# Why does $H_2$ form on such a long time scale?

If we were trying to figure out the time scale for a gas-phase reaction between two hydrogen atoms in a molecular cloud (which has density $~10^4/$cm$^3$), apparently the reaction would happen on a time scale proportional to the inverse of the density multiplied by $10^{15}$ years. Aside from the cloud not being dense and the probability that a collision will surpass the activation energy is small, is the time elongated because you need to induce a dipole moment between two hydrogen atoms to actually bind them together?

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## 1 Answer

The rate of formation is much higher in the presence of dust. There needs to be a mechanism for the energy of formation of the hydrogen molecule to be dissipated. Dissipating energy via a photon involves a forbidden transition. Instead, the energy can be transferred to the vibrational lattice of a dust particle.

See The Interstellar Abundance of the Hydrogen Molecule. I. Basic Processes for a detailed explanation.

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