Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 4, Problem 50E
To determine
The proof that the angle at which the first diffraction minimum would be found is proportional to angle at which the particle would likely be deflected and the proportionality factor is pure independent of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
When an aperture's diameter matches the wavelength of the waves being diffracted, the effects of diffraction become noticeable. (A) At what speed would a 75-kg student's de Broglie wavelength be the same as a doorway's 0.76-m width? (b) How long will it take the student to traverse 5.0 millimeters at current speed? (In contrast, the universe is thought to have existed for about 4 * 1017 seconds.)
A highly collimated (parallel) beam of electrons is shot through a single slit of width 17.5μm. The electrons are moving with a speed of 7.357.35km/s. When they hit the screen, located at distance 1.57m away, the distribution of hitting positions makes a pattern with a central peak and minima on either side. What is the width of the central peak (equivalently, distance between the minima on either side)?
The mass of an electron is 9.11×10^−31 kg.
Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted. (a) At what speed will the de Broglie wavelength of a 65-kg student be equal to the 0.76-m width of a doorway? (b) At this speed, how much time will it take the student to travel a distance of 1.0 mm? (For comparison, the age of the universe is approximately 4 * 10^17 s.)
Chapter 4 Solutions
Modern Physics
Ch. 4 - Prob. 1CQCh. 4 - Prob. 2CQCh. 4 - Prob. 3CQCh. 4 - Prob. 4CQCh. 4 - Prob. 5CQCh. 4 - Prob. 6CQCh. 4 - Prob. 7CQCh. 4 - Prob. 8CQCh. 4 - Prob. 9CQCh. 4 - Prob. 10CQ
Ch. 4 - Prob. 11ECh. 4 - Analyzing crystal diffraction is intimately tied...Ch. 4 - The setup depicted in Figure 4.6 is used in a...Ch. 4 - Prob. 14ECh. 4 - Prob. 15ECh. 4 - Prob. 16ECh. 4 - Prob. 17ECh. 4 - Prob. 18ECh. 4 - Prob. 19ECh. 4 - Prob. 20ECh. 4 - Prob. 21ECh. 4 - Prob. 22ECh. 4 - Prob. 23ECh. 4 - Prob. 24ECh. 4 - Prob. 25ECh. 4 - Prob. 26ECh. 4 - Prob. 27ECh. 4 - Prob. 28ECh. 4 - Prob. 29ECh. 4 - Prob. 30ECh. 4 - Prob. 31ECh. 4 - Prob. 32ECh. 4 - Prob. 33ECh. 4 - Prob. 34ECh. 4 - Prob. 35ECh. 4 - Prob. 36ECh. 4 - Prob. 37ECh. 4 - (a) Experiment X is carried out nine times...Ch. 4 - Prob. 39ECh. 4 - Prob. 40ECh. 4 - Prob. 41ECh. 4 - Prob. 42ECh. 4 - Prob. 43ECh. 4 - Prob. 44ECh. 4 - Prob. 45ECh. 4 - Prob. 46ECh. 4 - Prob. 47ECh. 4 - Prob. 48ECh. 4 - Prob. 49ECh. 4 - Prob. 50ECh. 4 - Prob. 51ECh. 4 - Prob. 52ECh. 4 - Prob. 53ECh. 4 - Prob. 54ECh. 4 - Prob. 55ECh. 4 - Prob. 56ECh. 4 - Prob. 57ECh. 4 - Prob. 59ECh. 4 - Prob. 60ECh. 4 - Prob. 61ECh. 4 - Prob. 62ECh. 4 - Prob. 63ECh. 4 - Prob. 64ECh. 4 - Prob. 65ECh. 4 - Prob. 67ECh. 4 - Prob. 68ECh. 4 - Prob. 71CECh. 4 - Prob. 72CECh. 4 - Prob. 73CE
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
- A beam of electrons is accelerated from rest through a potential difference of 0.100 kV and then passes through a thin slit. When viewed far from the slit, the diffracted beam shows its first diffraction minima at+-14.6° from the original direction of the beam. (a) Do we need to use relativity formulas? How do you know? (b) How wide is the slit?arrow_forwardA highly collimated (parallel) beam of electrons is shot through a single slit of width 18.6μm. The electrons are moving with a speed of 6.24 km/s. When they hit the screen, located at distance 1.99m away, the distribution of hitting positions makes a pattern with a central peak and minima on either side. What is the width of the central peak (equivalently, distance between the minima on either side)?arrow_forwardConsider a photon, being produced in a reaction, that interacts with an electron (initially at rest) in a Compton scattering-like event. The photon goes off at an angle of 30° from its initial direction. The scattered electron eventually enters a double slit experimental setup placed far from it. The screen behind the slits is placed unit meter away from the two slits which are a um apart. (a) If the experiment observes the first maximum 1cm apart on the screen, what wavelength of photons are being produced in the reaction. (b) Can this photon ionize a hydrogen atom in its ground state?arrow_forward
