Question

Two free protons are separated by a distance of 1 Ao . if they are released, what is the kinetic energy of each proton when at infinite separation.

Answer 1

The kinetic energy of each proton is given by total kinetic energy = total initial potential energy
Therefore total potential energy of protons in the system is given by
$u = \frac{1}{4\pi \epsilon(o) } \times \frac{q1q2}{r}$
then after substitute the values we get
$u = 9 \times {10}^{9} \times \frac{1.6 \times {10}^{ - 19} \times 1.6 \times {10}^{ - 19} }{1 \times {10}^{ - 10} }$
Therefore total kinetic energy is posses by system of protons is
u = 23.04 × 10^-19 J

Therefore kinetic energy possessed by each proton is given by
$= \frac{23.04 \times {10}^{ - 19} }{2} = 11.52 \times {10}^{ - 19} joules$