Why a helium balloon that rises into the atmosphere will eventually burst.

, a balloon filled with helium floats because of the air and helium density. Since the weight of helium is less than the wieight of air if you take the same volume of both, then the baloon will float. When you fill the balloon with helium, you need a helium pressure equal to that of air at the ground level. In order to know the air pressure on the ground level, you have to know the how high the atmosphere goes. 

The air pressure as in any fluid correspond to the next equation. 

Pressure=density*gravity acceleration*profoundity 

of course, the higher you get, the gravity's acceleration and profoundity will be lower, so the air pressure will be lower. 

At certain height, the air that surrounds the balloon will be much lower than the pressure of the helium inside the balloon. This difference makes the helium make force to get out of the balloon and the bigger the difference of pressure, the bigger the force is. 

When the force is big enough, the material of the balloon won't resist anymore and it will end up bursting. 

hope this helps.