The Tevatron accelerator at the Fermi National Accelerator Laboratory (Fermilab) outside

Chicago boosts protons to 1TeV (1000GeV) in five stages (the numbers given in parentheses
represent the total kinetic energy at the end of each stage):Cockcroft-Walton (750keV), Linac
(400MeV), Booster (8GeV), Main ring or injector (150GeV), and finally the Tevatron itself
(1TeV).
What is the speed of the proton at the end of each stage?

To determine the speed of the proton at the end of each stage, we need to use the equation for kinetic energy:

KE = (1/2)mv^2

where KE is the kinetic energy, m is the mass of the proton, and v is the velocity of the proton.

Stage 1: Cockcroft-Walton (750 keV)

To convert kiloelectron volts (keV) to joules (J), we use the conversion factor 1 keV = 1.602 x 10^-16 J. Therefore, the kinetic energy at the end of this stage is 750 keV = 750 x 1.602 x 10^-16 J.

Next, we can rearrange the kinetic energy equation to solve for velocity:

v = √(2KE/m)

Since we know the mass of a proton is approximately 1.67 x 10^-27 kg, we can calculate the velocity.

Stage 2: Linac (400 MeV)

Again, we need to convert the kinetic energy from megaelectron volts (MeV) to joules (J). We use the conversion factor 1 MeV = 1.602 x 10^-13 J. So, the kinetic energy at this stage is 400 MeV = 400 x 1.602 x 10^-13 J.

Using the same velocity equation, we can calculate the velocity at this stage.

Stage 3: Booster (8 GeV)

Like before, we convert gigaelectron volts (GeV) to joules (J). The conversion factor is 1 GeV = 1.602 x 10^-10 J. Thus, the kinetic energy at this stage is 8 GeV = 8 x 1.602 x 10^-10 J.

Calculate the velocity using the kinetic energy equation.

Stage 4: Main ring or injector (150 GeV)

Convert the kinetic energy from gigaelectron volts (GeV) to joules (J). The kinetic energy becomes 150 GeV = 150 x 1.602 x 10^-10 J.

Use the kinetic energy equation to calculate the velocity.

Stage 5: Tevatron itself (1 TeV)

Convert the kinetic energy from teraelectron volts (TeV) to joules (J). The kinetic energy is 1 TeV = 1 x 10^12 eV = 1 x 10^12 x 1.602 x 10^-19 J.

Calculate the velocity using the kinetic energy equation.

By plugging in the appropriate values into the kinetic energy equation for each stage, you can determine the velocity of the proton at the end of each stage.