Line Spectra of Li2+ & Be3+: Shortest Wavelength

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In summary, doubly ionized lithium and triply ionized beryllium emit a line spectrum. The shortest wavelength for a certain series of lines in the lithium spectrum is 1222.2 nm. To find the shortest wavelength for the same series of lines in the beryllium spectrum, we can use the equation 1/lambda = 1.097 x 10^7 (z^2) (1/nf^2 - 1/ni^2). The values of n1 and n2 can be determined by solving for them using the given wavelength and substituting them into the equation. The answer does not depend on the particular values of n1 and n2.
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StudentofPhysics
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1. Doubly ionized lithium Li2+ (Z = 3) and triply ionized beryllium Be3+ (Z = 4) each emit a line spectrum. For a certain series of lines in the lithium spectrum, the shortest wavelength is 1222.2 nm. For the same series of lines in the beryllium spectrum, what is the shortest wavelength?



2. 1/ lamba = 1.097 x 10^7 (z^2) (1/nf^2 - 1/ni^2)



3. My only question is what I use for the n's? Since its the smallest I assume ni = 0. What about nf?
 
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Assuming an equation like (2) is valid, does the answer depend on the particular values of n1 and n2?
 
  • #3
ok, i misunderstood what nf should be.

I figured it out now by solving for it by the first given wavelength then applying that number as the nf for the second.

Thank you.
 

FAQ: Line Spectra of Li2+ & Be3+: Shortest Wavelength

What is a line spectrum?

A line spectrum is a pattern of discrete lines of different colors or wavelengths that are produced when an element is heated or excited. Each element has a unique line spectrum, which can be used to identify it.

How are line spectra of Li2+ & Be3+ produced?

The line spectra of Li2+ and Be3+ are produced when these ions are excited by either heat or electricity. The energy from the excitation causes the electrons in the ions to jump to higher energy levels, and when they return to their original energy levels, they emit photons of specific wavelengths, creating the line spectrum.

Why do Li2+ & Be3+ have the shortest wavelengths in their line spectra?

Li2+ and Be3+ have the shortest wavelengths in their line spectra because they have the highest energy levels and therefore, the largest energy gaps between their levels. When the electrons return to their lower energy levels, they emit photons with shorter wavelengths, resulting in the shortest lines in their spectra.

How are the wavelengths of the lines in the line spectra of Li2+ & Be3+ calculated?

The wavelengths of the lines in the line spectra of Li2+ and Be3+ are calculated using the Rydberg formula, which takes into account the energy levels of the ions and the charge of the nucleus. This formula can be used to determine the exact wavelengths of the lines in the spectra.

What can the line spectra of Li2+ & Be3+ tell us about these ions?

The line spectra of Li2+ and Be3+ can tell us about the energy levels and electronic structure of these ions. By analyzing the patterns and wavelengths of the lines, we can determine the number of energy levels, the charge of the nucleus, and the arrangement of electrons in these ions.

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