Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 32 - Elementary Particles - General Problems - Page 946: 61

Answer

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Work Step by Step

In Section 32–1, page 920, it is stated that the interaction energy for a collision in the LHC is about 14 TeV. Example 32–1 shows us how to calculate the wavelength corresponding to this energy. $$\lambda=\frac{hc}{E}=\frac{(6.626\times10^{-34}J \cdot s)(3.0\times10^8 m/s)}{(14\times10^{12}eV)(1.60\times10^{-19}J/eV)}=8.9\times10^{-20}m$$ This is approximately the level of detail that can be resolved by the collision of the proton beams. We are asked to confirm that this is about 1/10000 the size of a nucleus. From equation 30–1, we know that a nuclear radius is about $1.2\times10^{-15}m$, so 1/10000 of that is $1.2\times10^{-19}m$. This is indeed very comparable to the wavelength we just calculated.
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