Specifying Thumbnail that Displays on Facebook When Somebody Likes My Post

I have this problem on several sites. I am using both the Socialize plugin and Facebook Like Button on different sites. My problem is that when people like a post that does not have an image added to it, Facebook is displaying a random image from my sidebar that is totally inappropriate. If the post contains an image, it shows the thumbnail of that image, so it’s only a problem for posts without an image. Is there a way to specify a site-wide default thumbnail that would be posted on Facebook for posts that don’t include an image?

Thanks for any help you can give.