Finding Components of Recoiling Electron

[matpo39]

i am having a little bit of trouble with this problem

An x-ray photon of initial energy 1*10^5 eV traveling in the +x direction is incident on a free electron at rest. The photon is scattered at right angles into the +y direction. Find the components of the recoiling electron.


since we are given the initial energy i used the relation
$$E=\frac{hc}{\lambda}$$
to find lambda, i then used comptons equation
$$\lambda'-\lambda=\frac{h}{m_ec}(1-cos\theta) ; \theta=90$$

then using
$$P=E/C = 1*10^5 \frac{eV}{c} \hat{x}$$
$$\lambda'=\frac{h}{m_ec}+\lambda$$

where $$\lambda'$$ is the wavelength after the collision so

$$E'=\frac{hc}{\lambda'}$$

$$P'=\frac{E'}{c}=8.4*10^4 \hat{y}$$

since P_initial=P_final
P_initial= $$1*10^5\hat{x} +0\hat{y}$$

p_final=$$1*10^5\hat{x} + 8.4*10^4-8.4*10^4\hat{y}$$

therefor $$P_e= 1*10^5\hat{x} - 8.4*10^4\hat{y}$$

just wondering if this seems right, if not some help would be great thanks.

 

[anathema]

Hello, it seems like you have approached the problem correctly. The only thing I would suggest is to double check your calculations and units to ensure accuracy. Also, it would be helpful if you could provide the values you used for h and m_e in your equations. Overall, your solution looks reasonable and correct. Keep up the good work!

 

[quicknote]

Your approach and calculations seem correct. Just make sure to double check your units and conversions. Additionally, it would be helpful to include a brief explanation of the physical meaning behind each equation you used. Overall, great work!