According to Archimedes' principle, the buoyant force on an object in a fluid is equal to the weight of the fluid displaced by the object. For a balloon to float, the buoyant force must be greater than the weight of the balloon and its contents.

When a balloon is filled with helium, the helium displaces air, which is heavier than helium. This creates a difference in density between the balloon and the surrounding air, which results in a net upward force that causes the balloon to float.

If a balloon is filled with a vacuum, there is no gas inside the balloon to displace air. This means that the density of the balloon and its contents is greater than the density of the surrounding air, resulting in a net downward force that will cause the balloon to sink.