Total energy of the particle on surface of Earth
= KE + PE = KE - G Me m / Re
KE needed for escaping from the gravity of Earth = G Me m /Re. Then the total energy of the particle will be zero. Hence, it will escape from the gravitational field.
Energy given to the particle = 1/2 * G Me m / Re
Total energy of the particle on surface of Earth = KE + PE = -1/2 G Me m / Re
Total energy of a particle in an orbit (radius R) around Earth has a total energy =
- G Me m / R + 1/2 G Me m /R = - 1/2 * G Me m / R
Comparing the two above equations and as per the principle of conservation of energy, The radius of the orbit = R = Re.
hence, the particle stays on the surface of Earth.