Book cover for Classical Mechanics

Classical Mechanics

John R. Taylor

ISBN #9781891389221

1st Edition

744 Questions

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Learning Objectives

Key Concepts

Example Problems

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Common Mistakes

Summary

Collision theory, through scattering experiments, serves as a powerful tool in uncovering the structure and interactions of atomic and subatomic particles. The Rutherford experiment exemplifies how such experiments can challenge and reshape our understanding of the atom, transitioning from classical models to quantum mechanical descriptions. Key ideas such as scattering cross sections and the use of lab and center-of-mass reference frames bridge classical and quantum territories, highlighting the evolution of experimental physics.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

A blueberry pancake has diameter 15 cm and contains 6 large blueberries, each of diameter 1 cm. Find the cross section $\sigma$ of a blueberry and the "target" density $n_{\text {tar }}$ (number/area) of berries in the pancake, as seen from above. What is the probability that a skewer, jabbed at random into the pancake, will hit a berry (in terms of $\sigma$ and $n_{\text {tar }}$ and then numerically)?

Example 2

(a) A certain nucleus has radius $5 \mathrm{fm}$. ( $1 \mathrm{fm}=10^{-15} \mathrm{m}$.) Find its cross section $\sigma$ in barns. (1 barn $=10^{-28} \mathrm{m}^{2} .$ ) (b) Do the same for an atom of radius $0.1 \mathrm{nm}$. $\left(1 \mathrm{nm}=10^{-9} \mathrm{m} .\right)$

Example 3

A beam of particles is directed through a tank of liquid hydrogen. If the tank's length is $50 \mathrm{cm}$ and the liquid density is 0.07 gram/cm $^{3}$, what is the target density (number/area) of hydrogen atoms seen by the incident particles?

Example 4

The cross section for scattering a certain nuclear particle by a copper nucleus is 2.0 barns. If $10^{9}$ of these particles are fired through a copper foil of thickness $10 \mu \mathrm{m}$, how many particles are scattered? (Copper's density is 8.9 gram/cm $^{3}$ and its atomic mass is $63.5 .$ The scattering by any atomic electrons is completely negligible.)

Example 5

The cross section for scattering a certain nuclear particle by a nitrogen nucleus is 0.5 barns. If $10^{11}$ of these particles are fired through a cloud chamber of length $10 \mathrm{cm},$ containing nitrogen at STP, how many particles are scattered? (Use the ideal gas law and remember that each nitrogen molecule has two atoms. The scattering by any atomic electrons is completely negligible.)

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