Week 9 (Dec 5) In-Class Problem

Due Dec 9, 2022 by 11:59pm
Points 10
Submitting a text entry box or a file upload

Molecules: $H_2$ Formation

Part 1:

Write down the three equations that will give you the volumetric rates of each reaction, separately, in units of $LaTeX: cm^{-3}\:s^{-1}$ $cm^{-3}\:s^{-1}$ .

Part 2:

Set up the rate balance equation that will give you the steady-state ratio of $LaTeX: \frac{n\left(H^-\right)}{n_H}$ $\frac{n\left(H^-\right)}{n_H}$ and solve for this ratio at 100K.

Part 3:

What fraction of the LaTeX: H^- $H^-$ ions undergo the associative detachment reaction?

Part 4:

The rate coefficient for the formation of LaTeX: H_2 $H_2$ via the LaTeX: H^- $H^-$ channel is just $LaTeX: R_{H^-}\:\equiv\frac{\kappa_{ad}n\left(H^-\right)}{n_H}$ $R_{H^-}\:\equiv\frac{\kappa_{ad}n\left(H^-\right)}{n_H}$ , where this value is evaluated at the steady-state ratio you determined in Part 2.

Evaluate this rate coefficient, and compare it to the empirical rate coefficient for the formation of LaTeX: H_2 $H_2$ via dust-grain catalysis, $LaTeX: R_{dc}\approx3\:\times10^{-17}\:cm^3\:s^{-1}$ $R_{dc}\approx3\:\times10^{-17}\:cm^3\:s^{-1}$ .

Part 5:

If the value for $LaTeX: R_{H^-}$ $R_{H^-}$ actually has a temperature dependence of $LaTeX: T^{0.67}_2$ $T^{0.67}_2$ , where $LaTeX: T_2\:\equiv\frac{T}{100\:K}$ $T_2\:\equiv\frac{T}{100\:K}$ , what is the temperature of gas in which $LaTeX: R_{H^-}\:=\:R_{dc}$ $R_{H^-}\:=\:R_{dc}$ ? Is this physically plausible for the neutral ISM?