CHEMISTRY CHAPTER ZERO

Physics of the Mass Spectrometer (without symbols)

We are going to neglect any affects due to the resistance of the air to the motion of the foam atoms. This is a pretty good, but not perfect, assumption. [The mass spectrometer performs pretyy much as expected for foam atoms with cores. However, a piece of foam by itself is so light that the air resistance effects cause it not to travel very far -- a clear violation of this assumption.]

The amount of energy stored in stretching the elastic depends only on the elastic itself and on the elongation of the elastic. Thus, when the elastic returns to its unstressed length, and the energy has become the kinetic energy of the cradle assembly plus the foam atom, the velocity of the cradle assembly is set. The more the stretching of the elastic, the greater the velocity of the foam atom. And, the greater the weight of the atom, the lower its velocity [Sorry, you just have to accept this last statement -- I agreed not to use symbols on this page.]

We can make it easier to understand the subsequent motion of the foam atom by consider the independent motions of the foam atom in the horizontal direction --parallel to the floor -- and in the vertical direction -- perpendicular to the floor. In order to keep the main idea front and center, we first consider the case in which the foam atom is lauched horizontally -- with no intial vertical compent of the velocity. The key idea here is that both the heavy atom and the light atom will take the same amount of time to reach the floor. However, the light atom is moving faster in the horizontal direction. With the same amount of time until the heavy and light atoms reach the floor (and end the experiment as far as we are concerned), the light (faster) atom travels farther than the heavy (slower) atom.

If the atoms start out with a small vertical component of velocity -- as shown in the figure above -- the argument is very much the same, except that the times to fall to the floor are no longer exactly equal. The difference in fall times is small, and the argument in the paragraph above works fine.

If we choose to launch the atoms pretty much vertically, then they will fall pretty close to each other. There is no need to analyze this case, since we are smart enough not to operate our mass spectrometer in that fashion.