To solve this problem we will rely on the theorems announced by Newton and Coulomb about the Gravitational Force and the Electrostatic Force respectively.
In the case of the Force of gravity we have to,
Here,
G = Gravitational Universal Constant
= Mass of Proton
= Mass of Electron
d = Distance between them.
In the case of the Electric Force we have,
k = Coulomb's constant
= Charge of proton
= Charge of electron
d = Distance between them
Therefore
We can here prove that the statement is True
Initial momentum = 2 * m v
so if 1 ball popped out with 2 v momentum would be conserved
but the initial kinetic energy of the two balls is
1/2 m v^2 + 1/2 m v^2 = m v^2
But the kinetic energy of one ball with twice the speed would be
KE = 1/2 m (2 v)^2 = 2 m v^2 thus violating conservation of energy
I don't understand what you are looking for. I can tell you that the speed of molecules does change during state changing.