It’s rather the graphics card and driver, not the processor. (EDIT: I have Core 2 Duo, too, but with a much newer Nvidia card. Works well in Kubuntu with Nvidia proprietary drivers.)
Most low power notebooks have the “graphics card” included in the cpu. Especially if it is an intel cpu.
[daniel@hardwork ~]$ lspci | grep VGA
00:02.0 VGA compatible controller: Intel Corporation Mobile 945GM/GMS, 943/940GML Express Integrated Graphics Controller (rev 03)