Question

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ_1, λ₂, and λ₃ from the energy-level diagram shown below.

Solution

Bohr's Quantisation Rule:
According to Bohr, an electron can revolve only in certain discrete, non-radiating orbits for which the total angular momentum of the revolving electron is an integral multiple of $fraction numerator straight h over denominator 2 straight pi end fraction$ ; where h is the Planck's constant.
That is, $mvr space equals space fraction numerator nh over denominator 2 straight pi end fraction$
b)
Using Rydberg's formula for spectra of hydrogen atom, we have
$1 over straight lambda subscript 1 space equals space R space open parentheses 1 over n subscript 2 squared space minus space 1 over n subscript 3 squared close parentheses space space space space space space space space space space space space... space left parenthesis 1 right parenthesis thin space 1 over straight lambda subscript 2 space equals space R space open parentheses 1 over n subscript 1 squared space minus space 1 over n subscript 2 squared close parentheses space space space space space space space space space space space space... space left parenthesis 2 right parenthesis thin space 1 over straight lambda subscript 3 equals space R space open parentheses 1 over n subscript 1 squared space minus space 1 over n subscript 3 squared close parentheses space space space space space space space space space space space space space... space left parenthesis 3 right parenthesis thin space Now comma space adding space left parenthesis 1 right parenthesis thin space and space left parenthesis 2 right parenthesis comma space we space get 1 over straight lambda subscript 1 space plus space 1 over straight lambda subscript 2 space equals space space R space open parentheses 1 over n subscript 1 squared space minus space 1 over n subscript 3 squared close parentheses space equals space 1 over straight lambda subscript 3 space semicolon space$
Hence, the relation between 3 wavelengths from the energy-level diagram is obtained.

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Wave Optics

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ_1, λ₂, and λ₃ from the energy-level diagram shown below.

Some More Questions From Wave Optics Chapter

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

Wave Optics

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits? (ii) Find the relation between three wavelengths λ1, λ2, and λ3 from the energy-level diagram shown below.

Some More Questions From Wave Optics Chapter

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a _____________ but has a highly non-uniform mass distribution in __________ (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?

(ii) Find the relation between three wavelengths λ_1, λ₂, and λ₃ from the energy-level diagram shown below.

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)