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Chapter 12: Q23E (page 556)

To produce new particle accelerators often smash two equal mass objects together proton and proton or electron and positron. The threshold energy is the kinetic energy before the collision needed simply to produce the final particle their mass thermal energy alone with no leftover kinetic energy. Consider a colliding beam accelerator in which two initial particles of mass m are moving at the same speed relative to the lab. Assume that the total mass of the stationary particles after the collision is M. Show that the threshold energy is M-2mc2.

Short Answer

Expert verified

Threshold energy M-2mc2 is proved.

Step by step solution

01

Given data 

Threshold energy is M-2mc2

02

Concept of Threshold energy

The threshold energy is the minimum kinetic energy required by the particles to produce the resulting product when they collide.

03

Proof of threshold energy

The total mass of the particles after the collision is M .

Choose the reference frame to be the one in which the final product is at rest.

The massenergy of the two particles before the collision is 2mc2 .

The energy needed to produce the final particle of mass M is Mc2.

The difference in energy is the threshold energy due to the energy conservation law, that is:

=Mc2-2mc2=M-2mc2

Threshold energyM-2mc2 is proved.

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Most popular questions from this chapter

If a neutrino interacted with a quark every time their separation was within the 10−18 m range generally accepted for the weak force, then the cross-section of a neutron or proton “seen” by a neutrino would be on the order of 10−36 m2. Even at such separation, however the probability of interactions is quite small. The nucleon appears to have an effective cross-section of only about 10−48 m2.

(a) About how many nucleons are there in a column through the earth’s center of 1 m2 cross-sectional area?

(b) what is the probability that a given neutrino passing through space and encountering earth will actually “hit”?

Suppose a force between two particles decreases distance according to F=k/rb. What is the limit on b if the energy required to separate the particlesInfinitely far is not to be infinite?

Equation (12·5) would apply to any given chunk of an expanding spherical mass. provided that no chunks overtake any others-if, for instance,speed increases, with distance from the origin. Why? (Think of Gauss’­ law from electrostatics).

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→Σ++p+K0

Sketch the Feynman diagram if the proposed decay is possible.

K+→μ++v¯μ
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