Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 10.1, Problem 10.1P
(a)
To determine
The impact parameter to the scattering angle.
(b)
To determine
The differential scattering cross-section.
(c)
To determine
The total cross-section for Rutherford scattering.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Explain the following
a. Is there any effect of the mass of nucleus on the scattering angle in Rutherford
experiment?
b. How can we use the formulas of expectation values for energy and momentum to extract their values? Explain.
c. Consider an electron moving in a circle of radius r (first level) about a proton, Determine the magnetic dipole moment of an electron.
d. Is there any variation in probability density as a function of distance from the nucleus in
hydrogen atom? Explain.
Assuming that the radius of the circular path of the electron is 4.9cm when voltage is 100v and coil current is 1A and The Helmholtz coils have 130 turns and a radius of 15 cm. With N=130 and R=0.15
What is the velocity of the electrons at 100 V, assuming the known charge and mass of the electron from the accepted universal constants that are the basis of SI units?
Hints: Do a classical calculation of the kinetic of the electon assuming you know its mass (in kg) and its charge (in coulomb). That will be 1/2 mv2. Equate that to the energy of the electron gained by accelerating in the electric field, that is, eV where "e" is the charge and "V" is the difference potential in volts. Solve for "v", the velocity.
Enter your answer in km/s, 103 m/s, without units. It is best to enter only a number, without an "e". For example, if you found 2000 m/s you would enter "2" for the velocity in km/s. Electrons have low mass and achieve high velocity in modest fields.
Calculate the integral section of the Rutherford scattering.
Knowledge Booster
Similar questions
- A one-dimensional infinite potential well has a length of 2L. a) What are the energy eigenvalues? b) Calculate the ground state energy if ten protons are confined in the box. Assume that the protons don’t interact with each other. c) If the ten protons are replaced by ten neutral hydrogen atoms, what is the total ground state energy resulting from the confinement? Again, assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.arrow_forwardA one-dimensional infinite potential well has a length of 2L. What are the energy eigenvalues? Calculate the ground state energy if ten protons are confined in the box. Assume that the protons don’t interact with each other. If the ten protons are replaced by ten neutral hydrogen atoms, what is the total ground state energy resulting from the confinement? Again, assume that the hydrogen atoms do not interact with each other. You can treat the mass of proton and hydrogen atom to be identical.arrow_forwardIn an alpha particle (42He) scattering experiment, using a thin gold (19779Au) foil, the initial kinetic energy of the alpha particle is 2.0MeV. What is the potential energy of the alpha particle/gold nucleus system at closest impact?arrow_forward
- Consider a model of an electron as a hollow sphere with radius R and the electron charge -e spread uniformly over that surface. a. Calculate the electric field inside and outside of the sphere. b. Calculate the electric potential that creates this field, and has a zero value at infinity. c. Calculate the work required to create this electron. d. Use Einstein’s equation relating rest mass to energy to derive a value for R. Unfortunately, your answer will be model-dependent. The traditional “Classical radius of the electron” is derived by setting the electrostatic work to be e2/(4pi e0 R)arrow_forwardShow that the kinetic energy of a nonrelativistic particle can be written in terms of its momentum as KE = p2/2m. (b) Use the results of part (a) to find the minimum kinetic energy of a proton confined within a nucleus having a diameter of 1.0 x 10-15 m.arrow_forwardProve that the equation provided in the first image is an energy eigenfunction for the hydrogen atom with the appropriate eigenvalue. (Hint: See the provided Example 6.3)arrow_forward
- In a Millikan oil-drop experiment using a setup like that as shown, a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?arrow_forwardIn a Millikan oil-drop experiment using a setup like that in Figure below, a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere withthe density of olive oil?arrow_forwardIn an alpha particle (42He) scattering experiment, using a thin gold (19779Au) foil, the initial kinetic energy of the alpha particle is 2.0MeV.(a.) What is the potential energy of the alpha particle/gold nucleus system at closest impact?(b.) Calculate the distance of closest approach. Compare this distance with the radius of the gold nucleus.arrow_forward
- a) What are the cherenkov angles for electrons and pions of 1000 MeV/c in a medium with n =1.4? b) What is the quotient of the number of photons radiated by electrons and incident pions?arrow_forwardA.The probability of finding a particle in an infinite potential well is always maximum at the midpoint of the boundaries B.Sketch schematically the graphs of intensity of radiation verses wavelength from a blackbody at two different increasing temperatures of the body, indicating the characteristic features of this emission. C .Show that at long wavelengths, Planck’s radiation law reduces to the Rayleigh–Jeans law. Answer allarrow_forwardShow that the hydrostatic equation and gradient Richardson number are dimentionless.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning