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Modern Physics

John R. Taylor, Chris D. Zafiratos, Michael A. Dubson

Chapter 18

Elementary Particles - all with Video Answers

Educators


Section 1

Elementary Particles: The Story So Far

03:06

Problem 1

- To measure distances of order $d$ with quanta of wavelength $\lambda$ requires $\lambda \lesssim d$. Find the minimum energies of photons required to measure $d$ with (a) $d \approx 10^{-4} \mathrm{~m}$, (b) $d \approx 10^{-8} \mathrm{~m}$, and
(c) $d \approx 10^{-12} \mathrm{~m}$.

Mayank Tripathi
Mayank Tripathi
Numerade Educator
02:10

Problem 2

- To investigate distances of order $10^{-15} \mathrm{~m}$ requires a probe whose wavelength $\lambda$ is of this same order. (a) Supposing that the probe particle has mass $m$, derive an expression for its total (relativistic) energy in terms of $\lambda$. (b) Show that the minimum energy that gives $\lambda \approx 10^{-15} \mathrm{~m}$ is of order $1 \mathrm{GeV}=10^{9} \mathrm{eV}$

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator
03:01

Problem 3

- To "see" spatial details of a size $d$, you need a probe (light, for example) whose wavelength satisfies $\lambda \lesssim d$. What energy of photons do you need to "see" spatial details of (a) atomic size $\left(d \sim 10^{-10} \mathrm{~m}\right)$, (b) nuclear size $\left(d \sim 10^{-14} \mathrm{~m}\right),(\mathbf{c})$ the distribution of "sub-elementary" constituents inside a proton (distances of order $10^{-17} \mathrm{~m}$, say). [Your answer to part (a) may surprise you, since it suggests that energies of order keV's are needed to probe an atom, whereas we know that we can learn about atomic energy levels with photons of a few $\mathrm{eV}$. However, the latter tell us about energy levels, but not about spatial details. It remains true that to learn about spatial details one needs keV's.]

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator
04:20

Problem 4

(a) Given particles of total relativistic energy $E$ and mass $m$, what is the minimum distance, $d_{\min }$, that can be probed with these particles? (b) For given $E$, what mass $m$ would give the best resolution? (c) If $E=1 \mathrm{TeV}=10^{12} \mathrm{eV}$, what is the best possible resolution?

Ashwin Banarsee
Ashwin Banarsee
Numerade Educator