Answer:
2.37 * 10^4 m/s
Explanation:
Constants :
Mass of electron = 9.11 * 10^(-31) kg
Electric charge of an electron = 1.602 * 10^(-19) C
Parameters given:
Radius of sphere = 1.3cm = 0.013m
Charge of sphere = 2.3 * 10^(−15) C
Using the law of conservation of energy, we have that:
K. E.(initial) + P. E.(initial) = K. E.(final) + P. E.(final)
K. E.(final) = 0, since final velocity is zero and P. E.(final) = 0 since the electron reaches a final distance of infinity.
Hence,
K. E.(initial) = P. E.(initial)
0.5mv^2 = (kqQ)/r
Where k = Coulumbs constant
Q = charge of the sphere.
r = radius of the sphere.
=> 0.5*m*v^2 = (kqQ)/r
0.5 * 9.11 * 10^(-31) * v^2 = (9 * 10^9 * 1.602 * 10^(-19) * 2.3 * 10^(-15))/0.013
4.555 * 10^(-31) * v^2 = 2550.88 * 10^(-25)
=> v^2 = 2550.88 * 10^(-25) / 4.555 * 10^(-31)
v^2 = 560 * 10^6 = 5.60 * 10^8
=> v = 2.37 * 10^4 m/s
