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प्रश्न
(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.
उत्तर
(a) Bohr's quantisation condition: According to Bohr, an electron can revolve only in certain discrete, non-radiating orbits for which total angular momentum of the revolving electron is an integral multiple of `h/(2pi)`where h is the Planck's constant.
`:.mvr=(nh)/(2pi)`
(b) Using the Rydberg formula of the spectra of hydrogen atom, we write
`1/lamda_1=R(1/n_(2^2)-1/n_(3^2)) ......(1)`
`1/lamda_2=R(1/n_(1^2)-1/n_(2^2)) ......(2)`
`1/lamda_3=R(1/n_(1^2)-1/n_(3^2)) ......(3)`
Adding (1) and (2), we find that
`1/lambda_1+1/(lambda_2)=R(1/n_(1^2)-1/n_(3^2))=1/lambda_3`
This is the required relation between the three wavelengths.
संबंधित प्रश्न
Find the frequency of revolution of an electron in Bohr’s 2nd orbit; if the radius and speed of electron in that orbit is 2.14 × 10-10 m and 1.09 × 106 m/s respectively. [π= 3.142]
If the velocity of the electron in Bohr’s first orbit is 2.19 × 106 ms-1, calculate the de Broglie wavelength associated with it.
The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is
(A) – 1
(B) 2
(C) 1/2
(D) – 0.5
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