Science Question Help!! Which planet...?

Since Venus has the longest rotation period of any planet, approximately 243 days, the result would yield the longest periods of darkness to the surface.
Also, URanus muahahah.

This isn't something that you need to find in a book.

All you need to remember is that day and night on a planet is due to the planet's rotation.  So the planet that rotates the slowest will have the longest night.

So all you have to find is how long it takes each planet to rotate once.
Here are a few to get you started:
- Earth - 24 hours
- Mars - 24.6 hours
- Jupiter 9.9 hours

The planet Uranus has an Axis Tilt of 97.7°, meaning the rotational axis is nearly in the plane of the planets orbit around the Sun.  The result is that when one of the poles is point in the direction of the Sun its opposite pole is in long period darkness that can last up to half the planet's orbital period.  The duration of the darkness depends on the latitude or distance from the planet's equator.  Since the orbital period of Uranus is 84.323 326 years, the dark period at the pole can last for half an orbit or approximately 42 years.

Read more at http://en.wikipedia.org/wiki/Uranus

The planet with the longest night is Venus; a night on Venus takes 243 Earth days. (A night on Venus is longer than its year; a year on Venus takes only 224.7 Earth days).

They used to think Mercury was in a tidal lock with the Sun (that is, same side always faces the Sun), but beginning in 1965, radar mapping of Mercury revealed that it had a 3:2 resonance, and that  night on Mercury lasts 176 Earth days.

Pluto.