Photorefractive keratectomy (PRK) is a laser-based surgical procedure that corrects near- and farsightedness by removing part of the lens of the eye to change its curvature and hence focal length. This procedure can remove layers 0.25 mm thick using pulses lasting 12.0 ns from a laser beam of wavelength 193 nm. Low-intensity beams can be used because each individual photon has enough energy to break the covalent bonds of the tissue. (c) If a 1.50-mW beam is used, how many photons are delivered to the lens in each pulse?

Video transcript

Hey everyone. Let's go through this practice problem. The utilization of lasers for Carr's removal and cavity preparation is based on the ablation technique in which dental heart tissues are removed during laser irradiation. The laser beam of wavelength 2.94 microns emitted by an erbium doped itch reum aluminum garnet or yag laser is efficiently absorbed by the carbonated hydroxy appetite mineral of the tooth. For an er yag laser, the power of a laser pulse with a pulse duration of microseconds is about 200 milli watts, calculate the number of photons hitting a tooth in each pulse. And we're given four options to choose from. Option A 4.44 multiplied by 10 to the power of photons. Option B 2.22 multiplied by 10 to the power of 15 photons. Option C 2.96 multiplied by 10 to the power of photons. And option D 1.48 multiplied by 10 to the power of photons. Now, since we're told about the power, the first thing we want to do is find a relationship between the photons and the energy that they have. Now recall that the energy in one photon is equal to the plank constant multiplied by the speed of light C divided by the wavelength of the laser. We can relate this information to the power we're given by using the definition of power. And recall that power is equal to a rate of change of energy divided by an amount of time. However, since the energy formula we wrote only applies to a single photon, this power is going to be proportional to the number of photons N. And this N is what the problem is asking us to find the number of photons hitting the tooth in each pulse. So the first thing I'm going to do is solve for the amount of energy in one photon. So we're called that the plank constant H is equal to 6. multiplied by 10 to the power of negative 34 dual seconds. And we're multiplying that by the speed of light C which is equal to about three multiplied by 10 to the power of 8 m per second. And this is being divided by the wavelength which is given to us in the problem as 2.94 microns or multiplied by 10. The power of negative 6 m. If you put this into a calculator, then we find an amount of energy of about 6. multiplied by 10 to the power of negative 20 Jews. Now let's use this as our value for E in the power formula. Now remember that we're trying to solve for the number of photons N. So let's algebraically rewrite this equation to solve for N by multiplying both sides of the equation by T and dividing both sides of the equation by E. So we find that the number of photons N is equal to the power involved multiplied by the amount of time divided by the energy. So now we just plug in the values given to us for this part of the problem. So the pressure P is given to us in the problem is 200 milli watts. So 200 multiplied by 10 to the power of negative three watts multiplied by a time period of 100 and 50 microseconds. So 100 50 multiplied by 10 to the power of negative six seconds all divided by the amount of energy 6.76 multiplied by 10 to the power of negative 20 Jews. And if we put that into a calculator, then we find a number of photons of about 4.44 multiplied by 10 to the power of 14 photons. And so that is our answer to this problem. And if we scroll up and look back at our options, we can see that. Option A says exactly this 4.44 multiplied by 10 to the power of 14 photons. So option A is our answer to this problem. I hope this video helped you out if you need more practice, please check out some of our other tutoring videos which will give you more experience with these types of problems, but that's all for now and I hope you all have a lovely day. Bye bye.