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
What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is –2.18 × 10–11 ergs.
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 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
Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?
A positive ion having just one electron ejects it if a photon of wavelength 228 Å or less is absorbed by it. Identify the ion.
Calculate the magnetic dipole moment corresponding to the motion of the electron in the ground state of a hydrogen atom.
A beam of light having wavelengths distributed uniformly between 450 nm to 550 nm passes through a sample of hydrogen gas. Which wavelength will have the least intensity in the transmitted beam?
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.
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.
If l3 and l2 represent angular momenta of an orbiting electron in III and II Bohr orbits respectively, then l3: l2 is :
In form of Rydberg's constant R, the wave no of this first Ballmer line is
The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10–11m. The radius of the n = 3 orbit is ______.
The ground state energy of hydrogen atoms is -13.6 eV. The photon emitted during the transition of electron from n = 3 to n = 1 unknown work function. The photoelectrons are emitted from the material with a maximum kinetic energy of 9 eV. Calculate the threshold wavelength of the material used.
An electron in H-atom makes a transition from n = 3 to n = 1. The recoil momentum of the H-atom will be ______.
A 100 eV electron collides with a stationary helium ion (He+) in its ground state and exits to a higher level. After the collision, He+ ions emit two photons in succession with wavelengths 1085 Å and 304 Å. The energy of the electron after the collision will be ______ eV.
Given h = 6.63 × 10-34 Js.
The energy of an electron in the first Bohr orbit of the H-atom is −13.6 eV. The energy value of an electron in the excited state of Li2+ is ______.
In hydrogen atom, transition from the state n = 6 to n = 1 results in ultraviolet radiation. Infrared radiation will be obtained in the transition ______.
The energy of an electron in the nth orbit of the hydrogen atom is En = -13.6/n2eV. The negative sign of energy indicates that ______.
What is the velocity of an electron in the 3rd orbit of hydrogen atom if its velocity in the 1st orbit is v0?
Which conversion relates an electron volt to joules?
