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Wave Optics

Question

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Using Bohr's formula for energy quantisation, determine the longest wavelength in the Lyman series of hydrogen atom spectrum.

Solution

Wavelengths of radiation of the Lyman series is given by,

λ_{n} = \frac{64 π^{3} ε_{0}^{2} h^{3} c}{{me}^{4}} (\frac{n^{2}}{n^{2} - 1^{2}})

For longest wavelength in the lyman series, we have n=2.

Therefore,
Wavelength assosciated with n=2 is,

λ_{2} = \frac{64 π^{3} {ε_{o}}^{2} h^{3} c}{{me}^{4}} (\frac{2^{2}}{2^{2} - 1^{2}}) = 1225 \overset{o}{A}

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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