An electron-positron pair (positron is electron's antiparticle, it has the same mass as electron, but opposite charge) can be produced what two photon are collided. two photons of frequency w are collided head-on. what will be the electron's momentum? electron's rest mass is m(e).

Explanation:

If the photons got frequency w, the energy of each photon must be

,

so the total energy of the system must be

.

The momentum for each photon will be:

.

But, as they are colliding head on, the total momentum of the system must be zero.

Now, for the particles, the energy must be

.

Momentum conservation implies that the total momentum must be zero, so:

,

so the squares of the momentum will be the same.

Now, this implies that the energies for the electron and the positron must be the same, so we can write:

.

Taking conservation of energy in consideration:

.

.

.

.

.

.

.

And this its the electron's momentum

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .