Section A
Q1.
(a) The lifetime of a given atom in an excited state is 10^{-8} s. It comes to the ground state by emitting a photon of wavelength 5800 Å. Find the energy uncertainty and wavelength uncertainty of the photon.
(b)
An electron is confined to an infinite well whose width L (=100 pm) is roughly the size of an atom.
(i) What are the energies of four least energetic quantum states? (ii) What energy must be imparted to the electron to raise it from a state with n = 12 to a higher energy state with n = 25?
(c) (i) Find the lowest energy of an electron confined in a three-dimensional cubic box of each side 1 Å. (ii) Find the temperature at which the average energy of the molecule would be equal to the lowest energy of the electron. [Given : k = 1.38 imes 10^{-23} J/K]
(d)
The quantum numbers of the two optical electrons in a two-valence electron atom are
n1 = 6, l1 = 3, s1 = rac{1}{2}
n2 = 5, l2 = 1, s2 = rac{1}{2}
Assuming j-j coupling, find the possible values of J.
(e) Describe the basic principle of nuclear magnetic resonance (NMR) and mention its different applications.
