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
The energy associated with the first orbit in the hydrogen atom is - 2.18 × 10-18 J atom-1. What is the energy associated with the fifth orbit?
Explain, giving reasons, which of the following sets of quantum numbers are not possible.
- n = 0, l = 0, ml = 0, ms = + ½
- n = 1, l = 0, ml = 0, ms = – ½
- n = 1, l = 1, ml = 0, ms = + ½
- n = 2, l = 1, ml = 0, ms = – ½
- n = 3, l = 3, ml = –3, ms = + ½
- n = 3, l = 1, ml = 0, ms = + ½
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of the hydrogen atom.
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.
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?
According to Bohr, 'Angular momentum of an orbiting electron is quantized'. What is meant by this statement?
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
Which of the following is/are CORRECT according to Bohr's atomic theory?
(I) Energy is emitted when electron moves from a higher stationary state to a lower one.
(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.
(III) The energy of an electron in the orbit changes with time.
According to Bohr's model of hydrogen atom, an electron can revolve round a proton indefinitely, if its path is ______.
Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.
The angular momentum of electron in nth orbit is given by
The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be
B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)
This last expression is not correct because ______.
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 ______.
When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?
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 wavelength in Å of the photon that is emitted when an electron in Bohr orbit with n = 2 returns to orbit with n = 1 in H atom is ______ Å. The ionisation potential of the ground state of the H-atom is 2.17 × 10−11 erg.
The total energy of an electron in the nth orbit of the hydrogen atom is proportional to ______.
The radius of the nth orbit in the Bohr model of hydrogen is proportional to ______.
