1. Not finding help here? Sign up for a free 30min 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!

Bohr model

  1. Oct 10, 2004 #1
    Here's my problem:
    Show that the speed of an electron in the nth Bohr orbit of hydrogen is (alpha*c)/n, where alpha is the fine structure constant. What would be the speed in a hydrogenlike atom with a nuclear charge of Ze?

    We didn't talk about the fine structure constant in class, so could someone explain to me what it is? Hints on how to show that speed = alpha c/n would also be appreciated.

    Thanks,
    eku_girl83
     
  2. jcsd
  3. Oct 10, 2004 #2

    Kane O'Donnell

    User Avatar
    Science Advisor

    Hi,

    In the Bohr model we assume that angular momentum is quantised:

    [tex] L = mvr = n\hbar [/tex]

    From this you can find the expression for the tangential velocity of the electron. You then need to find the expression for the Bohr radius for a particular value of n, which turns out to be (for Z = 1, for Hydrogen-like atoms just replace e^2 with Z(e^2)):

    [tex] r_{n} = \frac{4\pi\epsilon_{0}\hbar^{2}n^2}{me^2} [/tex]

    When you sub in for r you get:

    [tex] v_{n} = \frac{e^2}{4\pi\epsilon_{0}\hbar} [/tex]

    From this you should be able to work out what the fine structure constant is - just compare the equation you were given to the one above. In undergrad physics courses the name "fine structure constant" is often applied to a few dimensionless constants that all look similar. It's just a number that happens to arise in a lot of Quantum Mechanical situations. You'll see it a fair bit :)

    Cheerio!

    Kane
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Bohr model
  1. Bohr Model (Replies: 11)

  2. Neils Bohr Model (Replies: 3)

  3. Bohr's model (Replies: 3)

  4. Bohr model (Replies: 3)

Loading...