The correct answer is option 3: at ocean bottoms. The Earth`s crust is the outermost layer of the Earth, and it is divided into two types: continental crust and oceanic crust. The continental crust is thicker than the oceanic crust.

Option 1, under the mountain ranges, is not correct because mountain ranges are formed by the collision of tectonic plates, and these collisions often result in the thickening of the Earth`s crust rather than thinning it.

Option 2, under continental masses, is also not correct because, as mentioned earlier, the continental crust is thicker than the oceanic crust.

Option 4, at mid-oceanic ridges, is incorrect as well. Mid-oceanic ridges are underwater mountain ranges formed by the tectonic activity where new oceanic crust is being created through volcanic activity. While the crust is thinner near these ridges, it is actually the thinnest at the ocean floor, not specifically at the ridges themselves.

In conclusion, the thinnest part of the Earth`s crust is found at ocean bottoms.