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

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The discussion centers on calculating the escape speed of an electron from a charged glass sphere with a diameter of 1.0 cm and a charge of 10 nC. The user initially miscalculated the radius as 0.05 cm instead of the correct 0.5 cm, leading to an incorrect escape speed of 2.5 x 10^8 m/s. After receiving clarification on the radius, the user recalculated and found the correct escape speed to be 8.0 x 10^7 m/s. The importance of correctly identifying the radius in potential energy calculations is emphasized. The thread concludes with the user expressing gratitude for the assistance in resolving the error.
mitchy16
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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
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!
 
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Your mistake is in the radius of the glass sphere Its 0.5cm=0.005m!
 
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Delta² said:
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!
 

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