Question: Derive the expression for a de Broglie wavelength of a relativistic particle moving with kinetic energy T. At what values of T does the error

Derive the expression for a de Broglie wavelength λ of a relativistic particle moving with kinetic energy T. At what values of T does the error in determining λ using the non-relativistic formula not exceed 1 % for an electron and a proton?

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

For a relativistic particle Squaring Hence SO Tmc total energy cp m c TT2mc cp I... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

P-A-P-W-P (7).docx

120 KBs Word File

Students Have Also Explored These Related Atomic And Nuclear Physics Questions!

An electron has a de Broglie wavelength = 5.0 x 1010m. (a) What is its momentum? (b) What is its speed? (c) What voltage was needed to accelerate it to this speed?

An electron has a de Broglie wavelength of 2.80 X 10-10 m. Determine (a) The magnitude of its momentum and (b) Its kinetic energy (in joules and in electron volts).

An electron and a proton have the same kinetic energy and are moving at speeds much less than the speed of light. Concepts: (i) How is the de Broglie wavelength l related to the magnitude p of the...

(a) A non-relativistic free particle with mass m has kinetic energy K. Derive an expression for the de Broglie wavelength of the particle in terms of m and K. (b) What is the de Broglie wavelength of...

It is stated in the text that special relativity must be used to calculate the de Broglie wavelength of electrons in an electron microscope. Let us discover how much of an effect relativity has....

Consider a particle of mass m that can exist only between x = 0 m and x = +L on the x axis. We could say that this particle is confined to a box of length L. In this situation, imagine the standing...

Explain how the principles of quantum mechanics are able address the issues. The development of quantum mechanical theory stems from several issues that could not be addressed by the principles of...

Space science Assume that the magnetic field can be represented as a dipole in spherical coordinates given by: R 3 B1- : ZBO (i) cose (1) T BU a 3.12 x 105T 3 N . . 39 = 30 (E) sine (2) Re ~ 6370...

My Solar System Name Period Introductien: Every physics student has had a lot of experience with the force of gravity. Unfortunately, their experience is limited to the interaction between a very...

CHARGE TO MASS RATIO FOR THE ELECTRON OBJECTIVE: To measure the ratio of the charge of an electron to its mass. METHOD: A stream of electrons is accelerated by having them "fall" through a measured...

Suppose that you made some wine whose alcohol content was 10% w/v (i.e., 10 g of ethanol per 100 mL of wine). The initial fermentation mixture would have had to contain what molar concentration of...

Waterloo Wholesale Ltd. (WWL) is wholly owned by Barbara, a resident of Canada, who also owns all of the shares of Kitchener Closets Ltd. (KCL). Both corporations have a December 31 year-end. KKL had...

2.80 The probability of an automobile being filled with gasoline also needing an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and...

Presented below is the Governmental Funds Statement of Revenues, Expenditures, and Changes in Fund Balances for the Trinity Parish Fire District, a special-purpose entity engaged in a single...

The motor A accelerates uniformly from zero to 3600 rev/min in 8 seconds after it is turned on at time t = 0. It drives a fan (not shown) which is attached to drum B. The effective pulley radii are...

In problem use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms in Appendix III as needed. y'' + y = f(t), y(0) = 1, y'(0) = 0, where Appendix III...

Assume that Sarazan SA has a shareoption plan for top management. Each share option represents the right to purchase a R$1 par value ordinary share in the future at a price equal to the fair value of...

A fenced enclosure consists of a rectangle of length L and width 2R, and a semicircle of radius R, as shown in Figure P20. The enclosure is to be built to have an area A of 1600 ft 2 . The cost of...

A molten 50.0-kg quantity of gold at 1063 C is to be solidified without changing its temperature. What must be done?

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 52.2 degrees. Low Temperature ( OF) 40-44 45-49 50 -54 55-59 60-64 Frequency...

\ table [ [ , State of Nature ] , [ , Rezoning Approved,Rezoning Not Approved ] , [ Decision Alternative, s 1 , s 2