Advertisements
Advertisements
Question
Use Bohr's postulate to prove that the radius of nth orbit in a hydrogen atom is proportional to n2.
Advertisements
Solution
The necessary centripetal force for the rotation of an electron is supplied by the electrostatic force between the electron and the nucleus.
`"mv"^2/"r" = (1/(4πε_0))("e"^2/"r"^2)` ....[putting Z = 1]
Or, mv2 = `"e"^2/(4πε_0"r")` .....(i)
From Bohr's theory,
mvr = `"nh"/(2π)`
∴ v = `"nh"/(2π"mr")`
Putting in equation (i)
`"m"("nh"/(2π"mr"))^2 = "e"^2/(4πε_0"r")`
Or, r = `(ε_0"n"^2"h"^2)/(π"me"^2)`
In general,
rn = `(ε_0"n"^2"h"^2)/(π"me"^2)`
∴ `"rn" ∝ "n"^2`
APPEARS IN
RELATED QUESTIONS
(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.
- 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.
The gravitational attraction between electron and proton in a hydrogen atom is weaker than the Coulomb attraction by a factor of about 10−40. An alternative way of looking at this fact is to estimate the radius of the first Bohr orbit of a hydrogen atom if the electron and proton were bound by gravitational attraction. You will find the answer interesting.
Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
The value of angular momentum for He+ ion in the first Bohr orbit is ______.
A hydrogen atom in its first excited state absorbs a photon of energy x × 10-2 eV and exited to a higher energy state where the potential energy of electron is -1.08 eV. The value of x is ______.
What is the energy associated with first orbit of Li2+ (RH = 2.18 × 10-18)?
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
