Yamato Cannon deals 300 damage and Immortals have 100 shields and 200 hit points, but they also have a hardened shield ability that reduces incoming damage greater than 10 to 10. However, I am not sure if this applies to Yamato Cannon or if Yamato Cannon does reduced damage because of armor/shields.
The Battlecruiser's Yamato Cannon will ignore the Immortals special ability and kill it in one shot.
I made this video to show it in action:
It also ignores armor, even with 3 in shield and armor the Immortal will be killed in 1 shot.