Consider two point particles that have charge +e, are at rest, and are separated

Question

Consider two point particles that have charge +e, are at rest, and are separated by 2.9 x 10-15 m.

1) How much work was required to bring them together from a very large separation distance? Express your answer in keV, where 1 eV = 1.6 x 10-19 J. keV

2) If they are released, how much kinetic energy will each have when they are separated by twice their separation at release? keV

3) The mass of each particle is 1.00 u (1.00 amu). What speed will each have when they are very far from each other? (1 amu = 1.67 x 10-27 kg) m/s

Explanation / Answer

q = charge on each particle = e = 1.6 x 10-19 c

r = distance between particle = 2.9 x 10-15 m

1)

work done = kq2/r = (9 x 109) (1.6 x 10-19 )2/ (2.9 x 10-15 ) = 7.94 x 10-14 = 7.94 x 10-14 /(1.6 x 10-19) = 4.9625 x 105 eV

W= 496.25 keV

2)

Using conservation of energy

kq2/r = kq2/(2r) + KE

KE = kq2/2r = 7.94 x 10-14 /2 = 3.97 x 10-14 J = 3.97 x 10-14 /(1.6 x 10-19) = 248.125 keV

3)

using conservation of energy

kq2/r = KE

7.94 x 10-14 = (0.5) (1.67 x 10-27) v2

v = 9.75 x 106 m/s

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