What Is the Escape Speed of an Electron from a Charged Glass Sphere?

[mitchy16]

Homework Statement

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?

Homework 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

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
½m_e(v_e)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 v_e= 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!

 

[Delta2]

Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!

 

[mitchy16]

Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!

Thank you, can't believe I didn't catch that. I re-did and got the correct answer!