# Is there a limit to the height to which a helium balloon can rise?

My professor's answer to this is "It will rise until the weight of air displaced equals the mass of the balloon". I am a bit confused by this. Wouldn't it depend on densities rather than weights and masses? I thought it will keep rising till the density of air is the same as helium. Can anyone point out where I am wrong?

• You are correct in only if the weight of the balloon material is negligible. Jan 2 at 22:12

You are correct that the balloon will keep rising until the density of the air equals the density of the helium in the balloon. But since $$W=\rho g V$$ the weight $$W$$ of the volume $$V$$ of air displaced by the equal volume of helium will also be the same as the weight of the helium (neglecting the weight of the balloon material) when the densities $$\rho$$ are equal .