The mass of a π^0 can be measured by observing the reaction...

Key Concepts

Mass-Energy Equivalence

Expressed by Einstein’s equation E=mc², this principle defines the relationship between mass and energy, allowing the conversion of mass differences into measurable energy differences. In particle reactions, this concept is key to understanding how changes in the mass of a particle are reflected in the energy distribution among the products.

Reaction Kinematics

This area focuses on the movement of particles during interactions and the use of conservation laws to relate the masses, velocities, and energies involved in a reaction. By analyzing the kinematics, one can derive equations that connect the observed kinetic energies and momenta with the rest masses of the participating particles.

Conservation of Energy

This principle asserts that the total energy of an isolated system remains constant, where energy includes both the rest mass energy and the kinetic energy of the particles. In the context of particle reactions, it allows one to set up equations equating the energy before and after the reaction, which is crucial for determining unknown quantities such as the mass of a particle.

Conservation of Momentum

This concept states that the total momentum of an isolated system is conserved during an interaction. In particle physics reactions, applying momentum conservation ensures that the vector sum of the momenta before the event is equal to that after the event, facilitating the derivation of relationships between the momenta and, indirectly, the masses and kinetic energies of the particles involved.

Transcript

00:01 Okay, so problem number 56 wants us to calculate the rest mass or the mass of a neutral pion.

00:10 And we're given the fact that a neutral pion is formed through the reaction of a minus pion plus a proton, so minus pion proton basically annihilating, colliding, and forms a neutral pion plus a neutron.

00:30 And we're given the fact that basically the kinetic energy of the pion is zero, and that the kinetic energy, when this collision happens and these products are created, the neutron is created with the kinetic energy.

00:52 So a kinetic energy of neutron is created with 0 .60 mep.

00:58 So we want to calculate, so first, in order to calculate the mass of this, we need to know the energy of this.

01:08 So we know a few things.

01:11 So conservation of energy states that the energy on this side has to equal the energy on this side.

01:17 So there can't be, you know, they have to be the same.

01:22 So we can use that to state the rest energy of the pion, since this side has zero kinetic energy.

01:34 So the rest energy of the pion plus the rest mass energy of the proton is going to be equal to the total energy of the neutral pion squared, sorry, not squared, the total energy of the neutral pion plus the total energy of the neutron, which is going to be its rest mass, its rest energy, c squared, plus its kinetic energy.

02:08 Okay, so yeah, when i say energy has to be conserved, i mean total energy.

02:13 The total energy is concerned.

02:16 So now we can rearrange this just to solve for the total energy of the pion.

02:21 So the total energy of the pion is going to be equal to the rest energy of the minus pion squared plus the rest energy of the proton squared minus the rest mass energy of the neutron plus.

02:38 It's kinetic energy.

02:41 So the total energy of the neutron.

02:43 So now we know all of these numbers so we can plug this in.

02:46 So we can say the total energy of the neutral pion is going to be equal to let's plug in these numbers 100 and so it's sorry equal to 139 .6 m e .v plus 9 38 .3m .3m .e .v minus 938 .6 m .e .v.

03:24 Plus 0 .60 m .e .v.

03:31 Now this totals, this gives you a total energy of the pion, the neutral pion of 137 m .ev.

03:41 All right.

03:42 So now that we have the total energy of it, we need to calculate what's the, what portion is the rest mass energy.

03:49 So if it's from the rest mass energy, then we can get the mass.

03:53 So we have from conservation and momentum, just that conservation of energy, the momentum on this side has to equal the momentum on that side.

04:03 So, and since the momentum on the reactions is zero, since we say that they basically have no kinetic energy, that means that the total moment.

04:11 Of the products must be zero...

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