Estimate the E-field required to ionize Hydrogen

In summary, the question is asking for the E-field required to ionize Hydrogen in a time similar to the electron's orbital time in the n=1 ground state. One possible approach is to relate the required E-field to the energy of a charged particle and use an equation that includes time in the ionization process. The given attempt at a solution calculates the electron's orbital time and mentions equating forces to get an estimate for E-field, but this approach does not consider the time requirement specified in the question. The course for which this question is relevant is not specified, but it could potentially pertain to either electromagnetism or quantum mechanics.
  • #1
Poirot
94
3

Homework Statement


Estimate the E-field required to ionize Hydrogen in a time comparable to the time taken for the electron to orbit the nucleus. (n=1 ground state) (hint: relate the required E field to the energy of a charged particle)

Homework Equations


F = mv^2/r (rotational)
F = Ze^2/Kr^2 (Coulombic)
F = eE (Lorentz)
W = F.s ?

The Attempt at a Solution


I have calculated the time it takes for the electron to orbit the nucleus
T = 1.52 x 10^-16 secs
using the rotational force and then solving for v and plugging it in T=2pi r/v with r being Bohr radius.

I'm just not sure what else to do? I can get an estimate just just equating the forces and solving for E but that doesn't take into account the time which is specifically asked for?

Thanks in advance!
 
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  • #2
For what course is this? Electromagnetism or quantum mechanics?

You would need an equation for ionization that includes time.
 

FAQ: Estimate the E-field required to ionize Hydrogen

What is the E-field required to ionize Hydrogen?

The E-field required to ionize Hydrogen is approximately 13.6 electron volts per atom. This value is known as the ionization energy of Hydrogen and is the minimum amount of energy needed to remove an electron from a Hydrogen atom.

How is the E-field related to the ionization energy of Hydrogen?

The E-field is directly proportional to the ionization energy of Hydrogen. This means that as the E-field increases, the ionization energy also increases.

Can the E-field required to ionize Hydrogen vary?

Yes, the E-field required to ionize Hydrogen can vary depending on factors such as temperature and pressure. Higher temperatures and pressures can lower the amount of E-field needed for ionization.

What is the significance of estimating the E-field required to ionize Hydrogen?

Estimating the E-field required to ionize Hydrogen is important for understanding the fundamental properties of atoms and molecules. It also has practical applications in fields such as plasma physics and atomic spectroscopy.

How is the E-field required to ionize Hydrogen measured?

The E-field required to ionize Hydrogen can be measured using various experimental techniques, such as photoionization spectroscopy or electron energy loss spectroscopy. These methods involve exposing Hydrogen atoms to different E-field strengths and measuring the ionization energy at each strength.

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