A 220 MW laser pulse is focused with a lens to a diameter of 2.1 m. Part A What

Question

A 220 MW laser pulse is focused with a lens to a diameter of 2.1 m. Part A What is the laser beam's electric field amplitude at the focal point? Express your answer to two significant figures and include the appropriate units. 12 Submit Previous Answers Request Answer Incorrect, Try Again; 8 attempts remaining Part 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 Express your answer using two significant figures. Eo/Enydrogen Submit Request Answer

Explanation / Answer

Given,

P = 220 MW ; d = 2.1 um

A = pi r^2 = 3.14 x (1.05 x 10^-6)^2 = 3.46 x 10^-12 m^2

we know that

I = P/A = 220 x 10^6/(3.46 x 10^-12) = 6.36 x 10^19 W/m^2

A)We know that

S = E^2/2 u c

E = sqrt (2 S u C)

where S is intensity

E = sqrt (2 x 6.36 x 10^-19 x 4 x 3.14 x 10^-7 x 3 x 10^8) = 2.19 x 10^11 N/C

Hence, E = 2.19 x 10^11 N/C

B)E = kq/r^2

E = 9 x 10^9 x 1.6 x 10^-19/(0.053 x 10^-9)^2 = 5.13 x 10^11 N/C

E0/E = 2.19 x 10^11/(5.13 x 10^11) = 0.43

Hence, E0/E = 0.43

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