Question

In the following exercises, two protons are smashed together in an attempt to convert kinetic energy into mass and new particles. Indicate whether the proposed reaction is possible. If not, indicate which rules are violated. Consider only those for charge, angular momentum, and baryon number If the reaction is possible, calculate the minimum kinetic energy required of the colliding protons.

$p+p\to p+p+p+\overline{p}$

Short answer

The proposed decay is possible.The required kinetic energy is $1876\text{MeV}$

Step-by-step solution

Given data

The proposed reaction is $p+p\to p+p+p+\overline{p}$

Concept of rest energy

A nucleus has mass . The rest energy can be calculated as $m{c}^2$.

Step 3:Find conservation of charge

Conservation of charge is shown below:

$\begin{array}{rcl}p+p& \to & p+p+p+\overline{p}\\ (+e)+(+e)& \to & (+e)+(+e)+(+e)+(-e)\\ (+2e)& \to & (+2e)\end{array}$

Thus, the charge before the decay and after the decay is equal.

Therefore, the charge is conserved.

Find conservation of baryons number

Conservation of baryons number is given below:

$$\begin{gathered} p+p\to p+p+p+\overline{p} \\ (+1)+(+1)\to (+1)+(+1)+(+1)+(-1) \\ (+2)\to (+2) \end{gathered}$$

Thus, the baryons number before the decay is equal to the baryons number after the decay.

Therefore, the baryons' number is conserved.

Find the minimum kinetic energy required of the colliding protons

From the above results, we conclude that the decay reaction is possible.

The rest mass energy of the proton is $m{c}^2=938\text{MeV}$ .

Thus, the minimum kinetic energy required of the colliding protons can be calculated as:

$\begin{array}{rcl}4m{c}^2-2m{c}^2& =& 2m{c}^2\\ & =& 2(938\text{MeV})\\ & =& 1876\text{MeV}\\ & & \end{array}$

Therefore, the minimum amount of kinetic energy required of the colliding protons is$1876\text{MeV}$.

The proposed decay is possible, and the required kinetic energy is $1876\text{MeV}$.