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Rydberg Constant for Beryllium

The beryllium (3) ion, Be 3+ is like the hydrogen atom in that it has a single electron. Its emission line spectrum is similar to that of hydrogen, except that the value of the Rydberg constant is different. The following lines were observed for a 'series' (i.e. all have the same value of nf) the Be 3+: 117.18 nm, 80.10nm, 68.35nm, 62.80nm.
a. Show that these follow the relationship (See attachment)
b. Find the values of nf for the series and ni for each line
c. Find a relationship between K and Rf, the Rydberg constant for hydrogen. To what property is beryllium is this connected?


Solution Preview

The mathematical symbols are more clear in the attached word file.

6. a. The change in energy level of an electron due to the transition between two energy levels is
given by ∆E = E0(1/nf2 - 1/ni2)
that is ∆E = (mee4Z2/8ε02h2) (1/nf2 - 1/ni2) ------------------- 1
since ∆E = hc (1/λ), where h = Planck's constant, we can write equation.1 as
(1/λ) = (mee4Z2/8ε02h3c) (1/nf2 - 1/ni2)
where me is the rest mass of the electron, e is the elementary charge, Z is atomic number, ε0 is
the permittivity of free space, c is the velocity of light, nf and ni are the final and initial quantum
numbers and λ is the wavelength of the spectral line resulting from the transition between nf and
ni levels
(1/λ) = RZ2(1/nf2 - 1/ni2) ------------------- 2
R is the Rydberg constant given by (mee4/8ε02h3c) ...

Solution Summary

This solution shows step-by-step calculations to determine the values of nf for series, ni for lines. It also shows the relationship bet K and Rf and the property of beryllium.