Will an accelerating potential accelerate a neutral atom? For example, consider an atom of hydrogen subjected to an accelerating potential of $V$. As the kinetic energy of a particle accelerated by a voltage is given by $qV$, where $q$ is the charge on the particle, won't the kinetic energy of the hydrogen atom be 0 as it is neutral? Does this mean it won't have any velocity?
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A hydrogen atom consists of an electron and a proton. In a uniform field $E$ the force on the electron will be $+eE$ and the force on the proton will be $-eE$ to the two forces sum to zero. A hydrogen atom is not accelerated by a uniform field.
However if the field is non-uniform the atom can be accelerated. This is because the hydrogen atom is polarisable and when an external field is applied the average position of the electron is shifted slightly relative to the proton.
Suppose we have a non-uniform field with a field strength given by:
$$ E = A + Bx $$
with $x$ being distance. The field will polarise the hydrogen atom and cause the average position of the electron to shift by a small distance $d$. If we take our origin for $x$ to be at the proton that means the force on the proton is $-eA$ while the force on the electron is $+e(A + Bd)$ and there is a non-zero net force on the atom of $Bd$. The atom will accelerate at $a=Bd/m$.
In practice a hydrogen atom is not very polarisable, and to achieve any measurable acceleration would require an enormous field gradient. However in principle it can be done.
John Rennie
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