Creating Z_0 boson via symmetric beams a. Z0 boson has a rest mass energy of 91.187 GeV. It is produced in collisions of positrons and electrons.
e^- + e^+ to Z_0
How much kinetic energy must the positrons and electrons in symmetric colliding beams have to produce the Z0 boson? The rest mass energy for electrons and positrons is 0.511 MeV.
To find the kinetic energy required for the positrons and electrons in the colliding beams to produce the Z_0 boson, we can use the conservation of energy equation.
The rest mass energy of the Z_0 boson is given as 91.187 GeV (giga-electron volts). We need to convert this into the corresponding kinetic energy.
1 GeV = 1 billion electron volts (GeV = 1 x 10^9 eV)
1 electron volt = 1.602 x 10^-19 joules (eV = 1.602 x 10^-19 J)
So, the rest mass energy of the Z_0 boson can be converted as follows:
91.187 GeV = 91.187 x 10^9 eV
= 91.187 x 10^9 x 1.602 x 10^-19 J
= 147 x 10^-10 J
Now, let's analyze the conservation of energy in the electron-positron collision for the production of the Z_0 boson.
The initial energy in the system is the sum of the kinetic energy and rest mass energy of the electrons and positrons.
Initial energy = (Rest mass energy of electron + Kinetic energy of electron) + (Rest mass energy of positron + Kinetic energy of positron)
Given that the rest mass energy of an electron or positron is 0.511 MeV (mega-electron volts), we can convert it to joules:
0.511 MeV = 0.511 x 10^6 eV
= 0.511 x 10^6 x 1.602 x 10^-19 J
= 0.819 x 10^-13 J
Let the required kinetic energy of the electron and positron be KE.
Therefore, the initial energy is:
(2 x 0.819 x 10^-13 J) + (2 x KE) = 147 x 10^-10 J
2 times each of the rest mass energies is considered because there are two particles (electron and positron).
Simplifying the equation:
(1.638 x 10^-13 J) + (2 x KE) = 147 x 10^-10 J
(2 x KE) = (147 x 10^-10 J) - (1.638 x 10^-13 J)
(2 x KE) = (1.469 x 10^-9 J) - (1.638 x 10^-13 J)
(2 x KE) = 1.467362 x 10^-9 J
KE = (1.467362 x 10^-9 J) / 2
KE ≈ 7.337 x 10^-10 J
Therefore, the positrons and electrons in the symmetric colliding beams must have a total kinetic energy of approximately 7.337 x 10^-10 Joules to produce the Z_0 boson.