Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
bartleby

Videos

Question
Book Icon
Chapter 26, Problem 92P
To determine

The kinetic energies (in the lab frame) of the neutron and pion after decay.

Expert Solution & Answer
Check Mark

Answer to Problem 92P

The kinetic energies (in the lab frame) of the neutron and pion after decay is 5.7MeV and kinetic energy pion after decay is 35.4MeV

Explanation of Solution

Write the equation for the relativistic energy of a particle.

  (pc)2=K2+2KE0        (I)

Here, p is the momentum of the particle, K is the kinetic energy of the particle, and  E0 is the rest energy of the particle.

Write the expression for the relativistic energy of a neutron.

  (pnc)2=Kn2+2KnE0n        (II)

Here, pn is the momentum of the neutron, Kn is the kinetic energy of the neutron, and  E0n is the rest energy of the neutron.

Write the expression for the relativistic energy of a neutron.

  (pπc)2=Kπ2+2KπE0π        (III)

Here, pπ is the momentum of the pion, Kπ is the kinetic energy of the pion, and  E0π is the rest energy of the pion.

Since lambda hyperon is at rest in the lab frame, by conservation of momentum pn=pπ .

Equate equation (II) and (III)

  Kn2+2KnE0n=Kπ2+2KπE0π        (IV)

Thus, total energy of the system is conserved. Apply conservation of energy for the decay process.

mΛc2=mnc2+mπc2+Kn+Kπ        (V)

Here, mΛ is the mass of the lambda hyperon, mn is the mass of neutron, mπ is the mass of the pion and c is the speed of light in vacuum.                   

Rearrange above equation to get Kn+Kπ

  (mΛmnmπ)c2=Kn+Kπ=K        (VI)

Here, K  is the total kinetic energy.

Rearrange the equation K=Kn+Kπ to get Kn

  Kn=KKπ        (VII)

Substitute (mΛmnmπ)c2 for K in expression (VII)                            Kn=(mΛmnmπ)c2Kπ        (VIII)

Substitute expression (VII) in expression (IV) and solve for Kπ.

    (KKπ)2+2(KKπ)E0n=Kπ2+2KπE0πK2+2KKπ+Kπ2+2KE0n=Kπ2+2KπE0π2Kπ(K+E0n+E0π)=K(K+2E0n)Kπ=K(K+2E0n)2(K+E0n+E0π)        (IX)

Substitute (mΛmnmπ)c2 for K, mnc2 for E0n, and mπc2 for E0π in expression (IX),

  Kπ=(mΛmnmπ)c2((mΛmnmπ)c2+2mnc2)2((mΛmnmπ)c2+mnc2+mπc2)        (X)

Conclusion:

Substitute the 1115.7MeV/c2 for mΛ939.6MeV/c2 for mn, 135.0MeV/c2 for mπ in expression (x)

  Kπ=(1115.7MeV/c2939.6MeV/c2135.0MeV/c2)c2((1115.7MeV/c2939.6MeV/c2135.0MeV/c2)c2+2(939.6MeV/c2)c2)2((1115.7MeV/c2939.6MeV/c2135.0MeV/c2)c2+(939.6MeV/c2)c2+(135.0MeV/c2)c2)=35.4MeV

Substitute the 1115.7MeV/c2 for mΛ939.6MeV/c2 for mn, 135.0MeV/c2 for mπ , and 35.4MeV for Kπ in expression (VII)

  Kn=(1115.7MeV/c2939.6MeV/c2135.0MeV/c2)c235.4MeV=5.7MeV

Therefore the kinetic energies (in the lab frame) of the neutron and pion after decay is 5.7MeV and kinetic energy pion after decay is 35.4MeV

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
When current is flowing through the coil, the direction of the torque can be thought of in two ways. Either as the result of the forces on current carrying wires, or as a magnetic dipole moment trying to line up with an external field (e.g. like a compass). Note: the magnetic moment of a coil points in the direction of the coil's magnetic field at the center of the coil. d) Forces: We can consider the left-most piece of the loop (labeled ○) as a short segment of straight wire carrying current directly out of the page at us. Similarly, we can consider the right-most piece of the loop (labeled ) as a short segment straight wire carrying current directly into the page, away from us. Add to the picture below the two forces due to the external magnetic field acting on these two segments. Then describe how these two forces give a torque and determine if the torque acts to rotate the loop clockwise or counterclockwise according to this picture? B
In each of the following, solve the problem stated. Express your answers in three significant figures. No unit is considered incorrect. 1. For the circuit shown, determine all the currents in each branch using Kirchhoff's Laws. (3 points) 6 5V 2 B C 4 A www 6 VT ww T10 V F E 2. Compute for the total power dissipation of the circuit in previous item. (1 point) 3. Use Maxwell's Mesh to find Ix and VAB for the circuit shown. (3 points) Ix 50 V 20 ww 21x B 4. Calculate all the currents in each branch using Maxwell's Mesh for the circuit shown. (3 points) www 5ი 10 24V 2A 2002 36V
If the mass of substance (1 kg), initial temperature (125˚C), the final temperature (175˚C) and the total volume of a closed container (1 m3) remains constant in two experiments, but one experiment is done with water ( ) and the other is done with nitrogen ( ). What is the difference in the change in pressure between water and nitrogen?

