SSD Vertex 4 in MacBook Core 2 Duo

Hi Guys

I have a 4 Years old Macbook (white) Model nr. A1181 with a 2.4 Ghz Processor. I would like to upgrade my Macbook with a Vertex 4 256gb. Would it Work? I see i can buy a Vertex 3 "only for macbook" ([linked product missing or disabled: IF107-085]) But 120GB is not as much and the price is high.

best regars, nax