Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 37: Q. 31 (page 1083)

The factor γappears in many relativistic expressions. A value γ=1.01implies that relativity changes the Newtonian values by approximately 1%and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is γ=1.01for

(a) an electron,

(b) a proton, and

(c) an alpha particle?

Short Answer

Expert verified

(a) The kinetic energy for an electron is Ek=5.12×103eV

(b) The kinetic energy for a proton is Ek==9.39×106eV

(c) The kinetic energy for an alpha particle is Ek=3.73×107eV

Step by step solution

01

Given Information

Kinetic energy according to relativity is given by γmc2-mc2=mc2(γ-1)=0.01mc2
Where c is the velocity of light in vacuum and is equal to .c=3×108

02

Part (a) Step 1 Calculation

For electron, m=9.1×10-31kg. So kinetic energy is,

Ek=0.01×9.1×10-31×3×1082=8.129×10-16J=5.12×103eV

03

Part (b) Step 1 Calculation

Mass of the proton is, m=1.67×10-27kg. So, kinetic energy is,

Ek=0.11.67×10-27×3×1082=1.50×10-12J=9.39×106eV

04

Part (c) Step 1 Calculation

The mass of the alpha particle is, m=6.64×10-27kg. So the kinetic energy is,

Ek=0.01×6.64×10-27×3×1082=5.98×10-12J=3.73×107eV

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The oxygen nucleus 16O has a radius of 3.0 fm.

a. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.

b. What is the proton’s kinetic energy in MeV?

Suppose that in a hypothetical oil-drop experiment you measure the following values for the charges on the drops:3.99×10-19C,6.65×10-19C,2.66×10-19C, 10.64×10-19C, and9.31×10-19C. What is the largest value of the fundamental unit of charge that is consistent with your measurements?

An alpha particle (a bare helium nucleus with q=+2e) accelerates across a 100Vpotential difference, starting from rest. What is the particle’s kinetic energy in eV when it reaches the negative electrode? This question requires no mathematics beyond what you can do in your head.

An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate electrodes that are 5.0mm apart. A 2.0mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is600V.

a. What is the electron’s speed?

b. If the potential difference between the plates is set to zero, what is the electron’s radius of curvature in the magnetic field?

The wavelengths in the hydrogen spectrum with m=1 form a series of spectral lines called the Lyman series. Calculate the wavelengths of the first four members of the Lyman series.
See all solutions

Recommended explanations on Physics Textbooks

Electric Charge Field and Potential

Read Explanation

Translational Dynamics

Read Explanation

Force

Read Explanation

Quantum Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Medical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free