Calculate the recoil momentum and kinetic energy of the atom

[tauristar]

Homework Statement

Suppose an atom of iron at rest emits an X-ray photon of energy 6.4 keV. Calculate the “recoil” momentum and kinetic energy of the atom. (Hint: Do you expect to need classical or relativistic kinetic energy for the atom? Is the kinetic energy likely to be much smaller than the atom’s rest energy?)

Homework Equations

Where E is the energy of the photon (in this case 6.4 KeV), Ei is the initial energy of the atom (I believe it is zero), Ef is the final energy of the atom and K is the "recoil" kinetic energy of the atom.
E = (Ei − Ef) − K

The Attempt at a Solution

Since the atom starts at rest Ei =0 and so I get
6.4 Kev=(0-Ef)-K
6.4 Kev = -Ef-K

Not sure where to go from here

 

[PietKuip]

Hint: Read the question. The problem starts with asking about the momentum.

 

[tauristar]

Hint: Read the question. The problem starts with asking about the momentum.

I tried going that route using P=E/c so P=6.4 kev/c now what...?

 

[PietKuip]

So you know the momentum of the atom. Why not try to calculate its velocity?

 

[tauristar]

So you know the momentum of the atom. Why not try to calculate its velocity?

Not sure what to use. pc/E=v/c --> v=pc^2/E so then v= (6.4 kev/c)c^2/(6.4 kev) --> v=c I feel like I'm going around in circles I have no clue what to do and I've been working on this for two days I just don't get this stuff. I feel like I'm missing a big piece of the puzzle and I just don't know where to find it.

 

[PietKuip]

I repeat my hint: read the question. Consider classical mechanics.

 

[tauristar]

I repeat my hint: read the question. Consider classical mechanics.

classical mechanics Ki+Ui=Kf-Uf so (1/2) m vi^2 + mgyi = (1/2) m vf^2 + mgyf
initial Ki=0 the Ui and Uf are zero so that doesn't leave me with anything useful

 

[PietKuip]

Ok, go back one step: you know the momentum of the atom. Why not calculate its velocity? (That is what I wrote in message #4.)

 

[tauristar]

Ok, go back one step: you know the momentum of the atom. Why not calculate its velocity? (That is what I wrote in message #4.)

I got v=c

 

[mfb]

You are overthinking this. Forget energy. What is the momentum of a particle in classical mechanics?

 

[tauristar]

You are overthinking this. Forget energy. What is the momentum of a particle in classical mechanics?

p=mv
if I plug in what i found for p then I get v= 6.88e28 eV/kg

 

[tauristar]

You are overthinking this. Forget energy. What is the momentum of a particle in classical mechanics?

6.4 keV = 9.3E-26 kg v
v= (6.4 keV)/(9.3E-26 kg) = 6.88E28 ev/kg

 

[mfb]

6.4 keV is not the momentum.

 

[tauristar]

6.4 keV is not the momentum.

I thought it was p=E/c and E (energy of the photon) is 6.4 keV which would give me p=6.4 keV/c

 

[PietKuip]

So convert to SI units. Or imperial, or whatever you prefer.

 

[tauristar]

So convert to SI units. Or imperial, or whatever you prefer.

(6400 eV/c)(c/1eV)(5.34e-28 kg m/s)= 3.42e-24 kg m /s

 

[PietKuip]

(6400 eV/c)(c/1eV)(5.34e-28 kg m/s)= 3.42e-24 kg m /s

Correct. I usually let Google handle unit conversions: https://www.google.se/webhp?q=6400+eV/c+=

Now what is the velocity of the iron atom?

 

[tauristar]

Correct. I usually let Google handle unit conversions: https://www.google.se/webhp?q=6400+eV/c+=

Now what is the velocity of the iron atom?

I can't seem to find that information out

 

[mfb]

You know p=mv.

You know p=3.42e-24 kg m /s
You know m.

What is v?

 

[tauristar]

so the velocity is (3.42e-24 kg m /s)(1/9.27e-27)= 36.7 m/s

I know i close but not sure how to finish it off

oh i just need to convert!

 

[mfb]

Correct.

Now you can calculate the recoil energy as you have mass and velocity.

You can edit your posts if you want to add something.