# 20.181:hw11 sols

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## Revision as of 18:03, 11 December 2006

**Solutions to HW 11**

Part 1:

To complete the code shell provided, you had to insert something like the following code snippet:

tau_new = (a_i_old[rxn] / (a_i_new[rxn]+eps)) * (tau_i[rxn] - t_cur) + t_cur tau_i[rxn] = tau_new a_i_old[rxn] = a_i_new[rxn]

note that you can't update a_i until after you've calculated a new tau.

Part 2:

An easy way to solve this question is with dimensional analysis. If you've never heard of dimensional analysis before, it's essentially a fancy way of saying: manipulate the data to produce a value with the correct units; more often than not, this value will also be the correct quantity.

For instance, we know that we're trying to calculate the probability per unit time that a particle collision causes a reaction. Our solution should therefore be in units of [1/time] (probabilities are unitless!).

There is only one way to combine the given data so as to produce our desired units: