Advertisements
Advertisements
Question
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Advertisements
Solution
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`
RELATED QUESTIONS
Using Bohr's postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr's radius.
Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has a duration of 2 ns and the number of photons emitted during the pulse source is 2.5 × 1015, calculate the energy of the source.
The numerical value of ionization energy in eV equals the ionization potential in volts. Does the equality hold if these quantities are measured in some other units?
Find the wavelength of the radiation emitted by hydrogen in the transitions (a) n = 3 to n= 2, (b) n = 5 to n = 4 and (c) n = 10 to n = 9.
The earth revolves round the sun due to gravitational attraction. Suppose that the sun and the earth are point particles with their existing masses and that Bohr's quantization rule for angular momentum is valid in the case of gravitation. (a) Calculate the minimum radius the earth can have for its orbit. (b) What is the value of the principal quantum number n for the present radius? Mass of the earth = 6.0 × 10−24 kg. Mass of the sun = 2.0 × 1030 kg, earth-sun distance = 1.5 × 1011 m.
Which of these statements correctly describe the atomic model according to classical electromagnetic theory?
In Bohr model of hydrogen atom, which of the following is quantised?
If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.
Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is ______.
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
