how do u derive Rydberg's constant?

Question

could u plz tell???

Answer 1

Janne Rydberg analyzed the spectra of many elements. He started using the wavenumber n instead of the wavelength lambda. The wavenumber is the number of waves per length. Rydberg found then that many line series are well described with the expression:

n = no − No/(m+m')2,

where m is a natural number. The quantum defect m' and no and are specific for a particular series. No turns out to be a universal constant, the Rydberg constant. Rydberg showed that the Balmer series of hydrogen is a special case with m'=0, no=4No.

Now Rydberg's constant No is denoted by R. In 1913, Niels Bohr showed that R can be expressed as a combination of the speed of light in vacuum c, Planck's constant h, the electrons charge e, and its mass m by

R=me4/(8εo2h3c),
where εo is the permittivity of vacuum.

Value
The 1998 accepted value of the Rydberg constant R∞ is:

* 10 973 731.568 548(83) m-1
* 3.289 841 960 367(25).1015 Hz (Rc)
* 13.605 691 72(53) eV (Rhc/e)
* 2.179 871 90(17).10-18 J (Rhc)


Early development of Quantum Theory established that Rydberg's constant for Hydrogen (a special case from which all other values can be derived) is:

m(k * k)(e**4)/4pi*ch**3 = 1.097 * (10**7) /m

In actual fact, Hc is measured experimentally, but matches the above theoretical calculation closely.
(where * is multiplication and ** is "to the power")

Answer 2

Go to:
http://en.wikipedia.org/wiki/Rydberg_constant

Answer 3

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