NEET-XII-Physics
43: Bohr's Model and Physics of the Atom
- #7The difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series. Explain.Ans : The 'series limit' refers to the 'shortest wavelength' (corresponding to the maximum photon energy).
The frequency of the radiation emitted for transition from n1 to n2 is given by
`` f=k\left(\frac{1}{{n}_{1}^{2}}-\frac{1}{{n}_{2}^{2}}\right)``
Here, k is a constant.
For the series limit of Lyman series,
n1 = 1
n2 = `` \infty ``
Frequency, `` {f}_{1}=k\left(\frac{1}{{1}^{2}}-\frac{1}{\infty }\right)=k``
For the first line of Lyman series,
n1 = 1
n2 = 2
Frequency, `` {f}_{2}=k\left(\frac{1}{{1}^{2}}-\frac{1}{{2}^{2}}\right)=\frac{3k}{4}``
For series limit of Balmer series,
n1 = 2
n2 = `` \infty ``
`` {f}_{1}=k\left(\frac{1}{{2}^{2}}-\frac{1}{\infty }\right)=\frac{k}{4}``
f1 `` -`` f3 = f2
Thus, the difference in the frequencies of series limit of Lyman series and Balmer series is equal to the frequency of the first line of the Lyman series.
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