# Rotational translations between L values and spectral lines

• jonesy101
In summary, the conversation discusses trying to find the corresponding L values for spectral lines observed from the HCl molecule using the equation w=h-bar(L+1)/I. The person has attempted to use a ratio between the wavenumbers and the equation to find a set of integrals for L, but was unsuccessful. It is suggested to graph the wave numbers to account for any measurement error.
jonesy101
The question: Given that w=h-bar(L+1)/I. Suppose that we observe spectral lines from the HCl molecule at wave numbers (in cm^-1) 85.03, 103.73, 124.30, 145.03, 165,51 and 185.86 (wavenumber here is simply in the inverse wavelength lambda^-1). What L values do these lines correspond to?

My attempt: Knowing that w=2*pi*c/lambda I tried to set up a ratio between to wavenumbers and relate it to the original equation but couldn't find a set of integrals for L that matched my ratios. I don't know what to do.

jonesy101 said:
The question: Given that w=h-bar(L+1)/I. Suppose that we observe spectral lines from the HCl molecule at wave numbers (in cm^-1) 85.03, 103.73, 124.30, 145.03, 165,51 and 185.86 (wavenumber here is simply in the inverse wavelength lambda^-1). What L values do these lines correspond to?

My attempt: Knowing that w=2*pi*c/lambda I tried to set up a ratio between to wavenumbers and relate it to the original equation but couldn't find a set of integrals for L that matched my ratios. I don't know what to do.

Perhaps you just need to allow for a little measurement error. You know ω is proportional to wave number (inverse wavelength). Try graphing those wave numbers and see what you get.

## 1. What is the relationship between L values and spectral lines?

The L values refer to the angular momentum quantum number in atomic structure, while spectral lines refer to the specific wavelengths of light emitted or absorbed by an atom. The L values determine the possible energy levels an electron can occupy in an atom, and the transition between these levels results in the emission or absorption of light at specific wavelengths, which correspond to spectral lines.

## 2. How do rotational translations between L values and spectral lines affect atomic spectra?

The rotational translations between L values and spectral lines result in the splitting of spectral lines into multiple components, known as fine structure. This is due to the influence of the electron's orbital angular momentum on its energy levels. This splitting allows for more precise measurement and analysis of atomic spectra.

## 3. Can the L values of an atom change?

Yes, the L values of an atom can change through various processes such as electron excitation, ionization, and electron capture. These changes in L values result in the shifting and splitting of spectral lines, which can provide valuable information about the atom's energy levels and structure.

## 4. How are rotational translations between L values and spectral lines observed?

Rotational translations between L values and spectral lines can be observed through spectroscopy, which involves passing light through a sample of atoms and measuring the resulting spectral lines. The fine structure of spectral lines can then be analyzed to determine the L values and other properties of the atoms.

## 5. What is the significance of rotational translations between L values and spectral lines in understanding atomic structure?

The rotational translations between L values and spectral lines are crucial in understanding the energy levels and structure of atoms. They provide insight into the behavior of electrons within atoms and can help in identifying and characterizing different elements. Furthermore, these translations play a vital role in fields such as quantum mechanics and atomic physics, contributing to our overall understanding of the fundamental building blocks of matter.

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