1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Size of He atom at 10^(-9)K

  1. May 18, 2006 #1
    Can anyone help me to find an approximation to the size of a He atom at very low temperature (10^(-9)K)?

    My attempt:

    At this very low temperature all electrons will be in the ground state, thus using the equipartition theorem:

    [tex] 1/2kT = h*c/lambda [/tex]

    now, for the zero point energy, lambda is 1/2 the diameter of the Helium atom.
    However, this approach does not yield the correct answer.

    I have had a look at several textbooks, but couldn't find any hints in there.
    Thanks a lot for your help! :smile:
  2. jcsd
  3. May 19, 2006 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Temperature, being a statistical concept, is not defined for an atom. I don't see how temperature would affect the size of any atom.

    But, assuming this question is asking what the uncertainty of a He atom's position would be if it had a kinetic energy in the range of He atoms in He gas at 10^-9 K, you would have to apply the Heisenberg uncertainty principle:

    [tex]\Delta x \Delta p = \hbar/2[/tex]

    You would have to work out [itex]\Delta p[/tex] from the energy range - which is roughly 0 < E < kT. Using [itex]E = p^2/2m[/itex] would give [itex]\Delta p = \sqrt{2mE} = \sqrt{2mkT}[/itex]


    [tex]\Delta x = \frac{\hbar}{\sqrt{8mkT}}[/tex]

  4. May 19, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I believe the question may be refering to the de Broglie wavelength (this might be the preamble to a discussion of BECs), which is of the same order as the number calculated by AM.
  5. May 20, 2006 #4
    it is indeed, as the question then asks to compare this with BEC.

    However, the solution manual says that d = 60 um, but with the uncertainty principle I got 2.45 *10^(-7)m ?
  6. May 20, 2006 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I get a number that's pretty close to 60um (I get p ~ 10^{-29} Ns). You must have made a numerical error. If you still can't find the error, post your calculation here, and someone will point it out.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook