Spock Prime shows Kirk what happens, with Kahn, with the fallen Enterprise, with Spock.
He watches Spock die and he realise how important he will be for him in the future,
how important he will be for Spock, he knows what is going to happen and he refuses to accept that, he can't let that happen, not to Spock, because Spock is his everything
so he goes to the radiation core alone and wenn Spock finds him, he dies with a smile on his face because he saved Spock