How Much Energy Does a Gamma Particle Have After Electron-Positron Annihilation?

[Ethan_Tab]

Homework Statement

Fluorine-18 is an isotope of fluorine often used in positron emission tomography, as it undergoes beta negative decay.

1. a) Determine the decay equation for fluorine-18.
2. b) If the positron emitted collides with an electron, it annihilates the electron and emits 2 gamma particles in the opposite direction. Determine the energy that one gamma particle has as a result of this collision. m(electron/positron) = 0.000549 u

Homework Equations

E=mc^2

The Attempt at a Solution

1) ¹⁸₉F---->¹⁸₈O+e^-1

2) I am not too sure about this one. I am assuming it has something to do with e=mc^2 but I'm not sure how to approach it

 

[SteamKing]

Homework Statement

Fluorine-18 is an isotope of fluorine often used in positron emission tomography, as it undergoes beta negative decay.

1. a) Determine the decay equation for fluorine-18.
2. b) If the positron emitted collides with an electron, it annihilates the electron and emits 2 gamma particles in the opposite direction. Determine the energy that one gamma particle has as a result of this collision. m(electron/positron) = 0.000549 u

Homework Equations

E=mc^2

The Attempt at a Solution

1) ¹⁸₉F---->¹⁸₈O+e^-1

2) I am not too sure about this one. I am assuming it has something to do with e=mc^2 but I'm not sure how to approach it

There's a couple of inconsistencies in the stated problem and your solution:

1) If fluorine-18 is used in PET, shouldn't it give off beta+ particles (positrons) instead of beta- particles (electrons)?

2) This is not how a beta decay reaction works:

¹⁸₉F---->¹⁸₈O+e^-1​

http://en.wikipedia.org/wiki/Beta_decay