Advertisements
Advertisements
Question
Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.
Advertisements
Solution
Mass of the electron, m = 9.1×10-31kg
Radius of the ground state, r = 0.53×10-10m
Let f be the frequency of revolution of the electron moving in ground state and A be the area of orbit.
Dipole moment of the electron (μ) is given by
μ = niA = qfA
`= e xx (me^4)/(4∈_0^2h^3n^3)xx(pi^2n^2)`
`= (me^5xx (pir^2n^2))/(4∈_0^2h^3n^3)`
Here,
h = Planck's constant
e = Charge on the electron
`epsilon_0` = Permittivity of free space
n = Principal quantum number
`therefore mu = ((9.1xx10^-13)(1.6xx10^-19)^5xxpi xx(0.53xx10^-10)^2)/(4 xx (8.85xx10^-12)^2xx(6.64xx10^-34)^3xx(1)^3`
= 0.000917 × 10-20
= 9.176 × 10-24 A-m25
APPEARS IN
RELATED QUESTIONS
Obtain an expression for the radius of Bohr orbit for H-atom.
The longest wavelength doublet absorption transition is observed at 589 and 589.6 nm. Calculate the frequency of each transition and energy difference between two excited states.
if `E_p` and `E_k` represent potential energy and kinetic energy respectively, of an orbital electron, then, according to B9hr's theory:
a)`E_k = -E_p"/"2`
b) `E_k = -E_p`
c) `E_k = -2E_p`
d) `E_k = 2E_p`
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of the hydrogen atom.
Write the expression for Bohr’s radius in hydrogen atom ?
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Taking the Bohr radius as a0 = 53 pm, the radius of Li++ ion in its ground state, on the basis of Bohr’s model, will be about ______.
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")`.
The number of times larger the spacing between the energy levels with n = 3 and n = 8 spacing between the energy level with n = 8 and n = 9 for the hydrogen atom is ______.
According to Bohr atom model, in which of the following transitions will the frequency be maximum?
The first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.
What is the energy of an electron in stationary state corresponding to n = 2?
Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ. If R is the Rydberg constant then the principal quantum number n of the excited state is ______.
What is meant by ionisation energy?
State three postulates of Bohr's theory of hydrogen atom.
How much is the angular momentum of an electron when it is orbiting in the second Bohr orbit of hydrogen atom?
The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li2+ ion (atomic number = 3) in a similar state is ______.
