EBK PHYSICS FOR SCIENTISTS AND ENGINEER
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
9th Edition
ISBN: 9780100460300
Author: SERWAY
Publisher: YUZU
bartleby

Videos

Textbook Question
Book Icon
Chapter 39, Problem 39.59P

The rest energy of an electron is 0.511 MeV. The rest energy of a proton is 938 MeV. Assume both particles have kinetic energies of 2.00 MeV. Find the speed of (a) the electron and (b) the proton. (c) By what factor does the speed of the electron exceed that of the proton? (d) Repeat the calculations in parts (a) through (c) assuming both particles have kinetic energies of 2 000 MeV.

(a)

Expert Solution
Check Mark
To determine
The speed of the electron.

Answer to Problem 39.59P

The speed of the electron is 0.979c .

Explanation of Solution

Given info: The kinetic energy of the electron and proton is 2.00MeV , the rest energy of the electron and proton are 0.511MeV and 938MeV respectively.

Formula to calculate the total energy of particle is,

E=γmc2 (1)

Formula to calculate the total energy of the particle is,

E=K+mc2 (2)

Here,

K is the kinetic energy.

m is the mass of particle.

c is the speed of the light in the vacuum.

E is the total energy of the particle.

Equate the equation (1) and equation (2).

γmc2=K+mc2γ=Kmc2+1 (3)

Formula to calculate the Lorentz factor is,

γ=11v2c2

Substitute 11v2c2 for γ in equation (3).

11v2c2=Kmc2+1

Rearrange the above equation for v ,

v=c[1(mc2K+mc2)2]1/2 (4)

Formula to calculate the rest energy of particle is,

ER=mc2

Substitute mc2 for ER in equation (4).

v=c[1(ERK+ER)2]1/2 (5)

The speed of the electron is,

velectron=c[1(ERK+ER)2]1/2 (6)

Here,

velectron is the speed of the electron.

Substitute 0.511MeV for ER , and 2.00MeV for K in equation (6) to find the velectron .

velectron=c[1(0.511MeV2.00MeV+0.511MeV)2]1/2=0.979c

Thus, the speed of the electron is 0.979c .

Conclusion:

Therefore, the speed of the electron is 0.979c .

(b)

Expert Solution
Check Mark
To determine
The speed of the proton.

Answer to Problem 39.59P

The speed of the proton is 0.0652c .

Explanation of Solution

Given info: The kinetic energy of the electron and proton is 2.00MeV , the rest energy of the electron and proton are 0.511MeV and 938MeV .

From equation (5), the speed of the particle is given as,

v=c[1(ERK+ER)2]1/2

The speed of the proton is,

vproton=c[1(ERK+ER)2]1/2

Here,

vproton is the speed of the proton.

Substitute 938MeV for ER , and 2.00MeV for K to find the vproton .

v=c[1(938MeV2.00MeV+938MeV)2]1/2=0.0652c

Thus, the speed of the proton is 0.0652c .

Conclusion:

Therefore, the speed of the proton is 0.0652c .

(c)

Expert Solution
Check Mark
To determine
The factor by which speed of electron exceed that of the proton.

Answer to Problem 39.59P

Answer The factor by which speed of electron exceed that of the proton is 15.0 .

Explanation of Solution

Given info: The kinetic energy of the electron and proton is 2.00MeV , the rest energy of the electron and proton are 0.511MeV and 938MeV .

The ratio of the speed of the electron and proton is,

ratio=velectronvproton

Substitute 0.0625c for vproton and 0.979c for velectron .

velectronvproton=0.979c0.0652cvelectronvproton=15.01velectron=15.01vprotonvelectron15vproton

Thus, the factor by which speed of electron exceed that of the proton is 15.0 .

Conclusion:

Therefore, the factor by which speed of electron exceed that of the proton is 15.0 .

(d)

Expert Solution
Check Mark
To determine
The speeds of the electron and proton and the factor by which speed of electron exceed that of the proton.

Answer to Problem 39.59P

The speeds of the electron and proton are 0.99999997c and 0.948c respectively and the factor by which speed of electron exceed that of the proton is 1.06 .

Explanation of Solution

Given info: The kinetic energy of the electron and proton is 2000MeV , the rest energy of the electron and proton are 0.511MeV and 938MeV .

