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Question : 21
Total: 26
(i) State Bohr's quantization condition for defining stationary orbits. How does de Broglie hypothesis explain the stationary orbits?
(ii) Find the relation between the three wavelengthλ 1 , λ 2 λ 3
(ii) Find the relation between the three wavelength
Solution:
(i) Statement of Bohr's quantization condition
de- Broglie explanation of stationary orbits
(ii) Relation betweenλ 1 , λ 2 λ 3
(i) Only those orbits are stable for which the angular momentum, of revolving electron, is an integral multiple of
[Alternatively
L =
According to de-Broglie hypothesis
Linear momentum( p ) =
And for circular orbitL = r n p r
=
L =
∴
=
⇒ 2 π r n = n λ
∴ λ
(ii)E C − E B =
E B − E A =
E C − E A =
Adding (i) & (ii)
E C − E A =
+
Using equation (iii) and (iv)
=
+
⇒
=
+
de- Broglie explanation of stationary orbits
(ii) Relation between
(i) Only those orbits are stable for which the angular momentum, of revolving electron, is an integral multiple of
[Alternatively
According to de-Broglie hypothesis
Linear momentum
And for circular orbit
(ii)
Adding (i) & (ii)
Using equation (iii) and (iv)
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