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# SSPD_Chapter1_Part 7continued_Theoretical Formulation of Rydberg Constant

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: This is the continuation of Chapter 1_Part 7. This gives the theoretical explanation of the five distinct series of LINE SPECTRA experimentally observed in Hydrogen Gas.

1.6.3.2. THEORETICAL DERIVATION OF RYDBERG CONSTANT.

When a photon of energy packet hν is incident on an atom of a given element , it excites an electron from ground state n1 to the excited state n2 in a way so as to satisfy the following condition:

ΔE = En2 – En1 = hν;

From Eq.(1.35) the condition to be satisfied is:

hν = (-13.6/n22 + 13.6/n12) eV;

or N= 1/λ = ν/c = (13.6eV/hc) (-1/n 2 2 + 1/n 1 2 ) 1.37

By comparing Eq(1.36) and Eq(1.37) we arrive at the numerical value of Rydberg Constant R to be:

R = (13.6eV/hc) 1.38

Substituting the numerical values of h and c in Eq.(1.38) we obtain :

R= 1.096×10 5 cm -1 1.39

The theoretical value of Rydberg Constant is close to the experimental value as given by Eq.(1.36).

Theoretical derivation of Rydberg Constant is considered as a definite vindication of the Quantum Theory of Atoms as proposed by Neil Bohr.

Based on this interpretation we get the underlying explanation for the various line spectra exhibited by Hydrogen Atom namely Lyman Series or K series, Balmar Series or L series, Paschen series or M series, Brackett series or N series and Pfund series or O series. The excitation states which create the five series of line spectra are shown in Fig.(1.17).

Fig.(1.17) Basic underlying cause for the generation of the five line spectra of Hydrogen Atom.

Based on these line spectra the shell corresponding to principal quantum number n=1 that is the innermost orbit is referred to as K Shell. Similarly the subsequent orbits corresponding to n= 2,3,4,5 are called L, M, N, O Shells respectively.

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