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Homework Help: Energy Needed to Remove an Electron

  1. Jun 15, 2008 #1

    LHC

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    1. The problem statement, all variables and given/known data

    If the total energy needed to remove an electron from a hydrogen atom is 24.6 eV, what is the distance that the electron is from the nucleus?


    2. Relevant equations

    I'm not really sure....I know that the answer is [tex]r = 5.85\times10^-11[/tex].

    3. The attempt at a solution

    As you can see, I know the answer, but I'm just not sure how to get to it. So far, I have thought of applying this process:

    [tex]E_{e} = \frac{kq_{1}q_{2}}{r}[/tex]

    Technically, I get the answer if I sub in:[tex]q_{1}=q_{2}=e[/tex], [tex]E_{e}=24.6e[/tex], and solve for r.

    Is this the correct process? I'm not really sure about the rationale behind it...lol I'm almost positive that there is another way.
     
    Last edited: Jun 15, 2008
    LHC, Jun 15, 2008
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  3. Jun 15, 2008 #2

    dynamicsolo

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    Homework Helper

    What you've written is the expression for the electrostatic potential energy between two charges q_1 and q_2 separated by a distance r. Yes, this is what you want to use.

    Make sure you put everything into SI units, which means you'll need to convert that energy of 24.6 electron-volts into Joules...
     
    dynamicsolo, Jun 15, 2008
  4. Jun 16, 2008 #3

    LHC

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    Thanks for the help!
     
    LHC, Jun 16, 2008
  5. Jun 16, 2008 #4

    Andrew Mason

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    Your answer is correct. You can figure out the rationale from the definition of work. Work = Force x distance. Since the force changes with distance, you have to integrate (from beginning and end points, r to infinity):

    [tex]W = \int_r^\infty F\cdot ds = \int_r^\infty -\frac{kQq}{r^2} dr = kQq/r - kQq/\infty[/tex]

    AM
     
    Andrew Mason, Jun 16, 2008
  6. Jun 16, 2008 #5

    Andrew Mason

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    Repeat of my above answer since Latex seems to be having problems:

    [tex]W = \int_r^\infty F\cdot ds = \int_r^\infty \frac{kQq}{r^2} dr = \frac{kQq}{r} - \frac{kQq}{\infty}[/tex]

    AM
     
    Andrew Mason, Jun 16, 2008
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