Well, you know the drive is SCSI-2 and the specs of the card are on the Adaptec Web site... The 2940U has 50-pin connector, the 2940UW has 68-pin. The UW will work with your drive, but you'll need a 50 to 68 pin adapter for the drive end (assuming the drive has a 50-pin connector).
I'd also prefer an external HD for backup anymore. Most tape is as dead as floppy drives. Backups are no good if they don't get done, anything that slows the process increases the chance they won't be done...
scsifaq.org has a lot of basic SCSI info. Perhaps since you seem not to already know what UW means, then perhaps SCSI isn't something to get involved with at this time.
And who knows how much data you need to back up. Have you considered how much a tape costs relative to good sized hard drives? And new tape sets (you'll want more than one set for best reliability) will be an annual expense, while you should get a good three years out of a top brand hard drive. I think if you thoroughly examine all the costs involved with SCSI tape, you'll find it comes out way higher than with an external HDD (even though you may be getting the tape drive for free - which I'm guessing is the only reason that the SCSI adventure came up anyway). Be aware that the compressed capacity of a tape (24GB max for this drive) is hardly ever achieved in the real world so you may get only 18GB per tape max. Totally impractical for backing up any modern sized hard drive...
Really consider all the angles and consequences before spending any money on this already obsolete tape format.
.bh.