Determine the resolution of an instrument that is capable of separating two adjacent peaks at 208.4 and 216.3 nm.
The correct answer and explanation is:
Answer:
To determine the resolution (R) of an instrument capable of separating two adjacent peaks, we use the formula for spectral resolution: R=λΔλR = \frac{\lambda}{\Delta \lambda}
Where:
- λ\lambda is the average wavelength of the two peaks.
- Δλ\Delta \lambda is the difference between the two wavelengths (peak separation).
Given:
- First peak = 208.4 nm
- Second peak = 216.3 nm
Δλ=216.3−208.4=7.9 nm\Delta \lambda = 216.3 – 208.4 = 7.9 \, \text{nm} λ=208.4+216.32=424.72=212.35 nm\lambda = \frac{208.4 + 216.3}{2} = \frac{424.7}{2} = 212.35 \, \text{nm}
Now calculate resolution: R=212.357.9≈26.87R = \frac{212.35}{7.9} \approx 26.87
Explanation (Approx. 300 Words):
Spectral resolution is a critical parameter in spectroscopy, defining how well an instrument can distinguish between two closely spaced wavelengths. It is especially important in applications like UV-Vis spectroscopy, where the accurate identification of compounds depends on resolving peaks that may be very close together in the spectrum.
Resolution (RR) is mathematically expressed as the ratio of the average wavelength (λ\lambda) of the two peaks to the wavelength difference (Δλ\Delta \lambda) between them. In this case, we are given two peaks at 208.4 nm and 216.3 nm. The difference between them is 7.9 nm, which represents how close the peaks are to each other in terms of spectral separation.
The average wavelength of the peaks is calculated to be 212.35 nm. This average is used because resolution depends on the relative separation compared to the position in the spectrum.
Substituting into the resolution formula: R=212.357.9≈26.87R = \frac{212.35}{7.9} \approx 26.87
This value means that the instrument can distinguish between two wavelengths that are approximately 1 part in 27 apart, around the 212 nm region.
A higher resolution value implies better capability to differentiate closely spaced spectral features. In practice, this resolution would be considered low to moderate, sufficient for resolving relatively distinct peaks but not suitable for highly detailed or fine structure analysis. For high-resolution applications (e.g., atomic spectroscopy), resolutions in the thousands or more may be required.
In summary, the instrument in question has a spectral resolution of approximately 26.87, meaning it can just resolve the two peaks at 208.4 nm and 216.3 nm.