Chapter 32, Problem 18P

To determine

The kinetic energy of proton and anti-proton (KE).

Answer to Problem 18P

Solution:

The kinetic energy of proton and anti-proton (KE)is 987.4MeV.

Explanation of Solution

Given Info:

The mass of K⁺is 493.7MeV/c².

The mass of K^-is 493.7MeV/c².

Formula Used:

The formula to calculate wavelength is,

• ‘ ${\text{KE}}_{\text{p}}$’ is the kinetic energy of the proton.

• ‘ ’is the kinetic energy of anti-proton.

• ‘ ${\text{m}}_{{\text{k}}^{\text{+}}}$’ is mass of K⁺.

• ‘ ${\text{m}}_{{\text{k}}^{\text{-}}}$’ is mass of K^-.

The required reaction is

Applying conservation of energy to find the relativistic energy of proton and antiproton by adding the energy of each proton and antiproton along with the energy of $K^{+}$ and ${\text{K}}^{-}$,

As the velocity of proton and anti-proton is equal, the kinetic energy is

So the formula used to get the kinetic energy of each proton and antiproton is,