Only possible if you are using NBU Vault option to eject or else if you have volmgr/debug logs enabled. Should be in robots log.
For tapes ejected using the vault - set it up to email you and keep them - that makes it much easier to find tape movement to and from Iron Mountain. We audit and match up EVERY tape at least once a year.
There have been several times that Iron Mountain has added the L# to the end of our tape VOLSER and then not been able to find it in their system. Being able to tell them the slot and date made the difference in passing our audits.
For manual ejects, I defined a script so that I create an eject list text file and then I run the eject script, which copies the eject text list to an archive directory. I usually am only doing this for tape destruction though. Mostly I use vault.