About $1 \mu \mathrm { s }$ after the Big Bang, the temperature of the universe was about $10 ^ { 13 } \mathrm {~K}$. What particle kinetic energy (in $\mathrm { eV } )$ does this correspond to? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , k = 1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } \right)$
A) $1 \mathrm { TeV }$
B) $1 \mathrm { keV }$
C) $1 \mathrm { GeV }$
D) $1 \mathrm { MeV }$

Question

Quizplus · Accepted Answer

The correct answer is C.The particle kinetic energy is given by:$$K = \frac{3}{2}kT$$where $k$ is the Boltzmann constant and $T$ is the temperature.Substituting the given values, we get:$$K = \frac{3}{2}(1.38 \times 10^{-23} \mathrm{J/K})(10^{13} \mathrm{K}) = 2.07 \times 10^{-10} \mathrm{J}$$Converting to eV, we get:$$K = \frac{2.07 \times 10^{-10} \mathrm{J}}{1.60 \times 10^{-19} \mathrm{J/eV}} = 1.30 \mathrm{GeV}$$Therefore, the particle kinetic energy corresponds to 1 GeV.

About 1μs1 \mu \mathrm { s }1μs After the Big Bang, the Temperature of the Universe Was

About $1 \mu \mathrm { s }$ After the Big Bang, the Temperature of the Universe Was