Advertisements
Advertisements
Question
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
Solution 1
`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)`
Solution 2
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)`
RELATED QUESTIONS
A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Nelgect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom ______.
- because of energy conservation.
- without simultaneously releasing energy in the from of radiation.
- because of momentum conservation.
- because of angular momentum conservation.
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.
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:
If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is ______.
The first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.
Find the angular momentum of an electron revolving in the second orbit in Bohr's hydrogen atom.
