Q0.
(a)
Q1.
(i) Justify that this principle is not just a negative statement but a useful tool, with one example. The lifetime of an excited state of an atom is about 10^-8 s.
(ii) Calculate the minimum uncertainty in the energy of the excited state.
(b)
Draw a neat sketch showing potential wells and energy levels of the following: Harmonic oscillator
(i) (ii) Hydrogen atom Particle in a box
(iii)
(c)
List the contrasting points and mention the variation of En with n of the above plots. Prove the following: [L2, Lx] = 0
(i) [Lx, Ly] = i ħ L3
(ii) The calcium line of wavelength λ = 4226.73 Å (P → S) exhibits normal Zeeman splitting when placed in a uniform magnetic field of 4 Weber/m^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.
(d) Zeeman splitting when placed in a uniform magnetic field of 4 Weber/m^3. Calculate the wavelength of three components of normal Zeeman pattern and the separation between them.
(e) A Raman line associated with a vibrational mode which is both Raman and infrared active is found at 4600 Å when excited by light of wavelength 4358 Å. Calculate the wavelength of the corresponding infrared band.