Ratio of the velocities of two atoms, based on kinetic energy

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SUMMARY

The discussion focuses on calculating the ratio of the velocities of a helium atom and an oxygen atom, given that the oxygen atom is four times as massive as the helium atom and both have the same kinetic energy. Using the kinetic energy formula K = 0.5mv², the solution derives the ratio vHe/vO = 2. This is achieved by manipulating the equation to isolate the velocity terms, demonstrating that the speed of the helium atom is twice that of the oxygen atom.

PREREQUISITES
  • Understanding of kinetic energy formula (K = 0.5mv²)
  • Basic algebraic manipulation skills
  • Knowledge of mass and velocity relationships in physics
  • Familiarity with the concept of atomic mass
NEXT STEPS
  • Study the implications of kinetic energy in different atomic masses
  • Learn about the conservation of energy in atomic collisions
  • Explore advanced topics in classical mechanics, such as momentum
  • Investigate the behavior of gases and the kinetic theory of gases
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and atomic theory, as well as educators looking for examples of kinetic energy applications in atomic interactions.

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Homework Statement



An oxygen atom is four times as massive as a helium atom. In an experiment, a helium atom and an oxygen atom have the same kinetic energy. What is the ratio vHe /vO of their speeds?



Homework Equations


K=.5mv2


The Attempt at a Solution



.5mHe(vHe)2=.5(4mHe)(vO)2

I'm not sure what to do with that though, how to solve for the ratio.
 
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Have you learned basic algebraic manipulation? You just have to rearrange the equation so as to get the ratio V(he)/V(o) on one side. eg. 5a = 3b, a/b = ?
 
Oh my, I was making that much harder than it needed to be.

What I got:
.5mHe(vHe)2=2mHe(vO)2
mHe cancels to give (vHe)2=4(vO)2
(vHe)2/(vO)2=4
vHe/vO=[tex]\sqrt{}4[/tex]=2
 
Last edited:

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