Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given: Ground state energy = −13.6 eV
For a hydrogen atom,
En = `(-13.6)/n^2 eV`
First excited state ⇒ n = 2
E2 = `(-13.6)/2^2`
= `(-13.6)/4`
= −3.4 eV
In the Bohr model:
K.E. = ∣En∣ = 3.4 eV
= 3.4 × 1.6 × 10−19
= 5.44 × 10−19 J
By using de-Broglie relation:
λ = `h/p`
Since,
K.E.= `p^2/(2 m)`
p = `sqrt(2 m K.E.)`
Thus,
λ = `h/sqrt(2 m K.E.)`
= `(6.63 xx 10^-34)/(sqrt(2 xx 9.1 xx 10^-31 xx 5.44 xx 10^-19))`
= 6.66 × 10−10 m
= 6.66 Å
संबंधित प्रश्न
The ratio of kinetic energy of an electron in Bohr’s orbit to its total energy in the same orbit is
(A) – 1
(B) 2
(C) 1/2
(D) – 0.5
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?
Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?
A neutron having kinetic energy 12.5 eV collides with a hydrogen atom at rest. Nelgect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.
According to Bohr, 'Angular momentum of an orbiting electron is quantized'. What is meant by this statement?
The energy of an electron in an excited hydrogen atom is - 3.4 eV. Calculate the angular momentum of the electron according to Bohr's theory. (h = 6.626 × 10-34 Js)
The wavelength of the first time line of Ballmer series is 6563 A°. The Rydberg constant for hydrogen is about:-
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.
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.
Specify the transition of an electron in the wavelength of the line in the Bohr model of the hydrogen atom which gives rise to the spectral line of the highest wavelength ______.
