A 140mW heliumneon laser emits a beam of circular cross sect

A 14.0-mW helium–neon laser emits a beam of circular cross section with a diameter of 2.30 mm.

(a) Find the maximum electric field in the beam.
kN/C

(b) What total energy is contained in a 1.00-m length of the beam?
pJ

(c) Find the momentum carried by a 1.00-m length of the beam.
kg · m/s

Solution

A)

Intensity I = power/area = 14*10^-3/(pi*(0.0023/2)^2) = 3369.6 W/m^2
Ipeak = 2I = 6739.2 w/m^2
E = sqrt(Ipeak*Z0) = sqrt(6739.2*376.7) V/m, = 1593.3 V/m = 1.59 kN/C <----answer
where free-space impedance Z0 = sqrt(µ0/e0) = 376.7303 ohms (ref.)

B)

1.5 m contains energy emitted in a time of 1.5/c s = power*time

= 0.014*1.00/(3*10^8)

= 4.67E-11 J

= 46.7 pJ

C)

Energy of one photon Ep = hc/lambda = 3.13914*10^-19 J
Number of photons in 1.5 m, N = 4.67*10^-11/(3.14*10^-19) = 1.49*10^8
Momentum of one photon Pp = Ep/c = 1.04710*10^-27 kg-m/s
Momentum in 1.5 m = Pp * N = 1.05*10^-27*1.49*10^8 = 1.56*10^-19 kg.m/s <------answer