Final answer:
The smallest detail observable with a microscope that uses ultraviolet light of frequency 1.20 × 10¹5 Hz is approximately 2.50 × 10^-7 meters.
Step-by-step explanation:
The smallest detail observable with a microscope that uses ultraviolet light of frequency 1.20 × 10¹5 Hz can be determined using the formula:
Smallest Detail = λ / 2
Where λ represents the wavelength of the light. The wavelength can be found using the formula:
λ = c / f
Where c is the speed of light and f is the frequency of the ultraviolet light.
Given that c is approximately 3.00 × 10^8 meters per second and f is 1.20 × 10^15 Hz, we can substitute these values into the equation:
λ = (3.00 × 10^8 m/s) / (1.20 × 10^15 Hz)
Simplifying this expression, we find that the wavelength is approximately 2.50 × 10^-7 meters. Therefore, the smallest detail observable with the microscope is approximately half of this value, giving us an answer of a) 2.50 × 10^-7 meters.