The first technology, Atomic Research, gives a +4% research speed bonus.
The second technology, Nuclear Reactor, unlocks the state level building titled "Nuclear Reactor" which can be found in the Construction screen. Built nuclear reactors provide the state with enriched uranium for use in nuclear weapons, but have no effect without the requisite technology to make nuclear bombs.
The final technology, Nuclear Bombs, allows the country to produce and stockpile nuclear bombs. Each reactor will provide approximately 1 bomb per year. The bomb production progress can be seen via a slowly progressing percentile bar.
It is possible to speed up research by:
Employing a theorist with either the Nuclear Scientist or Nuclear Enthusiast trait.
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units in the province take a random percentage between 10% and 90% of their current strength and organisation as damage
all province buildings get reduced to 0 HP
all state buildings are reduced to a random level below their current undamaged level (damaging airports also destroys airplanes located there)
the controller of the target province loses up to 20% war support. If the largest victory point in the state is smaller than 3 or the undamaged infrastructure is lower than level 10, the effect is proportionately lower respectively.
The first use, as well as uses on specific (capital) cities, will result in news messages, however those are purely informational
After the 2nd nuclear bomb has been dropped on a Japanese core state, Japan has a special decision for surrender (note: prior to dropping the 2nd nuclear bomb, Japan's navy must be reduced to less than 40 ships and Japan must not be the controller of Okinawa or Iwo Jima)