Question

Which of the eight pions in Fig. 44-2bhas the least kinetic energy?

Short answer

The ${\pi }^{-1}$ at the top has the least kinetic energy.

Step-by-step solution

Given data:

An anti-proton collides with a proton and creates four pions and four anti-pions.

Kinetic energy of produced particles:

The magnetic field deflection is proportional to the charged particle velocity. Hence the particles with the least deflection in the bubble chamber have the least kinetic energy.

Particles with the lowest energy come to rest faster.

Determining the pion with the least kinetic energy:

Kinetic energy is the energy possessed by a body by virtue of its motion.

$K=\frac{1}{2}m{v}^2$

Here, K is the kinetic energy, m is the mass of the body, and v is the velocity of the body.

Kinetic energy of pion is directly proportional to the square of its velocity. But, when a charged particle is moving in a uniform magnetic field, the velocity of the particle is directly proportional to its radius of curvature.

Therefore, the particle with a lease radius of curvature will have the least velocity thereby having to lease kinetic energy.

So, the pion from 1 to 2 will have lease kinetic energy.

The ${\pi }^{-1}$ at the top comes to rest fastest. It also has very low deflection. Hence that is the particle with the lowest kinetic energy.