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प्रश्न
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
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उत्तर
Since a hydrogen atom has only one electron, according to Bohr’s postulate, the angular momentum of that electron is given by:
`"mvr" = "n" "h"/(2pi) ` ....(1)
Where,
n = 1, 2, 3, …
According to de Broglie’s equation:
`lambda = "h"/("mv")`
or `"mv" = ("h"/lambda)` ....(2)
Substituting the value of ‘mv’ from expression (2) in expression (1):
`("hr")/lambda = "n" "h"/(2pi)`
or `2pi"r" = "n"lambda` .....(3)
Since ‘2π"r"’ represents the circumference of the Bohr orbit (r), it is proved by equation (3) that the circumference of the Bohr orbit of the hydrogen atom is an integral multiple of de Broglie’s wavelength associated with the electron revolving around the orbit.
संबंधित 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.
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if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:
a)`E_k = -E_p"/"2`
b) `E_k = -E_p`
c) `E_k = -2E_p`
d) `E_k = 2E_p`
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Obtain Bohr’s quantisation condition for angular momentum of electron orbiting in nth orbit in hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.
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The energy of an electron in hth orbit of hydrogen atom is –13.6/n2ev energy required to excite the electron from the first orbit to the third orbit is
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- because of energy conservation.
- without simultaneously releasing energy in the from of radiation.
- because of momentum conservation.
- because of angular momentum conservation.
State Bohr's postulate to explain stable orbits in a hydrogen atom. Prove that the speed with which the electron revolves in nth orbit is proportional to `(1/"n")`.
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The energy of an electron in the first Bohr orbit of the H-atom is −13.6 eV. The energy value of an electron in the excited state of Li2+ is ______.
What is the energy associated with first orbit of Li2+ (RH = 2.18 × 10-18)?
In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.
