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
Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.
Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?
Calculate the de-Broglie wavelength associated with the electron revolving in the first excited state of the hydrogen atom. The ground state energy of the hydrogen atom is −13.6 eV.
According to Bohr's theory, an electron can move only in those orbits for which its angular momentum is integral multiple of ____________.
What is the energy in joules released when an electron moves from n = 2 to n = 1 level in a hydrogen atom?
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.
How will the energy of a hydrogen atom change if n increases from 1 to ∞?
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 ______.
According to Bohr atom model, in which of the following transitions will the frequency be maximum?
A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ______.
(Given, Planck's constant = 6.6 × 10-34 Js)
