Why do individual helium atoms rise? Balloons full of helium rise because the buoyant force is great than the gravitational force and the buoyant force is due to a pressure difference between the top and bottom of a ballon but why exactly does a individual helium atom rise?
 A: The probability that an energy level, $E$, is occupied is given by the Boltzmann factor:
$$ P\propto e^{-\frac E {kT}} = e^{-\frac{mgh}{kT}}$$
where $m$ is the species mass. The scale height is then:
$$\bar h = \frac{kT}{mg}$$
For ${\rm N}_2$ you around 8,000 meters, while helium is 7x higher. Oxygen ($m\approx\,$32) is even lower at 7200 meters, so in the death zone (above 8000m) alpinist have less the $1/e$ the oxygen available at sea level.
A: Are you asking about an individual helium atom within the balloon?
If so, then the reason for this is rather simple. As you point out, there is an uneven distribution of pressure on the surface of the balloon. When integrated, that means unbalanced forces. So the "first" thing to rise is the balloon - the rubbery thing - itself. The moment this happens, the helium atoms inside are still just flying around as they usually would, in various random directions. But they are confined by the balloon material, and now from their point of view, the bottom of the enclosure has started to move up.
Hence, the bottom of the balloon will - quite soon - collide with some helium atoms. That sends them reeling back upward, where they then strike others, also sending them on an upward course. As the balloon continues to accelerate up, it strikes more and more atoms and this likewise impedes the ones further up to move even faster upward. As a result, the momentum gained by the balloon enclosure transfers to the gas atoms within, and the gas is impelled to move along with it in the upward direction.
A: The_Sympathizer gives a great answer to why the atoms in a balloon rise.  The lift doesn't come from the helium inside but from the atmosphere outside. If the balloon's surface were rigid so it occupied the same volume regardless of its contents, one would find that an empty balloon would have a net upward force on it greater than one filled with helium. They have the same upward buoyant force by the atmosphere but the empty balloon's weight is less.
JEB gives a great answer to why helium atoms in a gaseous mixture are disproportionally at the top. All the gas particles have the same KE on average because all the components of the mixture are at the same temperature. Less massive gas particles have greater speeds on average and achieve greater altitudes.
A: One thing to remember is the speed that the gas molecules travel is inversely related to the molecular mass. For example the average molecular speed is
v = (8kT/(pi*m))^0.5
[I don't know how to do math text]
Therefore the very light helium atom will have a higher average speed than nitrogen or oxygen.  In a gravity field, this tends to make it rise higher. In fact, hydrogen and helium are so light that this average speed is higher than the escape velocity of the Earth.   So the upper fringes of the atmosphere have huge concentrations of these gases, and the atmosphere is constantly losing a small trickle of its total H2 and He to space.
