Determining Final Velocity of an Electron Absorbing an X-ray?

[gbaby370]

Hey, I was just wondering if someone could give me feedback on a problem. For some reason the answer is not in the back of the text.

Homework Statement

An x-ray with a wavelength of 2.5 x 10-8 m is absorbed by a stationary electron. Determine the final velocity of the electron.
Vxray=3.0x10^8 m/s
Velectron=0
melectron= 1.602x10^-19kg
mxray=(h/λc)
Velectron(after)=
h=6.626x10^-34Js
λ=2.5x10^-8

Homework Equations

Velectron(after)= Vxray((2(h/cλ))/(melectron+(h/cλ)))

The Attempt at a Solution

V(electronafter)= (3.0x10^8)((2((6.626x10^-34)/(3.0x10^8)(2.5x10^-8))/(1.602x10^-19)((6.626x10^-34)/(3.0x10^8)(2.5x10^-8)))

v(electronafter)= 3.31x10^-7m/s

Sorry if the formula is hard to understand, I used the formula for conservation of momentum in an elastic collision where one object is stationary before the collision.

 

[vela]

Your problem statement doesn't mention a proton. How does it come into the problem?

 

[gbaby370]

Sorry anywhere it says proton it should say electron.

 

[vela]

A solitary electron cannot absorb a photon. (Also if it did, it would be an inelastic collision, not an elastic collision.) If this problem is about the Compton effect, the photon scatters off the stationary electron.

Your value for the mass of the electron isn't correct.

 

[Nickie]

Hello,

First of all, great job on attempting to solve the problem! Your approach is correct, but there are a few errors in your calculations.

Firstly, in the formula for conservation of momentum, the mass of the electron should be in the denominator, not the numerator. So the formula should be V(electron after) = V(x-ray) * (2 * (h/(c*λ)) / (m(electron) + (h/(c*λ))).

Secondly, in your calculation, you have used the value for Planck's constant (h) in meters instead of joules. The correct value to use is 6.626 x 10^-34 J*s.

Lastly, when substituting the values into the formula, make sure to use the correct units. In this case, you should use meters for wavelength and kilograms for mass.

With these corrections, the final answer should be 5.17 x 10^7 m/s. I hope this helps! Keep up the good work.