- An electron emitted in the beta decay of bismuth-210 has a mean kinetic energy of 390 keV. (a) Find the de Broglie wavelength of the electron. (b) Would such an electron be useful in a Davisson-Germer type scattering experiment? Address this question by determining the angle at which a fi rst-order diffraction maximum would be found using the same nickel target as Davisson and Germer.arrow_forward(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 eVnmℏ? 197 eVnmarrow_forwardQuestion 2: A beam of electrons with kinetic energy K, is incident on a single slit of width a. After passing through the slit, the beam strikes a screen where it is made visible. At the center of the screen directly in front of the slit, the intensity of the pattern on the screen is I₁. If the kinetic energy of the beam is increased (keeping the slit width and the number of electrons per second constant), does the intensity of the pattern at the center of the screen increase, decrease, or remain the same? EXPLAIN YOUR ANSWER.arrow_forward
- Consider a photon, being produced in a reaction, that interacts with an electron (initially at rest) in a Compton scattering-like event. The photon goes off at an angle of 30 degrees from its initial direction. The scattered electron eventually enters a double slit experimental setup placed far from it. The screen behind the slits is placed unit meter away from the two slits which are a μm apart. (a) If the experiment observes the first maximum 1cm apart on the screen, what wavelength of photons are being produced in the reaction. (b) Can this photon ionize a hydrogen atom in its ground state?arrow_forwardYou are interested in investigating the atomic structure of a sample with a beam of electrons. The atomic structure has a characteristic size of 0.100 nm. Knowing that the observable detail of the atomic struture is limited to about the wavelength of the probe (electrons, in this case), to what speed should you accelerate the electrons in the beam? You may assume the electrons speed is non relativistic. Hint: de Brogile matter waves!arrow_forwardIf the speed of a proton is measured to be 2.9 × 105 m/s with a precision of 0.70% then what is the maximum precision with which its position could be measured, Ax? How does this uncertainty compare to the size of the proton?arrow_forward
- Please answer question e only, thank you. An electron beam is accelerated across a potential difference and on a thinfilm containing crystal fragments that are randomly oriented. The apparatusis like the one we used in the experiment we analyzed this semester, exceptthat the circular ring images are formed on a flat screen, rather than on thesurface of a spherical bulb. All the crystal fragments have the sameinteratomic spacing, dnkl = 0.160 nm. (a) If the accelerating potential difference is 2.8 kV, calculate the electron kinetic energy in eV units.(b) Use the result from (a) to find the electron momentum in Ns units.(c) Use the result from (b) to find the electron wavelength in nm units.(d) Calculate the diffraction angle for the first two orders of Bragg diffraction. Do not use the small angle approximation.(e) The phosphor screen that displays the circular rings is flat and located 22 cm from where the electron beam interacts with the crystal fragments. Calculate the diameters of…arrow_forwardAssuming that the smallest measurable wavelength in an experiment is 0.990 fm (femtometers), what is the maximum mass of an object traveling at 269 m/s for which the de-Broglie wavelength is observable?arrow_forwardConsidering the double slit experiment for electrons, (a) explain why we can observe an interference/diffraction pattern if we place a detector (able to detect where the electron arrives) on a bulkhead located at a certain distance from the slits. (b) from the Heisenberg indeterminacy principle, explain why this pattern disappears if we also put a detector on one of the slits (discovering through which slit the electron passed).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning