What Is the Kinetic Energy of a Proton at 1/4 the Speed of Light?

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Homework Help Overview

The discussion centers around calculating the de Broglie wavelength of a proton moving at 1/4 the speed of light and comparing its kinetic energy to the expression p²/2m. Participants explore the implications of using classical versus relativistic mechanics in this context.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the de Broglie wavelength and its calculation, questioning how to find kinetic energy and whether classical or relativistic formulas should be applied. There is uncertainty about the meaning of p²/2m and its relation to kinetic energy.

Discussion Status

Some participants have offered insights into the need for relativistic considerations and have pointed out the relationship between momentum and kinetic energy. Multiple interpretations of the kinetic energy equations are being explored, but no consensus has been reached.

Contextual Notes

There is mention of the relativistic mass and the need to consider the relativistic factor γ, indicating that assumptions about classical mechanics may need to be revisited. The original poster expresses confusion about the relationship between kinetic energy and momentum in the context of relativistic speeds.

FlorenceC
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Homework Statement


Calculate the deBroglie wavelength of a proton moving at 1/4 the speed of light.

How does the kinetic energy of this proton compare to its p^2 /2m?

What does p^2 / 2m anyway conceptually (isn't it one of the triangle thingies in the lower version of E=mc^2)?

Homework Equations


deBroglie equation

The Attempt at a Solution


hf = KE + phi
lambda = h/mv
v = 0.25c, m = proton
that calculates lambda
then lambda = c/f to find frequency ...but i don't know how to find KE. (is it just 1/2mv^2?)
 
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##\frac{P^2}{2m}## is nothing but the kinetic energy in terms of momentum right?
I'm not sure but since they've given velocity to be in terms of "speed of light" don't you think you should consider the relativistic mass?
 
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Your equation hf = KE + phi is the photoelectric effect equation.

The de Broglie wavelength, λd = h/p, where as Suraj says you need to insert the relativistic momentum of a proton p = γmv. Where γ is the ubiquitous relativistic factor. Try this and if you get what I'm saying let me know.
 
FlorenceC said:

Homework Statement


Calculate the deBroglie wavelength of a proton moving at 1/4 the speed of light.

How does the kinetic energy of this proton compare to its p^2 /2m?

What does p^2 / 2m anyway conceptually (isn't it one of the triangle thingies in the lower version of E=mc^2)?

Homework Equations


deBroglie equation

The Attempt at a Solution


hf = KE + phi
lambda = h/mv
v = 0.25c, m = proton
that calculates lambda
then lambda = c/f to find frequency ...but i don't know how to find KE. (is it just 1/2mv^2?)

FlorenceC said:

Homework Statement


Calculate the deBroglie wavelength of a proton moving at 1/4 the speed of light.

How does the kinetic energy of this proton compare to its p^2 /2m?

What does p^2 / 2m anyway conceptually (isn't it one of the triangle thingies in the lower version of E=mc^2)?

Homework Equations


deBroglie equation

The Attempt at a Solution


hf = KE + phi
lambda = h/mv
v = 0.25c, m = proton
that calculates lambda
then lambda = c/f to find frequency ...but i don't know how to find KE. (is it just 1/2mv^2?)
I think you are being asked to compare classical kinetic energy ##(1/2) m v^2## with relativistic kinetic energy ##m c^2 (\gamma - 1)##, where ##\gamma = 1/\sqrt{1-(v/c)^2}##.
 

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