Question

A proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy. What is the TOTAL energy of the proton as measured by a physicist working with the accelerator? (c = 3.00 × 108 m/s, mproton = 1.67 × 10-27 kg)

Answer 1

Answer:

Total energy, $TE=3.006\times 10^{-10}\ J$

Explanation:

It is given that, a proton in a certain particle accelerator has a kinetic energy that is equal to its rest energy.  Let KE is the kinetic energy of the proton and E₀ is its rest energy. So,

$KE=E_o$              

The total energy of the proton is equal to the sun of kinetic energy and the rest mass energy.

$TE=KE+E_o$

$TE=2E_o$

$TE=2m_{proton}c^2$

$TE=2\times 1.67\times 10^{-27}\ kg\times (3\times 10^8\ m/s)^2$

$TE=3.006\times 10^{-10}\ J$

So, the total energy of the proton as measured by a physicist working with the accelerator is $3.006\times 10^{-10}\ J$