg and Planck’s constant is 6.626 × 10−34 J·s. In the reference frame of the protons, how long does it take the protons to go around the tunnel once? I know the answer is 10.8ns. The solutions posted on here, do not come within 1% of that answer so I cannot trust that the steps are correct. Please give step by step instructions on how to arrive at 10.8 nsarrow_forward
- 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_forwardA dust particle of 1.0 μm diameter and 10−15 kg mass is confined within a narrow box of 10.0 μm length. Planck’s constant is 6.626 × 10−34 J ∙ s. What is the range of possible velocities for this particle? What is the range of possible velocities for an electron confined to a region roughly the size of a hydrogen atom?arrow_forwardExplain why dimensional quantities (like Planck’s constant) can't be arguments of some functions like the exponential function e^h. Planck’s constant has units h: [kg][m]^2/[s]. Investigate e^h.arrow_forward
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