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

AI Thread Summary
To calculate the de Broglie wavelength of a proton moving at 1/4 the speed of light, the relevant equations include λ = h/p and p = γmv, where γ is the relativistic factor. The kinetic energy (KE) of the proton should be compared using both classical (1/2 mv^2) and relativistic (mc^2(γ - 1)) formulas. The discussion highlights the importance of considering relativistic effects due to the proton's significant speed relative to light. The relationship between kinetic energy and momentum is clarified, emphasizing that p^2/2m represents kinetic energy in terms of momentum. Understanding these concepts is crucial for accurately solving the problem.
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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