how deep are the alantic and pacific oceans?

The Mariana Trench is the deepest part of the Pacific Ocean at 35,827 ft.
The Puerto Rico Trench is the deepest part of the Atlantic Ocean at 30,246 ft.
The average depth of the Atlantic is 10,932 ft.
The average depth of the Pacific is14,000 ft.

Challenger Deep got its name from the British survey ship Challenger II, which pinpointed the deep water off the Marianas Islands in 1951. Then in 1960, the US Navy sent the Trieste (a submersible - a mini-submarine designed to go really deep) down into the depths of the Marianas trench to see just how far they would go (read the original press release). They touched bottom at 35,838 ft/10,923m. That means, while they were parked on the bottom in the bathyscaphe, there were almost seven miles/11km of water over their heads!

Water depths of more than 8 km (5 mi) make the Puerto Rico Trench the deepest part of the Atlantic Ocean. It is less deep near the Lesser Antilles, where the component of subduction is larger.

Did you mean at its deepest sections?

Puerto Rico Trench- Atlantic - 8,428 Meters
Marianas Trench- Pacific- 11,033 Meters

The planet is approximately 71% water and contains (5) five oceans, including the Arctic, Atlantic, Indian, Pacific and Southern.

(deepest oceans and seas)

#1 Pacific Ocean (35,837 ft) (10,924 meters)
#2 Atlantic Ocean (30,246 ft) (9,219 meters)
#3 Indian Ocean (24,460 ft) (7,455 meters)
#4 Caribbean Sea (22,788 ft) (6,946 meters)
#5 Arctic Ocean (18,456 ft) (5,625 meters)
#6 South China Sea (16,456 ft) (5,016 meters)
#7 Bering Sea (15,659 ft) (4,773 meters)
#8 Mediterranean Sea (15,197 ft) (4,632 meters)
#9 Gulf of Mexico (12,425 ft) (3,787 meters)
#10 Japan Sea (12,276 ft) (3,742 meters)
http://www.worldatlas.com/aatlas/infopage/deepest.htm