Advertisements
Advertisements
प्रश्न
In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 1011 m with orbital speed 3 × 104 m/s. (Mass of earth = 6.0 × 1024 kg)
Advertisements
उत्तर
Radius of the orbit of the earth around the sun, r = 1.5 × 1011 m
Orbital speed of the earth, v = 3 × 104 m/s
Mass of the earth, m = 6.0 × 1024 kg
According to Bohr’s model, angular momentum is quantised and given as:
mvr = `(nh)/(2pi)`
Where,
h = Planck’s constant = 6.62 × 10−34 Js
n = Quantum number
∴ n = `(mvr 2pi)/h`
= `(2pi xx 6 xx 10^24xx 3 xx 10^4 xx1.5 xx 10^(11))/(6.62 xx 10^(-34))`
= 25.61 × 1073
= 2.6 × 1074
Hence, the quantum number that characterises the earth’s revolution is 2.6 × 1074.
संबंधित प्रश्न
(i) State Bohr's quantization condition for defining stationary orbits. How does the de Broglie hypothesis explain the stationary orbits?
(ii) Find the relation between three wavelengths λ1, λ2 and λ3 from the energy-level diagram shown below.
Calculate the radius of Bohr’s fifth orbit for hydrogen atom
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.
If the photon of the wavelength 150 pm strikes an atom and one of its inner bound electrons is ejected out with a velocity of 1.5 × 107 ms–1, calculate the energy with which it is bound to the nucleus.
Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states?
A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state. (a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon. Neglecting the light emitted by the excited hydrogen atoms in the direction of the incident beam, what wavelengths may be observed in the transmitted beam? (b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.
A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (Φ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms in ground state. Find the maximum value of λ for which (a) hydrogen atoms may be ionized, (b) hydrogen atoms may get excited from the ground state to the first excited state and (c) the excited hydrogen atoms may emit visible light.
The light emitted in the transition n = 3 to n = 2 in hydrogen is called Hα light. Find the maximum work function a metal can have so that Hα light can emit photoelectrons from it.
Mention demerits of Bohr’s Atomic model.
According to Bohr’s theory, the angular momentum of an electron in 5th orbit is ______.
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 first ionization energy of H is 21.79 × 10-19 J. The second ionization energy of He atom is ______ × 10-19J.
The line at 434 nm in the Balmer series of the hydrogen spectrum corresponds to a transition of an electron from the nth to second Bohr orbit. The value of n is ______.
What is the energy of an electron in stationary state corresponding to n = 2?
Write the ionisation energy value for the hydrogen atom.
What is the velocity of an electron in the 3rd orbit of hydrogen atom if its velocity in the 1st orbit is v0?
The de Broglie wavelength of an electron in the first Bohr’s orbit of hydrogen atom is equal to ______.
Calculate the radius of the second orbit of He+.
The radius of hydrogen atom in the ground state is 0.53 Å. The radius of Li2+ ion (atomic number = 3) in a similar state is ______.
