Advertisements
Advertisements
प्रश्न
On the basis of Bohr's theory, derive an expression for the radius of the nth orbit of an electron of hydrogen atom.
Advertisements
उत्तर
Let r be the orbit's radius and e, m, and v represent the electron's charge, mass, and velocity. Ze represents the nucleus's positive charge. For an atom of hydrogen, Z = 1. The electrostatic force of attraction provides centripetal force.
Therefore,
`(mv^2)/r = 1/(4piε_0) (Ze xx e)/ r^2`
`mv^2 = (Ze^2)/(4piε_0r)` ...(i)
By first postulate:
`mvr = (nh)/(2pi)` ...(ii)
Where n is the quantum number.
Squaring equation (ii) and dividing by equation (i), we get:
`(m^2v^2r^2)/(mv^2) = (n^2h^2)/((4pi^2)/((Ze^2)/(4piε_0r)))`
Then, `r = (n^2h^2ε_0)/(piZe^2m)`
APPEARS IN
संबंधित प्रश्न
Using Bohr’s postulates for hydrogen atom, show that the total energy (E) of the electron in the stationary states tan be expressed as the sum of kinetic energy (K) and potential energy (U), where K = −2U. Hence deduce the expression for the total energy in the nth energy level of hydrogen atom.
According to Maxwell's theory of electrodynamics, an electron going in a circle should emit radiation of frequency equal to its frequency of revolution. What should be the wavelength of the radiation emitted by a hydrogen atom in ground state if this rule is followed?
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.
A neutron moving with a speed υ strikes a hydrogen atom in ground state moving towards it with the same speed. Find the minimum speed of the neutron for which inelastic (completely or partially) collision may take place. The mass of neutron = mass of hydrogen = 1.67 × 10−27 kg.v
The radius of the third Bohr orbit for hydrogen atom is ____________.
In Bohr model of hydrogen atom, which of the following is quantised?
According to the Bohr theory of H-atom, the speed of the electron, its energy and the radius of its orbit varies with the principal quantum number n, respectively, as:
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 ______.
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 ______.
