Q. 29 The Large Hadron Collider accele... [FREE SOLUTION]

Chapter 37: Q. 29 (page 1083)

The Large Hadron Collider accelerates protons to a total energy of $6.5 TeV$ per proton. ( $1 TeV = 1$ teraelectron volt $= 10^{12} eV$ .) What is the speed of a proton that has this energy? Give your answer as fraction of $c$ , using as many significant figures as needed.

Short Answer

Expert verified

The required speed (as a fraction of $c$ ) is $v = 0.9999999895 路 c$

Step by step solution

Given Information

Let us start the solution with the expression for relativistic total energy
$E = \frac{m c^{2}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

Calculation

$\begin{array}{rcl} E^{2} (1 - \frac{v^{2}}{c^{2}}) & = & m^{2} c^{4} \\ E^{2} \frac{v^{2}}{c^{2}} & = & E^{2} - m^{2} c^{4} \\ v & = & \sqrt{c^{2} - \frac{m^{2} c^{6}}{E^{2}}} \\ v & = & c \sqrt{1 - \frac{m^{2} c^{4}}{E^{2}}} \\ v & = & c 路 \sqrt{1 - \frac{{(1.67 路 10^{- 27})}^{2} 路 {(3 路 10^{8})}^{4}}{6.5 路 10^{12} 路 1.6 路 10^{- 19}}} \\ v & = & 0.9999999895 路 c \end{array}$

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91影视

The Large Hadron Collider accelerates protons to a total energy of $6.5 TeV$ per proton. ( $1 TeV = 1$ teraelectron volt $= 10^{12} eV$ .) What is the speed of a proton that has this energy? Give your answer as fraction of $c$ , using as many significant figures as needed.

Short Answer

Step by step solution

Given Information

Calculation

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91影视

The Large Hadron Collider accelerates protons to a total energy of 6.5TeVper proton. ( 1TeV=1teraelectron volt =1012eV.) What is the speed of a proton that has this energy? Give your answer as fraction of c, using as many significant figures as needed.

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Conservation of Energy and Momentum

Wave Optics

Linear Momentum

Kinematics Physics

Famous Physicists

Study anywhere. Anytime. Across all devices.

The Large Hadron Collider accelerates protons to a total energy of $6.5 TeV$ per proton. ( $1 TeV = 1$ teraelectron volt $= 10^{12} eV$ .) What is the speed of a proton that has this energy? Give your answer as fraction of $c$ , using as many significant figures as needed.