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A pulsed ruby laser emits light at 694.3 nm. For a 14.0 -ps pulse containing 3.00 $\mathrm{J}$ of energy, find (a) the physical length of the pulse as it travels through space and (b) the number of photons in it. (c) If the beam has a circular cross section 0.600 $\mathrm{cm}$ in diameter, what is the number of photons per cubic millimeter?

a) $4.20 \times 10^{-3} \mathrm{m}$

b) $1.05 \times 10^{19}$ photons

c) $8.6 \times 10^{16}$ photons$/\rm mm^3$

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Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Numerade Educator

Other Schools

in this exercise, we have a laser that, um, it's Fulton's with the wailing from 694.3 centimeters, and I have to consider it a post of 14 Biggles seconds that has a total energy e. It was two people, two threes. Use in question. A. We have to calculate the physical length of the post. So you know that the length of pulses just the speed of replication, which is just a speed of life, in this case times the length of time. So in this case, it's three points, 10 to the eight meters per second times, the times the time during which the deal, the post waas admit it. So this is 14 people seconds and one pickle. Second, it's is 10 to the minus 12 seconds. So this is equal to 4.2 times 10 to the minus three meters. Okay, this is 4.2 millimeters in question be we have to calculate the number of Fulton's that are emitted in this poll's, and we know that the number of Fulton's is just the total energy of the post. He divided by the energy of a single photo. Okay, and now what we have to do. First of all, ways to calculate the energy of a single folder and that's HC over Linda HC is 1240 electoral votes centimeters and Linda is 694.3 millimeters. So this here is equal to 1.79 electoral votes. That's the energy of a single photo. And I can also find this energy in used by multiplying. Actually, by dividing 1.79 yeah, should multiply, Multiply 1.79 times Ah, 1.6 times sent to the minors. 19 issues pre election vote. So I get that the energy gamma is equal to 2.86 times 10 to the minus 19. You and we can calculate the number of fortunes, um, as the total energy of the pulse, which is three jewels divided by 2.86 times 10 to the minus 19 Jews. So you'll for 40. So the total number of Fulton's is one point 05 times sent to the 19 folders. Okay, this is the answer to question. Be and in question. See, you have to sue that the diameter of the cross at the cross section of the laser beam is equal to 0.6 centimeters. Okay, uh, and we want to find how many photons for cubic millimeter are there in the laser in the laser beam. So first of all in that you have to find the volume the total value of the laser beam, and that's gonna be l. That's the physical length of the laser beam Times pi times are square. That's the cross sectional area. Pi times are square is the cross sectional area which is multiplied by l and R squared is D squared over over four. So the volume is no pi d square over four l I'm gonna talk about the bottom in in cubic millimeters. Okay, because the answer is has to be unfolding. Spur Cubic millimeters. So the length of the fiscal length of the beam is 4.2 millimeters times pi times the diameter, which is six millimeters squared, divided by four. So this is in squared millimeters, so the volume is equal to 118 cubic millimeters skin and being we can calculate m n over v by dividing the answer Depression B which waas 1.5 times 10 to the 19th Fulton's by the total volume, which is 118. We to be millimeters. So the answer is age 0.9 times 10 to the 16 fortunes per cubic millimeter. This is the answer to question, see?

Universidade de Sao Paulo