Advertisements
Advertisements
प्रश्न
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Advertisements
उत्तर
In the Bohr model of the hydrogen atom, the electron is modeled as a point negative charge rotating in a circular orbit about a fixed axis about a nucleus.
Let us consider,
r = radius of the orbit
v = velocity
e = charge of electron
m = mass of electron
Time period (T) = `"circumference"/"velocity"`
= `(2 pi r)/v`
Current (I) = `(-e)/T`
= `(-e)/((2 pi r)/v)`
= `(-e v)/(2 pi r)`
The magnetic moment due to a current loop enclosing an area A is given by:
ML = IA
= `(-e V)/(2 pi r) xx A`
= `(-e v)/(2 pi r) xx pi r^2`
= `(-e r v)/2`
= `(-m e r v)/(2 m)`
L = Angular momentum = mvr
So, ML = `(-e)/(2 m) L`
संबंधित प्रश्न
Calculate the radius of Bohr’s fifth orbit for hydrogen atom
Using Bohr's postulates, derive the expression for the orbital period of the electron moving in the nth orbit of hydrogen atom ?
Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states tan be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.
Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.
If l3 and l2 represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l3: l2 is :
Draw energy level diagram for a hydrogen atom, showing the first four energy levels corresponding to n=1, 2, 3 and 4. Show transitions responsible for:
(i) Absorption spectrum of Lyman series.
(ii) The emission spectrum of the Balmer series.
Mention demerits of Bohr’s Atomic model.
The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.
In Bohr's theory of hydrogen atom, the electron jumps from higher orbit n to lower orbit p. The wavelength will be minimum for the transition ______.
The wavelength of the second line of the Balmer series in the hydrogen spectrum is 4861 Å. Calculate the wavelength of the first line of the same series.
