I want to be more personal because your first death is going to be personal, no matter how hard you try to make it professional and there's nothing wrong with that.
Nobody can really prepare you for your first death, not fully. It does help to hear about someone elses experiences first though, so hear goes... My first death occured on my second placement, there hadn't been any on my first placement because it was a planned surgical ward so people who came in were there for elective surgery and therefore not too ill. Anywho, my first experience with death. This patient, let's call him Mr X, had been on the ward for a while and was gradually deteriorating. He had been poorly for a long time but he was always happy to chat and was in great spirits at all times. Everybody (including Mr X) knew that the end was coming so we were all trying to get it sorted so he could go home and have a peaceful and quiet death. One morning Mr X seemed to be in really high spirits, I had looked after him and helped him with his breakfast, he was happy because he was meant to be going home that afternoon. Unfortunately at about midday he took a turn for the worst, and I held his hand while he died, his wife had been rung to tell her that he might not make it, but she didn't make it to him on time. Me and another student, along with my mentor gave him his last offices after his family had spent their time with him. Last offices is where you wash a patient and wrap them up ready for them to go to Rose Cottage (the mortuary). It helps to talk to the patient through the process just to preserve their dignity and make sure everything is done as best as possible. I didn't cry whilst giving Mr X his last offices but it really affected the other student. This goes to show that no 2 people will have the same experience with death, whether it's their first or their twentieth death. I was thanked by his family for being there while he died and later on that evening I got home and cried until I couldn't cry anymore. It really affected me when I got home.
If any other Student nurse/ nurse/ healthcare worker has an experience with death that they'd like to share i'd really love for you to share it in the comments. I think anyone who hasn't experienced it can gain a lot from hearing about someone elses just so that they know how they're reacting isn't wrong. A third year student told me how she dealt with it when someone died on her placment and it made me feel like less of a wimp.

