Final answer:
The frequency of the 193-nm ultraviolet radiation used in laser eye surgery is 1.55 × 10¹⁵ Hz, which is option a. The accuracy with which this UV radiation can ablate corneal tissue is nearly twice that of the shortest visible wavelength of light.
Step-by-step explanation:
Frequency of Ultraviolet Radiation in Laser Eye Surgery
The frequency (f) of electromagnetic radiation can be calculated using the formula:
f = c / λ
where c is the speed of light in a vacuum (≈ 3.00 × 10¸ meters per second) and λ is the wavelength of the radiation. For 193-nm UV radiation used in laser eye surgery:
f = (3.00 × 10¸ m/s) / (193 × 10⁻⁹ m)
Converting the wavelength from nanometers to meters, we get:
f = (3.00 × 10¸ m/s) / (193 × 10⁻⁹ m) = 1.55 × 10¹⁵ Hz
Therefore, the correct frequency of the UV radiation used in laser eye surgery is 1.55 × 10¹⁵ Hz, which corresponds to option a.
Accuracy of UV Radiation for Corneal Ablation
Since accuracy is directly proportional to wavelength, the shorter the wavelength, the higher the accuracy. The shortest visible wavelength of light is approximately 380 nm. If we compare this with the 193 nm wavelength used in UV laser surgery:
Accuracy Ratio = Visible Wavelength / UV Wavelength = 380 nm / 193 nm ≈ 1.97
This means that the UV radiation can be nearly twice as accurate as the shortest visible light for ablating corneal tissue.