How much copper thermite should I use to light a particular size of motor?
How much thermite is needed to light a given motor is NOT a completely "settled" subject; there is still room for experiment and debate.
A general rule of thumb that has been used, successfully, by quite a few rocketeers is to use approximately one gram of copper thermite for every 1000 Newton-seconds of total impulse. So, for a K motor (between 1280 and 2560 N-s), use between 1.2 and 2.5 grams of copper thermite. (An Aerotech K550, with about 1500N-s of total impulse, will light instantly with 1.5 to 2.0 grams of copper thermite.)
Experience has proven that the exact total quantity of thermite used is not terribly critical, as long as it's "in the ballpark": The range of quantities that can work well in a given motor is quite wide -- often 50% more or less will both work fine.
It appears that the reason for this wide range of "successful working quantities" is the fact that the reaction products are all liquids or solids; without any gaseous products, there is very little risk of over-pressurizing the motor core. As long as you meet a minimum threshold of "hot copper droplets impacting the motor core", you'll light the motor. After that, up to a certain point, more copper thermite just results in more copper being pushed out the nozzle to deposit upon the blast deflector.
(Of course, if you WAY overdo it, you can clog the nozzle with slag, or penetrate too deeply into the surface of the propellant, resulting in a motor cato. It is generally quite difficult to do this, however -- in many cases, using 4 or 5 times more thermite than necessary to light a motor will NOT result in any problems.)
From a purely physical standpoint, motor core interior surface area and volume are probably the most significant factors determining how much thermite is "enough". However, due to the fact that motor volume scales roughly with total impulse, and interieor surface area of BATES grains scales roughly with the 2/3 power of total impulse, using a rough measure based upon motor total impulse is a reasonable thing to do -- espescially since there is little risk of problems from "over-thermiting" a motor.
Experimentation and data collection to determine the smallest thermite charges necessary to reliably and instantly light particular motors is a very worthwhile avenue for research. More data would be greatly appreciated!