Answered: Calculate the minimum uncertainty in…

Calculate the minimum uncertainty in momentum (expressed in MeV/?) for a proton confined to a nucleus of diameter 5.0 fm. (1 fm = 1 * 10-15 m).

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...

See similar textbooks

Related questions

Q: If the position of an electron in a membrane is measured to an accuracy of 3.58 µm, what is the…

Q: (Hand by writing ans.)A certain atom has an energy level of 3.50 eV above the ground state. When…

A: If you know the frequency of the photon, you can calculate the wavelength using the equation…

Q: (a) The x-coordinate of an electron is measured with an uncertainty of 0.30 mm. What is the…

A: Part (a) Given: The uncertainty in position co-ordinate of electron is ∆x=0.30 mm. The minimum…

Q: The radii of atomic nuclei are of the order of 5.0 * 10-15 m. (a) Estimate the minimum uncertainty…

A: Part-a Given: Radii of atomic nuclei ∆x = 5×10-15 m.

Q: A pesky 1.5 mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m…

A: a) Using Heisenberg’s uncertainty principle, the width of the room is equal to the horizontal…

Q: A pesky 1.5 mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m…

A: (a) Maximum uncertainty in the horizontal position of the mosquito is equal to the room's width.…

Q: Imagine another universe in which the value of Planck’s con- stant is 0.0663 J s, but in which the…

A: Part-a Given: The value of the Planck's constant in the new universe h = 0.0663 Js. The mass of…

Q: By measuring the go-and-return time for a laser pulse to travel from an Earth-bound observatory to a…

Q: A nucleus emits a gamma ray of energy 1.2 MeV from a state that has a lifetime of 2.1 ns. What is…

A: In quantum mechanics, there are pairs of variables that are complementary or canonically conjugate.…

Q: (a) The x-coordinate of an electron is measured with an uncer- tainty of 0.30 mm. What is the…

A: This problem is based on the uncertainty principle. The mathematical form of the uncertainty…

Q: A proton is confined within an atomic nucleus of diameter 4 fm (1 fm = 10-15 m). Estimate the…

A: To determine: The uncertainty in the speed of a proton in a nucleus Given: Diameter of nucleus,…

Q: The position of a 1 g object moving in the x direction at 1 cm/s is known to within +/- 10 nm. In…

A: The momentum in the x direction is given by: px = mvx = 0.001 kg x 0.01 m/s = 0.00001 kg m/s

Q: An electron is confined to a region of space of the size of an atom (0.1 nm). (a) What is the…

A: The uncertainty in position of the electron is Now, the Heisenberg uncertainty principle we have:…

Q: 2.1. Find the de Broglie wavelength of the following particles: (i) an electron in a semiconductor…

A: (i). Given, Temperature, T=300K Effective mass, me*=am0m0=me The thermal velocity is given as,…

Q: 2.25 An electron moves with a constant velocity 1.1 x 10 m/s. If the velocity is measured to a…

A: We are aware that an electron travels at a constant speed 1.1×106 m/s. To find: Maximum precision

Q: A 10.0 g marble is gently placed on a horizontal tabletop that is 1.75 m wide. (a) What is the…

A: Part (a) Given: The mass of marble is m=10.0 g. The width of table is w=1.75 m. The maximum…

Q: A proton is known to be within an interval ±6 fm (the radius of a large nucleus). Roughly what is…

A: Given data: Position uncertainty ∆x=±6 fm

Q: Calcúlate the uncertainty for momentum p, when the mass of the object is 15.0 (+-) 0.2kg with a…

Q: Suppose the position of a chlorine ion in a membrane is measured to an accuracy of 0.75 μm. a) What…

Q: The velocity of an electron is measured to a precision of 62 × 10-³ m/s. What is the minimal…

A: Find uncertainty in position

Q: The speed of a proton is measured to within an uncertainty of 1 × 103m/s. Calculate the length of…

Q: An atom of iron has a radius of 156. pm and the average orbital speed of the electrons in it is…

A: The given data are: Δx=156 pm=156×10-12 mv=5.7×107 m/s

Q: A nucleon (proton or neutron) is confined to a region of space (the nucleus) approximately 10 fm…

Q: (a) The position of an electron is known to within 14.5 Å (1.45×10-9 m). What is the minimum…

Q: An atom is in an excited state for 4.00 us before moving back to the ground state. Find the…

Q: Lunar astronauts placed a series of cube reflectors on the Moon as part of an experiment to mea-…

Question

(a) Calculate the minimum uncertainty in momentum (expressed in MeV/?) for a proton confined to a nucleus of diameter 5.0 fm. (1 fm = 1 * 10^-15 m).

(b) A proton (rest mass 938.3 MeV/?²) in a nucleus of radius 6.0 fm has a kinetic energy of 5.6 MeV. If the proton were represented by a de Broglie wave, how many wavelengths could fit across the diameter of that nucleus? (1 fm = 1 * 10^-15 m).

(c) Electrons (rest mass 0.51 MeV/?²) moving with a speed of 1.60 × 10⁵ m/s are described by a wave packet of width 2.65 nm. What range of values will most likely result from a measurement of the speed of the electrons?

Please use:
ℎ? 1240 eVnm
ℏ? 197 eVnm

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

If the uncertainty in the y -component of a proton's position is 2.0 pm, find the minimum uncertainty in the simultaneous measurement of the proton's y -component of velocity. What is the minimum uncertainty in the simultaneous measurement of the proton's x -component of velocity?
A nucleus emits a gamma ray of energy 1.2 MeV from a state that has a lifetime of 2.1 ns. What is the uncertainty in the energy of the gamma ray? The best gamma-ray detectors can measure gamma-ray energies to a precision of no better than a few eV. Will this uncertainty be directly measurable?
2.1. Find the de Broglie wavelength of the following particles: (i) an electron in a semiconductor having average thermal velocity at T = 300 K and an effective mass of me = amo, where a is a constant, (ii) a helium atom having thermal energy at T = 300 K, (iii) an a-particle (He4 nucleus) of kinetic energy 10 MeV.
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?
Imagine another universe in which the value of Planck’s con- stant 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 phys- ics 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 per- pendicular 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 students?
(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.
An electron is confined to a region of space of the size of an atom (0.1 nm). (a) What is the uncertainty in the momentum of the electron? (b) What is the kinetic energy of an electron with a momentum equal to Ap? (c) Does this give a reasonable value for the kinetic energy of an electron in an atom?
The radii of atomic nuclei are of the order of 5.0 * 10-15 m. (a) Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. (b) Take this uncertainty in momentum to be an estimate of the mag- nitude of the momentum. Use the relativistic relationship between energy and momentum, Eq. (37.39), to obtain an estimate of the ki- netic energy of a proton confined within a nucleus. (c) For a proton to remain bound within a nucleus, what must the magnitude of the (negative) potential energy for a proton be within the nucleus? Give your answer in eV and in MeV. Compare to the potential energy for an electron in a hydrogen atom, which has a magnitude of a few tens of eV. (This shows why the interaction that binds the nucleus together is called the “strong nuclear force.”)
The speed of a proton is measured to within an uncertainty of 1 × 103m/s. Calculate the length of the smallest region of space in which the electron can be confined.
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?
Needs Complete typed solution with 100 % accuracy.
I need the answer as soon as possible