Estimate the voltage you need with this appartus to ionize the atom

In summary, when trying to ionize an atom using a field, the dipole moment must be minimal in order to avoid excessive deformation.
  • #1
stunner5000pt
1,461
2
A hydrogen atom (with Bohr radius of half an angstrom) is situated between 2 metal places 1 mm apart which are connected topoosite terminals of a 500 V battery.
What fraction of the atomic radius does the separation distance d amount to, roughly?

Estimate the voltage you need with this appartus to ionize the atom



For the first part the radius is [itex] 5 \times 10^{-11} m[/tex]
the distance between the plates is 0.001 m
divide [itex] 5 \times 10^{-11} m/ 0.001 m = 5 \times 10^{-8} [/itex]

so far so good, right?

for the second part... since the atom is polarized it has a tiny dipole moment [itex] \vec{p} = \alpha \vec{E} [/itex]

[tex] p = qd = \alpha \frac{V}{d} [/tex]
so [tex] V = \frac{ q d^2}{\alpha} [/tex]

is that correct??

thank you for your input!
 
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  • #2
The argument is not all bad imho, but aren't you confusing the use of symbols here? You haven't defined 'd' in the statement of the problem (:mad: ) but I suspect it is just the distance btw the plates. If we call [itex]\vec{\delta}[/itex] instead the distance caracterizing the dipole moment, we have

[tex]\vec{p}=\alpha\vec{E} \Rightarrow q\delta = \alpha E \Rightarrow V=\frac{qd\delta}{\alpha}[/tex]

and now what? Well we could say that we want V to be such that it induces a dipole moment [itex]q\delta[/itex] such that the work done on the electron in moving a distance [itex]\delta[/itex] parallel to the field is 13.6eV, the ionization energy of the hydrogen atom. So in the end, we need V to be

[tex]V=\frac{qd(-E_0d/qV)}{\alpha}[/tex]

(E_0=-13.6eV)

This argument has a problem though. It is that the proportionality relation btw the field and the induced dipole holds only for weak fields, such that the deformity is not extreme, as it is in this case since we're literally ionizing the thing.

If I were you I would keep thinking for another way of going at this that does not come with such a defect.
 
Last edited:
  • #3
im sorry i didnt define d, sorry

well if we're going to ionize an atom (like hydreogen) what is the minimum value of dipole moment :confused: if that exists?
 
  • #4
How do you mean "minimal value"?

When there is no field, there is no external, there is zero dipole moment, is that what you mean?
 
  • #5
i can see the problem... but i think they are only caring about small pertubations at least with the tools we are given...
 
  • #6
ionization is not a small perturbation.

which implies maybe you ought to find a whole other route to the solution.
 

1. What is the purpose of ionizing an atom?

Ionizing an atom is the process of adding or removing one or more electrons from an atom, resulting in a charged particle called an ion. This is often done in scientific experiments to study the properties and behavior of atoms.

2. How is the voltage needed to ionize an atom determined?

The voltage needed to ionize an atom depends on the energy required to remove an electron from the atom's outermost shell. This is known as the ionization energy and can be calculated using the atomic number and electron configuration of the atom.

3. What factors affect the amount of voltage needed to ionize an atom?

The amount of voltage needed to ionize an atom can be affected by the type of atom, the number of electrons in its outermost shell, and the distance between the nucleus and the outermost shell. Other factors such as temperature and pressure can also play a role.

4. Can the voltage needed to ionize an atom be estimated without experimental data?

Yes, the voltage needed to ionize an atom can be estimated using theoretical models and calculations based on the atom's properties. However, experimental data is often needed to confirm these estimates.

5. Is there a standard voltage needed to ionize all atoms?

No, the voltage needed to ionize an atom can vary depending on the atom's properties. Some atoms may have a lower ionization energy and require less voltage, while others may have a higher ionization energy and require more voltage.

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