For the fusion reactions powering the Sun to take place, protons (with charge +1.6x10¹⁹C, and mass3.3x10-²7kg) must come within 2.4x10*¹5m of each other. (At that range the strong nuclear forceovercomes their electrical repulsion, and they merge into deuterium. Later, two deuterium fuse intohelium, completing the reaction.)a) If two protons have a head on collision at equal speeds, how fast must they be going in order toget close enough to react?b)Use the ideal gas equation for average kinetic energy: Kavg = (3/2)kT to find the temperature atwhich the average proton would be moving fast enough to undergo fusion. Note that this isBoltzman's constant, k, = 1.38x10²³ J/K, in this formula. (Note that this temperature is actuallymuch hotter than the core of the Sun - in the sun it's not the average H* that need to be movingfast enough to fuse, just the fastest ones.)

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Answered: For the fusion reactions powering the…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter14: Nuclear Physics Applications

Section: Chapter Questions

Problem 33P

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For the fusion reactions powering the Sun to take place, protons (with charge +1.6x10¹⁹C, and mass
3.3x10-²7kg) must come within 2.4x10*¹5m of each other. (At that range the strong nuclear force
overcomes their electrical repulsion, and they merge into deuterium. Later, two deuterium fuse into
helium, completing the reaction.)
a) If two protons have a head on collision at equal speeds, how fast must they be going in order to
get close enough to react?
b)
Use the ideal gas equation for average kinetic energy: Kavg = (3/2)kT to find the temperature at
which the average proton would be moving fast enough to undergo fusion. Note that this is
Boltzman's constant, k, = 1.38x10²³ J/K, in this formula. (Note that this temperature is actually
much hotter than the core of the Sun - in the sun it's not the average H* that need to be moving
fast enough to fuse, just the fastest ones.)

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Can you please solve this without using calculus? There has to be a way to use the formulas for kinetic energy and potential energy to solve for velocity.

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