Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर १
`n lambda = 2 pi r`
But ` lambda = n/(mv) `( By De Broglie)
`(n lambda) /(mv) = 2 pi r`
` therefore (lambda n) /(2 pi ) = mvr ` (mvr = L)
` therefore L = (lambda n)/(2 pi)`
उत्तर २
Bohr's second postulate states that the angular momentum of an electron has only those values that are integral multiples of `"h"/(2pi)` He thought that the motion of electrons within an atom is associated with the standing wave along the orbit as shown.
About standing waves in stretched strings, we know that only those waves survive for which the distances traveled in the round trip between the ends are integral multiples of the wavelength. Similarly, for an electron moving in the nth orbit of radius rn, the distance traveled in one trip is 2πrn, which should be an integral multiple of the wavelength.
2πrn = nλ (where n= 1, 2, 3, 4 etc)
By de-Broglie hypothesis, we have:
`lambda = "h"/"p" = "h"/("mv"_"n")`
Substituting the value of λ in the above expression, we get:
`2pi"r"_"n" = "n" "h"/"mv"_"n"`
⇒ `"mv"_"n""r"_"n" = "n" "h"/(2pi)`
Angular momentum `= "L" = "n" "h"/(2pi)`
संबंधित प्रश्न
Obtain an expression for the radius of Bohr orbit for H-atom.
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.
- Using the Bohr’s model, calculate the speed of the electron in a hydrogen atom in the n = 1, 2 and 3 levels.
- Calculate the orbital period in each of these levels.
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
For an electron in the second orbit of hydrogen, what is the moment of momentum as per the Bohr's model?
The angular momentum of electron in nth orbit is given by
For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true ______.
The Bohr model for the spectra of a H-atom ______.
- will not be applicable to hydrogen in the molecular from.
- will not be applicable as it is for a He-atom.
- is valid only at room temperature.
- predicts continuous as well as discrete spectral lines.
The radius of the nth orbit in the Bohr model of hydrogen is proportional to ______.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
