Advertisements
Advertisements
प्रश्न
Using Bohr’s Theory of hydrogen atom, obtain an expression for the velocity of an electron in the nth orbit of an atom.
Advertisements
उत्तर
Let ‘e’, ‘m’, and ‘v’ be the charge, mass, and velocity of electrons, respectively, and ‘r’ is the radius of the orbit.
The positive charge on the nucleus is Ze, where Z is the atomic number (in case of hydrogen atom Z = 1).
As the electrostatic force of attraction provides the centripetal force.
`(mv^2)/r = 1/(4piepsilon_0) (("Ze") xx "e")/r^2`
`=> mv^2 = "Ze"^2/(4piepsilon_0r)`
`=> v = sqrt("Ze"^2/(4piepsilon_0" rm"))`
APPEARS IN
संबंधित प्रश्न
Using Bohr's postulates, derive the expression for the total energy of the electron in the stationary states of the hydrogen atom ?
Using Bohr’s postulates, obtain the expression for the total energy of the electron in the stationary states of the hydrogen atom. Hence draw the energy level diagram showing how the line spectra corresponding to Balmer series occur due to transition between energy levels.
Balmer series was observed and analysed before the other series. Can you suggest a reason for such an order?
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10−27 kg. (c) Find the kinetic energy of recoil of the atom.
A filter transmits only the radiation of wavelength greater than 440 nm. Radiation from a hydrogen-discharge tube goes through such a filter and is incident on a metal of work function 2.0 eV. Find the stopping potential which can stop the photoelectrons.
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
Which of the following is/are CORRECT according to Bohr's atomic theory?
(I) Energy is emitted when electron moves from a higher stationary state to a lower one.
(II) Orbits are arranged concentrically around the nucleus in an increasing order of energy.
(III) The energy of an electron in the orbit changes with time.
Ratio of longest to shortest wavelength in Balmer series is ______.
Calculate the energy and frequency of the radiation emitted when an electron jumps from n = 3 to n = 2 in a hydrogen atom.
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.