Chapter 26 Solutions

Physics

Ch. 26 - Prob. 1CQCh. 26 - Prob. 2CQCh. 26 - Prob. 3CQCh. 26 - Prob. 4CQCh. 26 - Prob. 5CQCh. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - Prob. 8CQCh. 26 - Prob. 9CQCh. 26 - Prob. 10CQCh. 26 - Prob. 11CQCh. 26 - Prob. 12CQCh. 26 - Prob. 1MCQCh. 26 - Prob. 2MCQCh. 26 - Prob. 3MCQCh. 26 - Prob. 4MCQCh. 26 - 5. Which best describes the proper time interval...Ch. 26 - Prob. 6MCQCh. 26 - Prob. 7MCQCh. 26 - Prob. 8MCQCh. 26 - Prob. 9MCQCh. 26 - Prob. 1PCh. 26 - Prob. 2PCh. 26 - Prob. 3PCh. 26 - Prob. 4PCh. 26 - Prob. 5PCh. 26 - Prob. 6PCh. 26 - Prob. 7PCh. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - Prob. 10PCh. 26 - Prob. 11PCh. 26 - Prob. 12PCh. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Prob. 15PCh. 26 - Prob. 16PCh. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - Prob. 21PCh. 26 - Prob. 22PCh. 26 - Prob. 23PCh. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Prob. 27PCh. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - Prob. 32PCh. 26 - Prob. 33PCh. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - Prob. 36PCh. 26 - Prob. 37PCh. 26 - Prob. 38PCh. 26 - Prob. 39PCh. 26 - 40. A white dwarf is a star that has exhausted its...Ch. 26 - Prob. 41PCh. 26 - Prob. 42PCh. 26 - Prob. 43PCh. 26 - Prob. 44PCh. 26 - Prob. 45PCh. 26 - Prob. 46PCh. 26 - Prob. 47PCh. 26 - Prob. 48PCh. 26 - Prob. 49PCh. 26 - Prob. 50PCh. 26 - Prob. 51PCh. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54PCh. 26 - Prob. 55PCh. 26 - Prob. 56PCh. 26 - Prob. 57PCh. 26 - Prob. 58PCh. 26 - Prob. 59PCh. 26 - Prob. 60PCh. 26 - Prob. 61PCh. 26 - Prob. 62PCh. 26 - Prob. 63PCh. 26 - Prob. 64PCh. 26 - Prob. 65PCh. 26 - Prob. 66PCh. 26 - Prob. 67PCh. 26 - Prob. 68PCh. 26 - Prob. 69PCh. 26 - 70. At the 10.0 km long Stanford Linear...Ch. 26 - Prob. 71PCh. 26 - Prob. 72PCh. 26 - Prob. 73PCh. 26 - Prob. 74PCh. 26 - Prob. 75PCh. 26 - Prob. 76PCh. 26 - Prob. 77PCh. 26 - Prob. 78PCh. 26 - Prob. 79PCh. 26 - Prob. 80PCh. 26 - Prob. 81PCh. 26 - Prob. 82PCh. 26 - Prob. 83PCh. 26 - Prob. 84PCh. 26 - Prob. 85PCh. 26 - Prob. 87PCh. 26 - Prob. 86PCh. 26 - Prob. 89PCh. 26 - Prob. 88PCh. 26 - Prob. 90PCh. 26 - Prob. 92PCh. 26 - Prob. 91PCh. 26 - Prob. 94PCh. 26 - Prob. 93PCh. 26 - 96. The solar energy arriving at the outer edge of...Ch. 26 - Prob. 96PCh. 26 - Prob. 97PCh. 26 - Prob. 98P
Knowledge Booster
Background pattern image
Physics
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
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781285737027
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Time Dilation - Einstein's Theory Of Relativity Explained!; Author: Science ABC;https://www.youtube.com/watch?v=yuD34tEpRFw;License: Standard YouTube License, CC-BY