Advertisements
Advertisements
प्रश्न
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")`.
उत्तर
The stationary orbits are those orbits for which the angular momentum of the electron is an integral multiple of `"h"/(2π)`, where h is Planck's constant.
Electron in an atom revolves because of the balance of Coulomb force of attraction between the protons and electrons and the centripetal force.
In the nth orbit,
`("mv"_"n"^2)/"r"_"n" = 1/(4πε_0) "e"^2/"r"_"n"^2`
∴ vn = `"e"/(sqrt(4πε_0"mr"_"n"))` ......(i)
Again, rn = `(ε_0"h"^2"n"^2)/("e"^2π"m")` .....(ii)
Putting in equation (i)
vn = `"e"/sqrt(4πε_0"m"(ε_0"h"^2"n"^2)/("e"^2π"m"))`
= `"e"^2/(2ε_0"hn")`
∴ `"v"_"n" ∝ 1/"n"`
संबंधित प्रश्न
Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states tan be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.
Write the expression for Bohr’s radius in hydrogen atom ?
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (Φ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of λ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
Answer the following question.
Calculate the orbital period of the electron in the first excited state of the hydrogen atom.
Mention demerits of Bohr’s Atomic model.
Which of the following is/are CORRECT according to Bohr's atomic theory?
(I) Energy is emitted when electron moves from a higher stationary state to a lower one.
(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.
(III) The energy of an electron in the orbit changes with time.
The energy of an electron in an excited hydrogen atom is - 3.4 eV. Calculate the angular momentum of the electron according to Bohr's theory. (h = 6.626 × 10-34 Js)
Find the ratio of energies of photons produced due to transition of an election of hydrogen atom from its (i) second permitted energy level to the first level. and (ii) the highest permitted energy level to the first permitted level.
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 ______.
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
