The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is\[{\rm{1}}{{\rm{0}}^{{\rm{14}}}}{\rm{ GeV/}}{{\rm{c}}^{\rm{2}}}\]. (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity γ would have to be.)

Charged particles, such as protons or electrons, are propelled at high speeds near the speed of light by an accelerator. They are subsequently crushed against other particles flowing in the opposite direction or against a target. Physicists can examine the realm of the endlessly small by investigating these collisions.

Mass of the theoretical particle is m = 10¹⁴GeV/C².

a)

Dividing the theoretical particle's rest mass\(\left( m \right)\)by the rest masses of the proton\(\left( {{m_p}} \right)\), we get-

\[\frac{m}{{{m_p}}} = \frac{{{{10}^{14}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}}{{938 \times {{10}^{ - 3}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}} = 1.07 \times {10^{14}}\]

Therefore, the number of proton masses is\[{\rm{1}}{\rm{.07 \times 1}}{{\rm{0}}^{{\rm{14}}}}\].

b)

Dividing the theoretical particle's rest mass\(\left( m \right)\)by the rest masses of the proton\(\left( {{m_p}} \right)\), we get-

\[\frac{m}{{{m_e}}} = \frac{{{{10}^{14}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}}{{0.511 \times {{10}^{ - 3}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}} = 1.96 \times {10^{17}}\]

Therefore, the number of electron masses is\[{\rm{1}}{\rm{.96 \times 1}}{{\rm{0}}^{{\rm{17}}}}\].