Final answer:
Measurements of mercury's green line wavelength in a spectrometer using second-order interference are more precise due to greater angular separation and significant interference effects.
Step-by-step explanation:
When determining the wavelength of the bright green mercury line using a diffraction grating, the measurement based on the second-order interference is generally more precise than that based on the first-order interference. This is because, in a diffraction grating, the angular separation between wavelengths increases with the order number. The higher the order, the larger the angle for each wavelength, which leads to more precise measurements since small errors in angle measurement lead to smaller relative errors in wavelength determination. Additionally, for a given wavelength, the path difference and hence the interference effect is more significant in higher orders, contributing to increased precision.
The spectrometer and diffraction grating provide valuable tools for analyzing the spectra of light. A finely constructed grating with more lines per centimeter will result in greater dispersion and therefore allows for more detailed observations of spectra. However, this also implies that there is a limit to the order number beyond which different orders of spectra might overlap, making it harder to differentiate between them. It is important to choose the order that provides enough separation without causing overlap between different orders.