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Electron Escape Speed

  1. Dec 3, 2017 #1
    1. The problem statement, all variables and given/known data
    What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10nC?

    2. Relevant equations
    Given:
    d= 1.0cm
    r= 0.05cm= 0.0005m
    q1 = 10nC = 10 x 10-9 (sphere)
    q2 = -1.6 x 10-19 (electron)

    Equation:
    U = (kq1q2)/r
    KE= ½mv2
    3. The attempt at a solution
    So, if the sum of kinetic and potential energy is supposed to be zero, then I get:

    KE + U = 0
    ½me(ve)2 + (kq1q2)/r = 0
    ½(9.11 x 10-31)(v)2 + ( (8.99 x 109) (10 x 10-9) (-1.6 x 10-19) ) / (0.0005) = 0

    If I solve the above equation^^, I get ve= 2.5 x 108 m/s, which is incorrect. The correct answer is 8.0 x 107 m/s. I am not sure what I am doing incorrectly, any help is appreciated. Sorry about the mess, I can't seem to figure out how to use TeX!
     
  2. jcsd
  3. Dec 3, 2017 #2

    Delta²

    User Avatar
    Gold Member

    Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!
     
  4. Dec 3, 2017 #3
    Thank you, can't believe I didn't catch that. I re-did and got the correct answer!!
     
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