Polarization Problem: Estimating Voltage Needed to Ionize Hydrogen Atom

[pt176900]

a hydrogen atom (with radius of one half angstrom) is situated between two metal plates, 1mm apart, which are connected to opposite terminals of a 500V battery. What fraction of the atomic radius does the separation distance d amount to, roughly? Estimate the voltage needed to ionize the atom.

I understand that the battery will induce an electric field between the plates, which will cause the atom to become polarized. If this field is strong enough, then the electrons will be ripped from their orbits. What I don't know is how to go from the 500V to the electric field.

someone shed some light on this, please :)

 

[kuruman]

For a parallel plate capacitor, the electric field $E$ in terms of the plate separation $d$ and the potential difference $V$ between plates is given by $E=\frac{V}{d}$. Here, $E=5\times 10^5~ \mathrm{V/m}$.

 

[Charles Link]

Some additional introductory material might be in order here: With plasma lamps, generally, it takes a voltage on the order of kilovolts to get an electric arc established in a gas, but once that occurs, the voltage necessary to maintain that arc is just slightly above the ionization voltage, which in this case is 13.6 volts. It will be interesting to see if the calculations show that 500 volts over a distance 1 mm might be able to ionize hydrogen.

 

[kuruman]

Good point and thanks for the follow up.