The part of the Earth that contains mountains and valleys is called the Earth's surface or the crust.

Here's why:

* Crust: This is the outermost layer of the Earth, and it's what we walk on. Mountains and valleys are formed by geological processes that affect the crust, such as tectonic plate movement, erosion, and volcanic activity.

* Earth's surface: This refers to the visible, physical surface of the Earth, which includes all its landforms, like mountains, valleys, plains, deserts, etc.

So, while the crust is the specific geological layer, the Earth's surface is the more general term that encompasses all the features we see, including mountains and valleys.