I assume you have RewriteEngine On somewhere in the file too? The QUERY_STRING variable doesn't contain the question mark so drop that from the RewriteCond. If you are placing these directives in a .htaccess file, then also remove the forward slash from the /home part in your RewriteRule (if you are placing it in the VirtualHost however, it should be there). You should probably escape the dot in the RewriteCond by adding a forward slash to the start of it. Other than that you should be good to go.
If you still get the 500 server error then perhaps mod_rewrite isn't enabled. You can check by wrapping your rewrite directives in an IfModule block,
It won't make it work, but if it stops your server from crashing then you know mod_rewrite isn't enabled.
# your code here
On a side note, I generally find that it's best, when working with rewrites, to always use 302 status code. Once you are happy everything works OK, you can change it to a 301, but testing with a 301 is a pain because your local DNS / browser can cache the redirect meaning you may not be seeing what your current code is really doing.