Important Questions
1. Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?
OR
Using Bohr’s postulates of the atomic model derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr’s radius.
2. Determine the distance of closest approach when an alpha particle of kinetic energy 4.5 MeV projected towards a nucleus of Z = 80, stops and reverses its direction.
3. Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number of the atom.
4. 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.
5. When is Hα line in the emission spectrum of hydrogen atom obtained? Calculate the frequency of the photon emitted during this transition.
Or
Calculate the wavelength of radiation emitted when electron in a hydrogen atom jumps from n = ∞ to n = 1.
Sample Questions
1. An electron and a photon each have a wavelength 1.00 nm. Find
(i) Their momenta.
(ii) The energy of the photon and
(iii) The kinetic energy of electron.
2. 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.
3. A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. Up to which energy level the hydrogen atoms would be excited? Calculate the wavelength of the first member of Lyman and first member of Balmer series.
4. Asha’s mother read an article in the newspaper about a disaster that took place at Chernobyl. She could not understand much from the article and asked a few questions from Asha regarding the article. Asha tried to answer her mother’s questions based on what she learnt in Class XII Physics
(a) What was the installation at Chernobyl where the disaster took place?
(b) What, according to you, was the cause of this disaster?
(c) What are the values shown by Asha?
5. Using Bohr’s postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number ni) to the lower state, (nf). When electron in hydrogen atom jumps from energy state ni = 4 to nf = 3, 2, 1, identify the spectral series to which the emission lines belong.