Advertisements
Advertisements
प्रश्न
Find the maximum angular speed of the electron of a hydrogen atom in a stationary orbit.
Advertisements
उत्तर
Let the mass of the electron be m.
Let the radius of the hydrogen's first stationary orbit be r.
Let the linear speed and the angular speed of the electron be v and ω, respectively.
According to the Bohr's theory, angular momentum (L) of the electron is an integral multiple of h/2 `pi`, where h is the Planck's constant.
`rArr mvr= (nh)/(2pi)` (Here , n is an integer)
V = rω
`⇒ mr^2 omega = (nh)/(2pi)`
`⇒ omega = (nh)/(2pixxmxxr^2)`
`therefore omega = (1xx(6.63xx10^34))/(2xx(3.14)xx(9.1093xx10^-31)xx(0.53xx10^-10)^2`
`= 0.413 xx 10^17 (rad)//s = 4.13 xx 10^16 (rad)//s`
APPEARS IN
संबंधित प्रश्न
If Bohr’s quantisation postulate (angular momentum = nh/2π) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why then do we never speak of quantisation of orbits of planets around the sun?
Find the wavelength of the electron orbiting in the first excited state in hydrogen atom.
The first excited energy of a He+ ion is the same as the ground state energy of hydrogen. Is it always true that one of the energies of any hydrogen-like ion will be the same as the ground state energy of a hydrogen atom?
Which wavelengths will be emitted by a sample of atomic hydrogen gas (in ground state) if electrons of energy 12.2 eV collide with the atoms of the gas?
In which of the following transitions will the wavelength be minimum?
As one considers orbits with higher values of n in a hydrogen atom, the electric potential energy of the atom
Ionization energy of a hydrogen-like ion A is greater than that of another hydrogen-like ion B. Let r, u, E and L represent the radius of the orbit, speed of the electron, energy of the atom and orbital angular momentum of the electron respectively. In ground state
Find the binding energy of a hydrogen atom in the state n = 2.
Find the radius and energy of a He+ ion in the states (a) n = 1, (b) n = 4 and (c) n = 10.
(a) Find the first excitation potential of He+ ion. (b) Find the ionization potential of Li++ion.
Find the maximum Coulomb force that can act on the electron due to the nucleus in a hydrogen atom.
Whenever a photon is emitted by hydrogen in Balmer series, it is followed by another photon in Lyman series. What wavelength does this latter photon correspond to?
What is the energy of a hydrogen atom in the first excited state if the potential energy is taken to be zero in the ground state?
Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric field E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?
Consider an excited hydrogen atom in state n moving with a velocity υ(ν<<c). It emits a photon in the direction of its motion and changes its state to a lower state m. Apply momentum and energy conservation principles to calculate the frequency ν of the emitted radiation. Compare this with the frequency ν0 emitted if the atom were at rest.
In a hydrogen atom the electron moves in an orbit of radius 0.5 A° making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be ______.
What is the process called when an atom absorbs a photon whose energy exactly matches the energy required for an electronic transition?
What are absorption lines in a continuous spectrum?
When an electron in a rarefied gas atom absorbs a photon, from which energy state to which energy state does the electron transition?
