Hey
1)how do you estimate the line widths (full width half maximum) of the peaks arising from:
(a) The emission of a hollow cathode lamp
(b) The absorption peak of caffeine in the UV –visible spectrum
(c) The d-d transition observed for Ni2+ in aqueous solution
2)Comment on the effects which determine the linewidth in each case. In which case(s) are the observed linewidths likely to be limited by the resolution of the monochromator in the spectrometer itself?
Need help
Thank you
To estimate the line widths (full width half maximum) of the peaks arising from different phenomena, you need to consider the specific characteristics and factors affecting each case. Here's how you can estimate the line widths for each scenario:
1) Estimating line widths:
(a) Hollow Cathode Lamp Emission:
- The line widths of the emission peaks from a hollow cathode lamp can be estimated by analyzing the atomic spectroscopy data.
- Start by measuring the peak width at half height for each emission line.
- Then, multiply that width by a factor of 2.355 to obtain the full width half maximum (FWHM) value.
(b) Absorption Peak of Caffeine:
- To estimate the line width of an absorption peak, you need the UV-visible spectrum data of caffeine.
- Locate the absorption peak of interest and determine its peak width at half height.
- Multiply this width by 2.355 to calculate the FWHM value.
(c) d-d Transition of Ni2+ in Aqueous Solution:
- In this case, the line width estimation depends on the spectroscopic data obtained for the Ni2+ transition in aqueous solution.
- Identify the peak associated with the d-d transition and determine its width at half height.
- Multiply this width by 2.355 to determine the FWHM value.
2) Effects determining the linewidths and resolution limitations:
- The observed linewidths can be influenced by various factors, such as instrument resolution, natural broadening, Doppler broadening, and collisional broadening.
- Instrument Resolution: This refers to the ability of the spectrometer to differentiate between closely spaced peaks. If the inherent resolution of the monochromator in the spectrometer is higher than the linewidth, it will limit the observed linewidth.
- Natural Broadening: It is a quantum mechanical effect caused by the limited lifetime of excited states. This effect tends to produce narrow lines.
- Doppler Broadening: It arises due to the thermal motion of atoms or molecules, causing their emission or absorption to be broadened. This effect tends to produce wider lines.
- Collisional Broadening: It occurs when interaction with neighboring particles broadens the spectral lines. These collisions can be due to pressure or molecular collisions.
Considering the effects described above, the observed linewidths are likely to be limited by the resolution of the monochromator in the spectrometer when the instrument resolution is higher than the actual linewidth. This may be the case for all three scenarios mentioned (a), (b), and (c) if the resolution of the spectrometer is high enough to resolve the peak widths effectively.
I hope this helps! Let me know if you have any further questions.