- #1
freddie_mclair
- 43
- 2
Hi everyone!
So, I know that for a certain Synchrotron I have an output value of 1.5GeV/u for Uranium-238 particles, with a charged state of 28+ (## ^{238}U^{+28} ##). For this ion I would like to calculate the rest energy and the associated relativistic gamma factor. My approach was the following:
## E_0 = mc^2= (238 \cdot amu)c^2 = (238 \cdot 1.661\times 10^{-27})c^2 = 3.56 \times 10^{-8} J##
For eV units we just divide by the electron charge and get:
## E_0 = 3.56 \times 10^{-8} / e = 2.221 \times 10^{11} eV = 222.1 GeV##
## E_{total} = 1.5\times 238 = 357 GeV ##
##\gamma = E_{total}/E_0 = 357/222.1 = 1.607 ##
Do you think this is the right approach to do it?
What I'm not sure here is if the 1.5GeV/u is defining the total energy, or just the kinetic energy... Which would have an impact on the gamma factor.
What is more common to state in particle accelerators? Kinetic or total energy?
Thanks in advance! :)
So, I know that for a certain Synchrotron I have an output value of 1.5GeV/u for Uranium-238 particles, with a charged state of 28+ (## ^{238}U^{+28} ##). For this ion I would like to calculate the rest energy and the associated relativistic gamma factor. My approach was the following:
- Rest energy (ignoring the mass of electrons):
## E_0 = mc^2= (238 \cdot amu)c^2 = (238 \cdot 1.661\times 10^{-27})c^2 = 3.56 \times 10^{-8} J##
For eV units we just divide by the electron charge and get:
## E_0 = 3.56 \times 10^{-8} / e = 2.221 \times 10^{11} eV = 222.1 GeV##
- Total energy:
## E_{total} = 1.5\times 238 = 357 GeV ##
- Gamma factor:
##\gamma = E_{total}/E_0 = 357/222.1 = 1.607 ##
Do you think this is the right approach to do it?
What I'm not sure here is if the 1.5GeV/u is defining the total energy, or just the kinetic energy... Which would have an impact on the gamma factor.
What is more common to state in particle accelerators? Kinetic or total energy?
Thanks in advance! :)