(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 μm , what is the electron’s minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are theimplications of this energy, comparing it to typical molecular binding energies?

(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 μm , what is the electron’s minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are theimplications of this energy, comparing it to typical molecular binding energies?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 34P: If the uncertainty in the y -component of a proton's position is 2.0 pm, find the minimum...

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(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 µm , what is the electron’s minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?
(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 µm , what is its minimum uncertainty in velocity, given its mass is 5.86×10-26 kg ? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?
(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 μm, what is its minimum uncertainty in velocity, given its mass is 5.86 X 10-26 kg? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?
If the position of an electron in a membrane is measured to an accuracy of 3.58 µm, what is the electron's minimum uncertainty in velocity (in m/s)? a) If the electron has this velocity, what is its kinetic energy in eV? b) What are the implications of this energy, comparing it to typical molecular binding energies?
By measuring the go-and-return time for a laser pulse to travel from an Earth-bound observatory to a reflector on the Moon, it is possible to measure the separation between these bodies. (a) What is the predicted value of this time? (b) The separation can be measured to a precision of about 15 cm. To what uncertainty in travel time does this correspond? (c) If the laser beam forms a spot on the Moon 3 km in diameter, what is the angular divergence of the beam?
Consider the problem of using laser light to measure the distance from the Earth to the moon. (a) What is the maximum uncertainty in timing the round trip for a light pulse in order to determine the distance with an uncertainty of 1 meter? (b) Estimate the effect of the Earth’s atmosphere on this experiment, using the fact that the speed of light in air (at sea level) is slower than the speed of light in vacuum by a factor of 1.0003. Assume an 8-km-high atmosphere of uniform sea-level density.
Suppose the position of a chlorine ion in a membrane is measured to an accuracy of 0.75 μm. a) What is its minimum uncertainty in velocity in meters per second, given its mass is 5.86 × 10-26 kg? b) If the ion is measured to have a velocity of 8.9 × 103 m/s, what is the uncertainty in its kinetic energy in electron volts?
A 10.0 g marble is gently placed on a horizontal tabletop that is 1.75 m wide. (a) What is the maximum uncertainty in the horizon- tal position of the marble? (b) According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the horizontal velocity of the marble? (c) In light of your answer to part (b), what is the longest time the marble could remain on the table? Compare this time to the age of the universe, which is approximately 14 billion years. (Hint: Can you know that the horizontal velocity of the marble is exactly zero?)
(a) The x-coordinate of an electron is measured with an uncer- tainty of 0.30 mm. What is the x-component of the electron’s velocity, vx, if the minimum percent uncertainty in a simultaneous measurement of vx is 1.0%? (b) Repeat part (a) for a proton.
A 10.0 g marble is gently placed on a horizontal tabletop that is 1.75 m wide. (a) What is the maximum uncertainty in the horizontal position of the marble? (b) According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the horizontal velocity of the marble? (c) In light of your answer to part (b), what is the longest time the marble could remain on the table? Compare this time to the age of the universe, which is approximately 14 billion years.
A rectangular piece of aluminum is 7.60 ± 0.01 cm longand 1.90 ± 0.01 cm wide. Verify that the fractional uncertainty in the area is equal to the sum of the fractional uncertainties in the length and in the width.
(a) The position of an electron is known to within 14.5 Å (1.45×10-9 m). What is the minimum uncertainty in its velocity?(b) Repeat the calculation of part (a) for a helium atom.