The speed of the electron is,

velectron=c[1(ERK+ER)2]1/2 (7)

Substitute 0.511MeV for ER and 2000MeV for K in equation (7) to find the velectron .

velectron=c[1(0.511MeV2000MeV+0.511MeV)2]1/2=0.99999997c

The speed of the electron is,

vproton=c[1(ERK+ER)2] (8)

Substitute 938MeV for ER and 2000MeV for K in equation (8) to find the vproton .

vproton=c[1(938MeV2000MeV+938MeV)2]1/2=0.948c

The ratio of the speed of the electron and proton is,

ratio=velectronvproton (9)

Substitute 0.948c for vproton and 0.99999997c for velectron in equation (9).

velectronvproton=0.99999997c0.948cvelectronvproton=1.054velectron=1.0548vprotonvelectron1.06vproton

Thus, the speeds of the electron and proton are 0.99999997c and 0.948c respectively and the factor by which speed of electron exceed that of the proton is 1.06 .

Conclusion:

Therefore, the speeds of the electron and proton are 0.99999997c and 0.948c respectively and the factor by which speed of electron exceed that of the proton is 1.06 .

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
air is pushed steadily though a forced air pipe at a steady speed of 4.0 m/s. the pipe measures 56 cm by 22 cm. how fast will air move though a narrower portion of the pipe that is also rectangular and measures 32 cm by 22 cm
No chatgpt pls will upvote
13.87 ... Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another planet is by using a Hohmann transfer orbit (Fig. P13.87). If the orbits of the departure and destination planets are circular, the Hohmann transfer orbit is an elliptical orbit whose perihelion and aphelion are tangent to the orbits of the two planets. The rockets are fired briefly at the depar- ture planet to put the spacecraft into the transfer orbit; the spacecraft then coasts until it reaches the destination planet. The rockets are then fired again to put the spacecraft into the same orbit about the sun as the destination planet. (a) For a flight from earth to Mars, in what direction must the rockets be fired at the earth and at Mars: in the direction of motion, or opposite the direction of motion? What about for a flight from Mars to the earth? (b) How long does a one- way trip from the the earth to Mars take, between the firings of the rockets? (c) To reach Mars from the…

