A particle accelerator called Large Hadron Collider can accelerate protons to 14 TeV (tetraelectonvolts) (1TeV = 10^12eV) of energy. What is the relativistic mass of a proton that has total energy of 14 TeV? (express your answer in MeV/c^2)

Would I use E= M-relativistic *c^2?
And then to solve for M-relativistic I would get this:
M-relativistic = E/c^2

Also to convert 14 TeV into MeV would I get 1.4 x10^7 MeV?

To calculate the relativistic mass of a proton given its total energy, you can indeed use the equation E = M-relativistic * c^2.

First, let's convert the energy of 14 TeV into MeV. Since 1 TeV = 10^12 eV, you are correct that 14 TeV would be equal to 14 x 10^12 eV. Now to convert it to MeV, we need to multiply by 10^6 because there are 10^6 MeV in 1 eV. So 14 x 10^12 eV becomes 14 x 10^12 x 10^6 = 1.4 x 10^19 MeV.

Now, we can use the equation M-relativistic = E / c^2 to calculate the relativistic mass. The speed of light, c, is approximately 3 x 10^8 m/s. Therefore, c^2 is approximately (3 x 10^8 m/s)^2 = 9 x 10^16 m^2/s^2.

Plugging in the values, we have M-relativistic = (1.4 x 10^19 MeV) / (9 x 10^16 m^2/s^2).

However, the unit for relativistic mass is typically expressed in MeV/c^2. To convert the result into MeV/c^2, we need to divide by c^2. So, dividing both the numerator and denominator by (9 x 10^16 m^2/s^2), we get:

M-relativistic = (1.4 x 10^19 MeV) / (9 x 10^16 m^2/s^2)
= (1.4 x 10^19 MeV / 9 x 10^16 m^2/s^2)
≈ 156 MeV/c^2.

Therefore, the relativistic mass of a proton with a total energy of 14 TeV is approximately 156 MeV/c^2.