Nature of Orbits for a body projected from earth with different speeds

Minimum velocity required for an object to orbit around the Earth  is  Vs =√gR = 8KmSec⁻¹

Let Ve be the escape velocity  required for a body to escape Earth's gravitational field.

Let if  'V' be velocity with which a body is projected from Earth.

Then,

  1. V < Vs → body falls to ground
  2. V=Vs → body rotates round the Earth in circular orbit closer to surface of Earth.
  3. Vs < V < Ve → body revolves in elliptical orbit
  4. V=Ve → body just escapes from Gravitational Field
  5. V>Ve → body moves in interstellar space with velocity equal to √❲V²-Ve²❳
  6. V<Ve → Total Energy of body is Negative 
  7. V=Ve → Total Energy of body is Zero.

Pair Production - Conversion of Radiation into Matter

The cloud chamber experiments revealed that a Photon can give up its energy to materialize as two electrons of opposite charge. Certainly the Photon must have an energy of atleast 2mₑc² in order to produce a pair.

No photon, regardless of its energy, can produce a pair in a perfect vacuum.

Pair Production is strictly an Electromagnetic Process. It seems to occur mostly in the intense electric field near the nucleus rather than inside the nucleus.

At higher energies or with heavy targets it is typically reasonable to ignore the energy transferred to target, so that nearly all energy from Photon goes to electron-positron pair.

Energy equation

h𝜈 → 2mₑc²+E1+E2

holds approximately.

 mₑc²rest energy of each electron

 E1, E2 → Kinetic Energies of particles

 The heavier the target, the more nearly the equation is satisfied. 

Pair Production can occur in the vicinity of an electron.