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solutions 01

# Modern Physics

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PHY251 Homework Set 1 Reading: Chapters 1 and 2 Homework: Problems are listed below Problems, Hints, and Solutions Problem I.1 An atom of mass m is moving along the x -direction with speed v 0 . It collides elastically with an atom of mass 3 m at rest. After the collision the first atom moves along the y -direction. Calculate the velocities (speeds and directions!) of both atoms after the collision. Hints: Make sketch! Use conservation of momentum and kinetic energy. Solution: 1. Conservation of momentum in x -direction: ( v 0 - 0) = 3 V x ; V x = v 0 /3 2. Conservation of momentum in y -direction: (0 - v y ) = 3 V y ; v y = -3 V y >0 ("... moves along the y -direction") V y <0. 3. Energy conservation: ( v 0 2 - v y 2 ) = 3( V x 2 + V y 2 ); 1.+2. 3.: 9( V x 2 - V y 2 ) = 3( V x 2 + V y 2 ) 12 V y 2 = 6 V x 2 ; V y = - V x / 2 = - v 0 /(3 2) , and v y = + v 0 / 2 Problem I.2 Units and interaction strengths. Express the unit Volt in basic SI units. . Express the unit for magnetic field Tesla in basic SI units. b. Is the "right-hand-rule" a law of nature, or could we have started with a "left-hand-rule" and stayed in agreement with all empirical facts? Otherwise stated: is there experimental evidence for a "right-hand-rule" (and against a left-hand-rule), or is it just a question of definitions and consistency with that initial definition? Discuss this using the Lorentz force on a current in a magnetic field. c. Starting from Coulomb's Law, calculate the value and the units of the quantity e ²/(4 πε 0 ), where e is the magnitude of the electron charge, and ε 0

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