1. May 9, 2004

### Claire84

Hi there, I was wondering if you could help me with a question I have (I've posted it here as opposed to the homework help forums cos I alwso want a little bit of the theory explained ).

The relative permittivity of helium at STP is 1.000047. Estimate the magnitude of the dipole moment induced on each helim atom when the gas is subjected to an electric field E of stregnth 10^5 V/m. We're given Avogadro's number, the permittivity of a vacuum and that the volume o one mole of gas at zero degrees celsius and 1 atmosphere is 2.24x10^-2 m^3

I started off by looking at the induced dipole moment per unit volume and used P= (1.000074-1)x8.85x10^-12 x 10^5 because we have this in our notes as it being equal to induced polarization+molecular polarization+ dipole orientation polarization. As the last 2 are zero in this case, that's why I used the eqt that I did. So after calculating that, I worked out the number of atoms per unit volume by diving the volume of one mole of gas by avogadro's constant to get the volume of one molecule. Then I divided one by this to get the number of molecules per unit volume. Then I divided P by this to get the dipole moment induced on each atom. However, my answer if coming out at around x10^-36 so I'm convinced I'm doing something wrong. Can anyone help me with my method? Thanks?

For the second part we're given the inter-nuclear separationin sa completely ionic molecule to be 2.8x10^-10 m, and we're told to calculate it's permanent dipole moment and compare it with the value obtained in the earlier part. I got my answer from induced dipole moment=lq where l= the internuclear separation and q =1.6x10^-19, but I don't understand why I'd use this eqt because it's for induced dipole moments and not permanent. Also, it's to a different order than queston 1, so that's confusing me too. Can anyone shed any light on this for me? Thanks very much.

Btw, sorry I've posted this here and in another forum but I just wanted to see if someone in this forum could help me- I didn't intentionally want to clutter the place up!

2. May 9, 2004

### Gokul43201

Staff Emeritus
It sure looks like your answer is correct (10^-36) though that does look small. However, it should be small compared to the dipole created by a difference of an electron separated by the internuclear distance (10^-29), because that would require close to the ionization potential, and your applied field is about 6 orders of magnitude too low for that. Hmmm, that nearly seems to explain the difference...let's see if someone else spots a big error?

PS : Notice that the susceptibility is pretty small too.

3. May 9, 2004

### Claire84

Thanks very much for that.