Newbie question: Can Intel run 64-bit LINUX?

I have a 8 month notebook, 2GB RAM, with an Intel Core2 CPU T7200.

I am sure this can run RHEL 4, 64-bit LINUX but unfortunately my IT
department is convinced that it is only a 32 -bit processor and cannot
run 64-bit LINUX. :(

I tried the list of certified computer on Redhat.com but all I could
see is RHEL 5 systems.

Does RHEL 5 imply 64 bits or does 32 and 64 bit versions of RHEL 5
exist?

Does any body have another document somewhere that clearly outlines
what Intel Processors can run 64-bit LINUX?

Is this perception that current Intel chips cannot run 64 bits LINUX
very common?

thanks!

.

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