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Wave Optics

Question

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The wavelength of the first member of the Balmer series in hydrogen spectrum is 6563 A. What is the wavelength of the first member of Lyman series?

Solution

Wavelength of hydrogen spectrum in the balmer series ,

λ_{1}

= 6563

\overset{o}{A}

For Balmer series,

\frac{1}{λ_{1}} = R (\frac{1}{2^{2}} - \frac{1}{3^{2}}) = \frac{5 R}{36}

For Lyman series,

\frac{1}{λ_{2}} = R (\frac{1}{1^{2}} - \frac{1}{2^{2}}) = \frac{3 R}{4} \Rightarrow \frac{λ_{2}}{λ_{1}} = \frac{4}{3 R} \times \frac{5 R}{36} = \frac{20}{108} = \frac{5}{27} ∴ λ_{2} = \frac{5}{27} \times λ_{1} = \frac{5}{27} \times 6563 = 1215 Å .

is the wavelength of the first member of the Lyman series.

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?

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