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Wave Optics

Question
CBSEENPH12039838
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An electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths λ1:λ2 emitted in the two cases is

  • 7/5

  • 27/20

  • 27/5

  • 20/7

Solution

D.

20/7

Here, for wavelength λ1
n1 = 4 and n2 =3
and for λ2, n1 = 3 and n2 = 2
We space have space hc over straight lambda space equals space minus 13.6 open square brackets fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction close square brackets so comma space for space straight lambda subscript 1 rightwards double arrow space hc over straight lambda subscript 1 space equals space minus 13.6 open square brackets fraction numerator 1 over denominator left parenthesis 4 right parenthesis squared end fraction minus fraction numerator 1 over denominator left parenthesis 3 right parenthesis squared end fraction close square brackets hc over straight lambda subscript 1 space equals space minus 13.6 open square brackets 7 over 144 close square brackets space.... space left parenthesis straight i right parenthesis space simiarly comma space for space straight lambda subscript 2 rightwards double arrow space hc over straight lambda subscript 1 space equals space minus 13.6 open square brackets fraction numerator 1 over denominator left parenthesis 3 right parenthesis squared end fraction minus fraction numerator 1 over denominator left parenthesis 2 right parenthesis squared end fraction close square brackets hc over straight lambda subscript 1 space equals space minus 13.6 open square brackets 5 over 36 close square brackets... space left parenthesis ii right parenthesis Hence comma space from space Eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get straight lambda subscript 1 over straight lambda subscript 2 space equals space 20 over 7

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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