Question

In the LHC at CERN in Geneva, Switzerland, two beams of protons are accelerated to \(E=7\) TeV. The proton's rest mass is approximately \(m=1 \mathrm{GeV} / \mathrm{c}^{2} .\) When the two proton beams collide, what is the rest mass of the heaviest particle that can possibly be created? a) \(1 \mathrm{GeV} / \mathrm{c}^{2}\) b) \(2 \mathrm{GeV} / \mathrm{c}^{2}\) c) \(7 \mathrm{TeV} / \mathrm{c}^{2}\) d) \(14 \mathrm{TeV} / \mathrm{c}^{2}\)

Short answer

Answer: d) \(14 \mathrm{TeV} / \mathrm{c}^{2}\)

Step-by-step solution

Identify the collision energy

We know that each proton beam has an energy of \(E=7\text{ TeV}\). When they collide, the total energy available for creating new particles will be the sum of the energies of the two beams.

Calculate the total energy available for creating new particles

The total energy available is the sum of the energies of the two beams: $$ E_{total} = 2 \times E = 2 \times 7\text{ TeV} = 14\text{ TeV} $$

Convert the total energy to rest mass

Now we will convert the total energy to rest mass using the relation \(E=mc^2\). We divide the total energy by the speed of light squared to get the rest mass: $$ m_{new} = \frac{E_{total}}{c^2} = \frac{14\text{ TeV}}{\mathrm{c}^{2}} $$

Choose the correct answer

Comparing the expression for the rest mass of the heaviest possible particle with the given options, we find that the correct answer is: d) \(14 \mathrm{TeV} / \mathrm{c}^{2}\)