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")`.
Advertisements
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
An electron is orbiting in 5th Bohr orbit. Calculate ionisation energy for this atom, if the ground state energy is -13.6 eV.
In Bohr’s model of the hydrogen atom, the radius of the first orbit of an electron is r0 . Then, the radius of the third orbit is:
a) `r_0/9`
b) `r_0`
c) `3r_0`
d) `9r_0`
How will the energy of a hydrogen atom change if n increases from 1 to ∞?
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level:
What is the energy associated with first orbit of Li2+ (RH = 2.18 × 10-18)?
In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.
According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.
State three postulates of Bohr's theory of hydrogen atom.
For an orbit radius of \[5.3\times10^{-11}\,\mathrm{m}\] and an electron velocity of \[2.2\times10^6\,\mathrm{m\,s^{-1}}\], what is the approximate initial frequency of emitted light according to classical electromagnetic theory?
