The available energy ea when the proton and the antiproton have equal energies of 450gev is 29 GeV.
The available energy can be found out with the following formula.
[tex]E_a=\sqrt{2E_tE_k++(m_1c^2)^2+(m_2c^2)^2}[/tex]
Here C is the speed of light (3×10⁸ m/s), Et is the energy of proton, Ek is the rest energy.
A proton and an antiproton have equal energies of 450gev. The particles collide head-on. The rest energy of the proton is 938mev
Thus, put the given values in the above formula,
[tex]E_a=\sqrt{2(450\times\dfrac{10^9eV}{1MeV})(938\times\dfrac{10^6eV}{1MeV})+(938\times\dfrac{10^6eV}{1MeV})^2+(938\times\dfrac{10^6eV}{1MeV})}\\E_a=29\rm\; Gev[/tex]
Thus, the available energy ea when the proton and the antiproton have equal energies of 450gev is 29 GeV.
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