Very small. The radiation is shielded by all the water that is around it. As a rule of thumb... for every 2 feet of water, the amount of radiation is reduced to about 10%. (so for 4 feet of water it's reduced to 1% of it's original value) As long as the core is intact and surrounded by water, almost none. There are a wide range of variables, like what happened when the boat went down. Did it implode? Crash into the bottom at speed? Usually, even if implosion and a crash occur, the danger isn't great. Far and away the greatest radiation hazard is from damaged and leaking fuel elements. They'll put nasty stuff into the water, but they're pretty safe welded into a core assembly and stuck inside the pressure vessel.
Submarines do get sunk in the sea.
54
It was sunk by German u-boats (submarines).
The British lost 76 submarines during WWII.
There were no submarines sunk or damaged during the attack on Pearl Harbor; all vessels either sunk or damaged were capital ships (battleships, cruisers, etc.) or support vessels (tenders, tugs, etc.).
Mercury used as ballast
The Lusitania.
Counting warships & merchantman, US subs sunk about 1,000 vessels.
52 subs were sunk (lost).
4,837
These merchantmen are KNOWN to be sunk by Japanese submarines during WWII off the US West Coast (there are several others sunk by explosions, but cannot be verified as sunk by submarines):1941 - Emidio, tanker, torpedoed1941 - Montebello, tanker, torpedoed1942 - Coast Trader, freighter, torpedoed1942 - Larry Doheny, tanker, torpedoed
One accidental loss in the Atlantic; and 51 other subs sunk through out the Pacific; from south of the equator all the way towards Alaska and Japan.