Chapter 33, Problem 44GP

To determine

The temperature that corresponds to given collisions at the Fermi lab collider.

To identify: Era that corresponds to cosmological history.

Answer to Problem 44GP

The temperature that corresponds to $1.8\text{-TeV}$ collisions at the Fermi lab collider is $1.4\times {10}^{16}\text{ K}$ . It corresponds to Hadron Era.

Explanation of Solution

Given:

Collision energy at the Fermi lab collider is $1.8\text{-TeV}$ .

Formula used:

Kinetic energy is calculated as

  $\text{KE = }\frac{3}{2}\text{kT}$

Calculation:

The temperature that corresponds to kinetic energy is

  $\begin{array}{l}\text{KE = }\frac{3}{2}\text{kT}\Rightarrow \text{T = }\frac{2}{3}\frac{\text{KE}}{\text{k}}\\ \text{T =}\frac{2}{3}\frac{(1.8\times {10}^{12}\text{ eV})(1.60\times {10}^{-19}\text{ J/eV})}{(1.38\times {10}^{-23}\text{J/K})}\\ \text{T = 1}\text{.4}\times {10}^{16}\text{K}\end{array}$

Conclusion:

The temperature that corresponds to $1.8\text{-TeV}$ collisions at the Fermi lab collider is $1.4\times {10}^{16}\text{ K}$ . According to the cosmological calendar, this era corresponds to Hadron Era.