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?

Verified step by step guidance

1. Calculate the energy of a single photon using the formula: E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 x 10^{-34} J\cdot s), c is the speed of light (3.00 x 10^8 m/s), and \lambda is the wavelength of the laser (193 nm).
2. Convert the wavelength from nanometers to meters by multiplying by 10^{-9}.
3. Substitute the values into the formula to find the energy of one photon.
4. Determine the total energy delivered in each pulse by using the formula: Energy = Power \times Time, where Power is 1.50 mW and Time is the duration of the pulse (12.0 ns).
5. Calculate the number of photons per pulse by dividing the total energy delivered in each pulse by the energy of one photon.

Key Concepts

Photon Energy

Photon energy is determined by the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency of the light. The energy of a photon is crucial in understanding how it interacts with matter, such as breaking covalent bonds in biological tissues during procedures like PRK. For a laser with a specific wavelength, the energy can also be calculated using E = hc/λ, where c is the speed of light and λ is the wavelength.

Laser Power and Photon Delivery

Laser power, measured in watts (W), indicates the rate at which energy is delivered. In this context, a 1.50-mW beam means that 1.50 millijoules of energy are emitted per second. To find the number of photons delivered in each pulse, one must calculate the total energy delivered in the pulse duration and then divide that by the energy of a single photon, thus determining how many photons contribute to the total energy output.

Pulse Duration

Pulse duration refers to the length of time that the laser emits energy in a single pulse, which in this case is 12.0 ns (nanoseconds). This short duration is significant in laser applications, as it allows for precise energy delivery to the target tissue without excessive heat buildup. Understanding pulse duration is essential for calculating the total energy delivered in a pulse, which is necessary for determining the number of photons involved.