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Fig 14.16.

Formation of H2 on a grain surface.

Fig 14.16.

Formation of H2 on a grain surface.

surface, the energy can be efficiently transferred to the grain, resulting in a slight increase in grain temperature. The fact that the dust plays an important role in the formation of H2 and the protection of H2 once it is formed, results in an interesting situation. When a cloud has a visual extinction of less than one magnitude, almost all of the hydrogen is atomic. When the extinction is greater than 1 mag, almost all of the hydrogen is molecular. This explains the breakdown in the relationship between NH and AV above 1 mag.

Despite the important role that dust plays in the formation of the most abundant molecule H2, most of the interstellar chemistry cannot proceed in this way. Many of the molecules are formed in the gas. At the beginning of this section we calculated a very low rate for two atoms to collide in the gas to form a molecule. However, the densities in molecular clouds are at least 103 times those we used for our estimate, and the reaction rates go as the square of the density. Therefore, the reaction rates in molecular clouds are much faster than our initial calculation suggests. There is also another factor that increases the cross section for collisions if one of the reactants is an ion and the other is a neutral. Such a reaction is called an ion-molecule reaction.

Electrical Force

Electrical Force

Motion of Molecule

Motion of Molecule

Fig 14.17.

Dipole in an electric field. In this case, the electric field is provided by the positive charge, and weakens with distance from that charge.The negative end of the dipole is closer to the positive charge, so an attractive force felt by the negative end is greater than the repulsive force felt by the positive end.The dipole is thus attracted to the charge. (The same thing would happen with a negative charge.)

To see how the rate is enhanced, let's consider the case of a positive ion (as shown in Fig. 14.17). We have already said that the grains must be negatively charged, so the gas must be positively charged. In addition, Table 14.1 shows that many positive ions have been detected. The neutral atoms can still have an electric dipole moment, even though it has no net charge. The dipole will tend to line up with the electric field of the ion. Since the ion is positive, the negative end of the dipole will end up closer to the ion. The negative end of the dipole will therefore feel an attractive force which is slightly greater than the repulsive force felt by the positive end, which is farther away. The dipole will feel a net attractive force. This attractive force significantly increases the effective cross section of the reactants and speeds the reaction.

Theoreticians have tried to identify the chemical reactions that might be important in the interstellar medium. They then carry out model calculations in which they calculate the equilib rium abundances of various molecules. These are the abundances for which the rates of destruction and formation are equal. These theories have been quite successful at predicting the abundances of most of the simpler (especially two- and three-atom) molecules. More work is still needed for the heavier molecules. In addition, it may be that many interstellar clouds are not old enough to have reached an equilibrium situation. If that is the case, the abundances should still be changing.

14.5.3 Observing interstellar molecules

When we observe interstellar molecules, we are not observing transitions in which electrons jump from one level to another. Such transitions do exist for molecules, as they do for atoms. However, they require energies of the order of at least a few electron volts and are in the visible part of the spectrum. These transitions are not easily excited in the cool interstellar medium. Another type of transition in molecules, involving lower energies, is vibrational. We can think of a molecule as consisting of a number of balls connected by springs. The springs can stretch and bend at certain frequencies, with certain energies. Transitions between vibrational states are possible. The energies associated with vibrational transitions usually place the resulting photons in the infrared. This is still too energetic for the cool clouds.

There is another type of transition, with even lower energies. It involves the rotation of the molecules. The rotational motion is also quantized and transitions among rotational states can take place. The photons associated with these transitions are generally in the radio part of the spectrum. To see what the energy levels look like in this case, we consider a diatomic molecule (such as CO), rotating end-over-end about its center of mass. The rotational inertia is I. If the molecule is rotating with an angular speed m, the energy is given by

The angular frequency can be expressed in terms of the angular momentum L as

Using this, equation (14.19) becomes

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