Chapter 39 Solutions

EBK PHYSICS FOR SCIENTISTS AND ENGINEER

Ch. 39 - A spacecraft zooms past the Earth with a constant...Ch. 39 - As a car heads down a highway traveling at a speed...Ch. 39 - A spacecraft built in the shape of a sphere moves...Ch. 39 - An astronaut is traveling in a spacecraft in outer...Ch. 39 - You measure the volume of a cube at rest to be V0....Ch. 39 - Two identical clocks are set side by side and...Ch. 39 - Prob. 39.8OQCh. 39 - Which of the following statements are fundamental...Ch. 39 - A distant astronomical object (a quasar) is moving...Ch. 39 - In several cases, a nearby star has been found to...Ch. 39 - Prob. 39.2CQCh. 39 - A train is approaching yon at very high speed as...Ch. 39 - List three ways our day-to-day lives would change...Ch. 39 - Prob. 39.5CQCh. 39 - Prob. 39.6CQCh. 39 - Prob. 39.7CQCh. 39 - Prob. 39.8CQCh. 39 - Give a physical argument that shows it is...Ch. 39 - Prob. 39.10CQCh. 39 - Prob. 39.11CQCh. 39 - (i) An object is plated at a position p f from a...Ch. 39 - With regard to reference frames, how does general...Ch. 39 - Two identical clocks are in the same house, one...Ch. 39 - The truck in Figure P39.1 is moving at a speed of...Ch. 39 - In a laboratory frame of reference, an observer...Ch. 39 - The speed of the Earth in its orbit is 29.8 km/s....Ch. 39 - Prob. 39.4PCh. 39 - Prob. 39.5PCh. 39 - A meterstick moving at 0.900c relative to the...Ch. 39 - Prob. 39.7PCh. 39 - A muon formed high in the Earths atmosphere is...Ch. 39 - How fast must a meterstick be moving if its length...Ch. 39 - An astronaut is traveling in a space vehicle...Ch. 39 - A physicist drives through a stop light. When he...Ch. 39 - A fellow astronaut passes by you in a spacecraft...Ch. 39 - A deep-space vehicle moves away from the Earth...Ch. 39 - For what value of does = 1.010 0? Observe that...Ch. 39 - A supertrain with a proper length of 100 m travels...Ch. 39 - The average lifetime of a pi meson in its own...Ch. 39 - An astronomer on the Earth observes a meteoroid in...Ch. 39 - A cube of steel has a volume of 1.00 cm3 and mass...Ch. 39 - A spacecraft with a proper length of 300 m passes...Ch. 39 - A spacecraft with a proper length of Lp passes by...Ch. 39 - A light source recedes from an observer with a...Ch. 39 - Review. In 1963, astronaut Gordon Cooper orbited...Ch. 39 - Police radar detects the speed of a car (Fig....Ch. 39 - The identical twins Speedo and Goslo join a...Ch. 39 - An atomic clock moves at 1 000 km/h for 1.00 h as...Ch. 39 - Prob. 39.26PCh. 39 - A red light flashes at position xR = 3.00 m and...Ch. 39 - Shannon observes two light pulses to be emitted...Ch. 39 - A moving rod is observed to have a length of =...Ch. 39 - A rod moving with a speed v along the horizontal...Ch. 39 - Keilah, in reference frame S, measures two events...Ch. 39 - Figure P38.21 shows a jet of material (at the...Ch. 39 - An enemy spacecraft moves away from the Earth at a...Ch. 39 - A spacecraft is launched from the surface of the...Ch. 39 - Prob. 39.35PCh. 39 - Calculate the momentum of an electron moving with...Ch. 39 - Prob. 39.37PCh. 39 - Prob. 39.38PCh. 39 - Prob. 39.39PCh. 39 - Prob. 39.40PCh. 39 - Prob. 39.41PCh. 39 - Prob. 39.42PCh. 39 - An unstable particle at rest spontaneously breaks...Ch. 39 - Prob. 39.44PCh. 39 - Prob. 39.45PCh. 39 - Protons in an accelerator at the Fermi National...Ch. 39 - A proton moves at 0.950c. Calculate its (a) rest...Ch. 39 - (a) Find the kinetic energy of a 78.0-kg...Ch. 39 - A proton in a high-energy accelerator moves with a...Ch. 39 - Prob. 39.50PCh. 39 - The total energy of a proton is twice its rest...Ch. 39 - Prob. 39.52PCh. 39 - When 1.00 g of hydrogen combines with 8.00 g of...Ch. 39 - In a nuclear power plain, the fuel rods last 3 yr...Ch. 39 - The power output of the Sun is 3.85 1026 W. By...Ch. 39 - Prob. 39.56PCh. 39 - Prob. 39.57PCh. 39 - Prob. 39.58PCh. 39 - The rest energy of an electron is 0.511 MeV. The...Ch. 39 - Prob. 39.60PCh. 39 - A pion at rest (m = 273me) decays to a muon (m =...Ch. 39 - An unstable particle with mass m = 3.34 1027 kg...Ch. 39 - Prob. 39.63PCh. 39 - Prob. 39.64PCh. 39 - Review. A global positioning system (GPS)...Ch. 39 - Prob. 39.66APCh. 39 - The net nuclear fusion reaction inside the Sun can...Ch. 39 - Prob. 39.68APCh. 39 - A Doppler weather radar station broadcasts a pulse...Ch. 39 - An object having mass 900 kg and traveling at...Ch. 39 - An astronaut wishes to visit the Andromeda galaxy,...Ch. 39 - A physics professor on the Earth gives an exam to...Ch. 39 - An interstellar space probe is launched from...Ch. 39 - Prob. 39.74APCh. 39 - Prob. 39.75APCh. 39 - An object disintegrates into two fragments. One...Ch. 39 - The cosmic rays of highest energy are protons that...Ch. 39 - Spacecraft I. containing students taking a physics...Ch. 39 - Review. Around the core of a nuclear reactor...Ch. 39 - The motion of a transparent medium influences the...Ch. 39 - Prob. 39.81APCh. 39 - Prob. 39.82APCh. 39 - An alien spaceship traveling at 0.600c toward the...Ch. 39 - Prob. 39.84APCh. 39 - Prob. 39.85APCh. 39 - An observer in a coasting spacecraft moves toward...Ch. 39 - Prob. 39.87APCh. 39 - A particle with electric charge q moves along a...Ch. 39 - Prob. 39.89CPCh. 39 - Suppose our Sun is about to explode. In an effort...Ch. 39 - Owen and Dina are at rest in frame S. which is...
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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
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
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
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
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
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