Advertisements
Advertisements
प्रश्न
Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.
Advertisements
उत्तर
Since a hydrogen atom has only one electron, according to Bohr’s postulate, the angular momentum of that electron is given by:
`"mvr" = "n" "h"/(2pi) ` ....(1)
Where,
n = 1, 2, 3, …
According to de Broglie’s equation:
`lambda = "h"/("mv")`
or `"mv" = ("h"/lambda)` ....(2)
Substituting the value of ‘mv’ from expression (2) in expression (1):
`("hr")/lambda = "n" "h"/(2pi)`
or `2pi"r" = "n"lambda` .....(3)
Since ‘2π"r"’ represents the circumference of the Bohr orbit (r), it is proved by equation (3) that the circumference of the Bohr orbit of the hydrogen atom is an integral multiple of de Broglie’s wavelength associated with the electron revolving around the orbit.
APPEARS IN
संबंधित प्रश्न
State Bohr’s postulate of hydrogen atom which successfully explains the emission lines in the spectrum of hydrogen atom. Use Rydberg formula to determine the wavelength of Hα line. [Given: Rydberg constant R = 1.03 × 107 m−1]
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
State Bohr's postulate to define stable orbits in the hydrogen atom. How does de Broglie's hypothesis explain the stability of these orbits?
Light from Balmer series of hydrogen is able to eject photoelectrons from a metal. What can be the maximum work function of the metal?
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.
In which of the following systems will the wavelength corresponding to n = 2 to n = 1 be minimum?
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.
How are various lines of Lyman series formed? Explain on the basis of Bohr’s theory.
The energy associated with the first orbit of He+ is ____________ J.
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
According to Bhor' s theory the moment of momentum of an electron revolving in second orbit of hydrogen atom will be.
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 ______.
A set of atoms in an excited state decays ______.
An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state ______.
- the electron would not move in circular orbits.
- the energy would be (2)4 times that of a H-atom.
- the electrons, orbit would go around the protons.
- the molecule will soon decay in a proton and a H-atom.
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's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.
What is meant by ionisation energy?
