How to gain percentage of atoms that are ionized in balloon?

[TwoEG]

Homework Statement

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You have two inflated balloons. You rub them against your hair and hang them as shown in the figure. The length of the strings is 50 cm and the angle between them is 50°. For each balloon, what is the percentage of atoms that are ionized? Provide a rough estimate. You may find necessary information from the internet.

Homework Equations

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Coulomb's law

The Attempt at a Solution

I've tried to find a information about that underlined sentence, but I couldn't find any meaningful information that I can apply to this problem. Is there any formula type relationship between electric force and 'percentage of atoms that are ionized in object'?

 

[haruspex]

s there any formula type relationship between electric force and 'percentage of atoms that are ionized in object

No, it is up to you to figure it from first principles.
Suppose each balloon has mass m. What is the electrostatic force that would maintain them at that angle?
How many one electron charges (whether all positive or all negative) would be required to generate that force?

 

[TwoEG]

But does 'extra(or deficient) number of electrons' can really tell the 'percentage of ionized atoms'? What about distribution? If all electrons are gathered on, exaggeratedly, one point of the balloon, can I really say that balloon has same 'percentage of ionized atoms' as another balloon which all electrons are distributed evenly on its surface?

 

[haruspex]

But does 'extra(or deficient) number of electrons' can really tell the 'percentage of ionized atoms

Not yet... there are more steps.

What about distribution?

We do not know how exactly the balloons were charged. Typically they will be more charged on one side than the other, so they would rotate to have the more charged sides on the outer. But since we do not know the radius of the balloons that would leave us unable to figure out the force. So just assume the charge is uniformly distributed.