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Chapter 33: Q15PE (page 1212)

The mass of a theoretical particle that may be associated with the unification of the electroweak and strong forces is\[{\rm{1}}{{\rm{0}}^{{\rm{14}}}}{\rm{ GeV/}}{{\rm{c}}^{\rm{2}}}\]. (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity 纬 would have to be.)

Short Answer

Expert verified

a) 1014GeV/c2is equal to 1.07 x 1014 proton masses.

b)1014GeV/c2 is equal to 1.96 x 1017 electron masses.

Step by step solution

01

Concept Introduction

Charged particles, such as protons or electrons, are propelled at high speeds near the speed of light by an accelerator. They are subsequently crushed against other particles flowing in the opposite direction or against a target. Physicists can examine the realm of the endlessly small by investigating these collisions.

02

Given Data

Mass of the theoretical particle is m = 1014GeV/C2.

03

Calculating the proton masses

a)

Dividing the theoretical particle's rest mass\(\left( m \right)\)by the rest masses of the proton\(\left( {{m_p}} \right)\), we get-

\[\frac{m}{{{m_p}}} = \frac{{{{10}^{14}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}}{{938 \times {{10}^{ - 3}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}} = 1.07 \times {10^{14}}\]

Therefore, the number of proton masses is\[{\rm{1}}{\rm{.07 \times 1}}{{\rm{0}}^{{\rm{14}}}}\].

04

Calculating the electron masses

b)

Dividing the theoretical particle's rest mass\(\left( m \right)\)by the rest masses of the proton\(\left( {{m_p}} \right)\), we get-

\[\frac{m}{{{m_e}}} = \frac{{{{10}^{14}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}}{{0.511 \times {{10}^{ - 3}}\;{\rm{GeV/}}{{\rm{c}}^{\rm{2}}}}} = 1.96 \times {10^{17}}\]

Therefore, the number of electron masses is\[{\rm{1}}{\rm{.96 \times 1}}{{\rm{0}}^{{\rm{17}}}}\].

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Most popular questions from this chapter

Suppose you are designing a proton decay experiment and you can detect \({\rm{50}}\) percent of the proton decays in a tank of water.

(a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of \({\rm{1}}{{\rm{0}}^{{\rm{31}}}}{\rm{ y}}\)?

(b) How many cubic meters of water is this?

(c) If the actual lifetime is \({\rm{1}}{{\rm{0}}^{{\rm{33}}}}{\rm{ y}}\), how long would you have to wait on an average to see a single proton decay?

(a) How much energy would be released if the proton did decay via the conjectured reaction \({\rm{p}} \to {\pi ^{\rm{0}}}{\rm{ + }}{{\rm{e}}^{\rm{ + }}}\)?

(b) Given that the \({\pi ^{\rm{0}}}\) decays to two \(\gamma {\rm{ s}}\) and that the \({{\rm{e}}^{\rm{ + }}}\) will find an electron to annihilate, what total energy is ultimately produced in proton decay?

(c) Why is this energy greater than the proton鈥檚 total mass (converted to energy)?

(a) Do all particles having strangeness also have at least one strange quark in them?

(b) Do all hadrons with a strange quark also have nonzero strangeness?

Another component of the strong nuclear force is transmitted by the exchange of virtual \[{\rm{K - }}\]mesons. Taking \[{\rm{K - }}\]-mesons to have an average mass of \[{\rm{495}}\;{\rm{MeV/}}{{\rm{c}}^{\rm{2}}}\], what is the approximate range of this component of the strong force?

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