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Wave Optics

Question

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In Bohr's theory of hydrogen atom, calculate the energy of the photon emitted during a transition of the electron from the first excitated state to its ground state. Write in which region of the electromagnetic spectrum this transition lies.
Given Rydberg constant R = 1.03 × 10⁷ m^–1.

Solution

Energy for nth level of hydrogen atom is given by,

E_{n} = - \frac{13.6}{n^{2}} eV

Energy of the photon emitted during a transition of the electron from the first excited state (n=2) to its ground state (n=1) is,

E = E_{2} - E_{1} = - \frac{13.6}{2^{2}} - (- \frac{13.6}{1^{2}}) = - \frac{13.6}{4} + \frac{13.6}{1} = - 3.40 + 13.6 = 10.2 eV

This transition lies in the region of 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?

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