Question

A 190MW laser pulse is focused with a lens to a diameter of 2.5?m

A. What is the laser beam's electric field amplitude at the focal point?

B. What is the ratio of this electric field to the electric field that keeps the electron bound to the proton of a hydrogen atom? The radius of the electron's orbit is 0.053 nm

Answer 1

A. The intensity of the beam is,

Here, P is the power of the laser beam, and r is the radius of the beam.

Since the diameter of the beam is , the diameter of the beam is.

Then,

   

The amplitude of the electric field in terms of intensity of the beam is,

Here, is the permitivity of free space and c is the speed of light.

Therefore, the required electric field is.

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B. The electric field due to proton to bound the electron is,

Here, k is Coulomb's constant, q is the charge and a is the radius of the hydrogen atom.

     

Then, the ratio of the electric field due to laser beam and the electric field required to keep the electron bound to the nucleus of hydrogen atom is,

       

Therefore, the required ratio is .