According to Figure \(30.2,\) higher energies correspond with times that are closer to the origin of the universe, so particle accelerators at higher energies probe conditions that existed shortly after the Big Bang. At Fermilab's Tevatron, protons and antiprotons are accelerated to kinetic energies of approximately 1 TeV. Estimate the time after the Big Bang that corresponds to protonantiproton collisions in the Tevatron.

First, convert the given energy of proton-antiproton collisions, 1 TeV, to eV by multiplying by the conversion factor. 1 TeV * (10^12 eV/TeV) = 10^12 eV

Now, we'll find the temperature in Kelvin corresponding to the 1 TeV (10^12 eV) energy using the Boltzmann constant (k = 8.617 x 10^(-5) eV/K). \(E = kT\) \(T = \frac{10^{12} eV}{8.617×10^{-5} eV/K}\) \(T = 1.16 × 10^{16} K\)

According to Hubble's law, we have the equation relating temperature and time: \(T \propto \frac{1}{t^{1/2}}\) First, we need to know the temperature of the universe right after the Big Bang, denoted \(T_0\). To do this, we would refer to the text or graph given in Figure 30.2 (This step is required because the actual graph is not provided in the exercise). Suppose the value we get from the graph is \(T_0 = 1.0 × 10^{32} K\). Now, we will proceed to find the time after the Big Bang corresponding to the Tevatron's energy using the above two equations. To simplify the process, let's assume that the proportionality constant in Hubble's law is 1, meaning that the initial equation becomes a direct equality. \(\frac{T}{T_0} = \frac{t_0^{1/2}}{t^{1/2}}\) Solve for \(t\): \(t = t_0 \left(\frac{T_0}{T}\right)^2\) \(t = t_0 \left(\frac{1.0 × 10^{32}K}{1.16 × 10^{16}K}\right)^2\) Since time \(t_0\) (the time right after the Big Bang) is theoretically 0, we use the smallest unit of time, Planck time (\(5.39 × 10^{-44}s\), symbol \(t_P\)) as an approximation. Thus: \(t \approx t_P \left(\frac{1.0 × 10^{32}K}{1.16 × 10^{16}K}\right)^2\) \(t \approx 5.39 × 10^{-44}s \left(\frac{1.0 × 10^{32}K}{1.16 × 10^{16}K}\right)^2\) \(t \approx 3.37 × 10^{-12}s\) So, the estimated time after the Big Bang that corresponds to proton-antiproton collisions in the Tevatron is around \(3.37 × 10^{-12}\) seconds.