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

In summary, the ratio of the speeds of a helium atom and an oxygen atom, given that they have the same kinetic energy, is 2.
  • #1
buttermellow
8
0

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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  • #2
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 = ?
 
  • #3
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:

1. What is the relationship between the ratio of velocities of two atoms and their kinetic energy?

The ratio of velocities of two atoms is directly proportional to their kinetic energy. This means that as the ratio of velocities increases, the kinetic energy also increases.

2. How is the ratio of velocities of two atoms determined?

The ratio of velocities of two atoms can be determined by dividing the velocity of one atom by the velocity of the other atom. This will give a numerical value for the ratio.

3. Does the mass of the atoms affect the ratio of velocities and kinetic energy?

Yes, the mass of the atoms does affect the ratio of velocities and kinetic energy. Heavier atoms will have a lower velocity and less kinetic energy compared to lighter atoms.

4. Can the ratio of velocities of two atoms change?

Yes, the ratio of velocities of two atoms can change. This can happen if the atoms experience a change in temperature, pressure, or other external factors that can affect their velocity and therefore their kinetic energy.

5. How is the ratio of velocities of two atoms used in scientific research?

The ratio of velocities of two atoms is used in many scientific fields, such as thermodynamics, chemistry, and materials science. It can provide valuable information about the behavior and properties of atoms in different environments and help researchers better understand and predict the behavior of matter.

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