To determine the number of green lines with a wavelength of 546 nm from a mercury (Hg) lamp that should be visible in a spectrometer, we need to consider the resolution and range of the spectrometer.
A spectrometer is an instrument used to measure the intensity of light as a function of its wavelength. The number of distinct lines that can be resolved by a spectrometer depends on its resolution, which is determined by factors such as the grating or prism used and the detector's capabilities.
If we assume a spectrometer with a moderate resolution that can resolve wavelengths with a difference of around 1 nm, we can calculate the number of green lines within that range.
Given that the wavelength of the green line from a mercury lamp is 546 nm, and considering a resolution of approximately 1 nm, we can calculate the number of visible green lines as follows:
Number of visible green lines = (Maximum wavelength - Minimum wavelength) / Resolution
In this case, the maximum wavelength is 546 nm, and the minimum wavelength would be slightly lower, depending on the specific spectrometer's resolution capability.
Let's assume a minimum wavelength of 545 nm for the sake of calculation. Plugging these values into the formula, we get:
Number of visible green lines = (546 nm - 545 nm) / 1 nm = 1
Therefore, with a resolution of approximately 1 nm, only one green line with a wavelength of 546 nm from a mercury lamp would be visible in the spectrometer.