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Question:
How could one accelerate molecules to a very high speed without destroying them?



Replies:
Wait a minute -- what do you mean by ``destroy?'' When you destroy a macroscopic object you break it up into its constituent molecules, just as when destroying an object made of LEGOs (http://www.lego.com/) you break it up into its constituent little plastic bricks. Clearly you can't destroy, in the same sense, a single LEGO brick, and likewise you can't destroy in the ordinary meaning of the word a single molecule.

However, molecules are not elementary. They are usually composed of atoms, and the atoms themselves are composed of subatomic particles (protons, neutrons, electrons), and two of the subatomic particles (protons and neutrons) appear to be composed of still smaller particles (quarks). So you CAN destroy a molecule in the more general sense of deconstructing it into its components. I will assume you mean ``destroy'' this sense.

What is also at issue is the point at which you consider a molecule destroyed. Consider destroying a car: merely removing the mirrors is not destroying it, but pulling every piston, breaking up the transmission, scattering the wiring and ripping apart the bodywork is. Somewhere between these extremes lies a line where ``damage'' turns into ``destroy''. Same thing with a molecule.

To accelerate completely intact molecules, your only method is to whack them with other molecules or the walls of your container. That is, you heat the material. You can do this until the speed of the molecules is so high that they break each other's chemical bonds when they collide. To find out how fast this is, we compare energies: the energy of a typical chemical bond is about 400 kJ/mol, for example the O-H bond energy in water is 467 kJ/mol. When the average kinetic energy of the molecules reaches this point, then a typical collision liberates enough energy to break the bond. Kinetic energy is related to speed via E_k = m/2 v^2, where m is the molar mass of the molecule and v is the velocity. Suppose we accelerate water, with its molar mass of 18 g/mol. Then the maximum speed is given roughly by (note that 1 J = 1 kg m^2/s^2):

467,000 J/mol = 0.018 kg/mol (v_max in m/s)^2

Hence v_max = 5100 m/s or about 11,400 miles per hour. Fast.

To figure the temperature we have needed, we use the equipartition formula < E_k > = 3/2 R T, where < E_k > is the average kinetic energy, and R is the gas constant 8.31451 J/(K mol):

467,000 J/mol = 3/2 8.31451 J/(K mol) T_max in K

Hence T_max = 37,400 K or about 67,000 degrees Fahrenheit. Hot.

Now let's suppose you are accelerating atoms. The limit for intact atoms occurs when the kinetic energy is high enough to ionize the atom -- break off an electron -- upon collision. Typical first ionization energies for light atoms range between 1000 and 2000 kJ/mol. O atoms, for example, lose their first electron when they absorb 1314 kJ/mol of energy. They weigh 16.0 g/mol. Hence:

1,314,000 J/mol = 0.016 kg/mol (v_max in m/s)^2

And v_max = 9100 m/s or 20,000 MPH. T_max = 105,000 K, which is not easy to achieve. Note that atoms can stand higher temperatures than molecules, which tells you atoms are sturdier.

If you are willing to regard an atom missing one of its electrons as damaged only, not destroyed, then you can now begin to accelerate

your atoms electrically, because they are now charged, and reduce the density so that they are in no danger of colliding with other atoms. There is no limit other than relativity on how fast they can go, because the only forces on them are the forces of acceleration and you can makes these as small as you want, by taking longer to accelerate the ionized atoms.


Since you're not a K-12 student or educator, I wouldn't normally reply to a question like this on NEWTON, but since I know the answer... one uses a molecular beam setup, wherein one lets a gas under pressure escape into a chamber which has been evacuated through a very very small nozzle. The expansion produces gas molecules moving at supersonic speeds.

Best regards,

Topper



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