why is time machine crashing my computer?

After visiting an Apple Genius Bar this morning and, as a result, purchasing an esternal hard drive to back up my computer using Time Machine, I am having issues.

I have around 500GB to back up, but each time it reaches 947Mb (or about that), I get a kernel panic restart.

It has happened 4 times so far...

I am not sure where to from here? I am using an early 2011 Macbook Pro, with OS X 10.6.8

thanks