The correct answer is : en

Il y a eu trois explosions en une journée.

It should be : en

Not : dans

For dates we uses : en

Example : en 1992 not dans 1992

With une journée (one day), en is expected:

Il y a eu trois explosion en une journée. (… in one day)

En is used here to specify the amount of time that was necessary for the three events to occur.

However, if the last part of the sentence had been la journée, dans would have been used:

Il y a eu trois explosions dans la journée. (… during the day/through the day)

Dans means here "inside", not inside a given space which is the main acception for dans but inside a given period of time.

See the very same difference in these sentences:

La petite aiguille fait 24 fois le tour du cadran en une journée.

The minute hand makes 24 turns of the dial in one day.

Il y a 24 heures dans une journée.

There are 24 hours in one day.

Similarily:

Il y a eu trois explosions en vingt-quatre heures. (… during a period of 24 hours)

Il y a eu trois explosions dans la même journée. (… in a single day)

Note that dans can also be used to tell the time that will elapse before some event occur:

Dans trois jours, on vide la piscine.

Three days from now, we’ll empty the swimming pool.

En trois jours, on vide la piscine.

To empty the swimming-pool, we need/take three days.