2.2 Problems 93
What additional quantum numbers are needed to specify fully an atomic quan-
tum state and what physical quantities do they quantify? List the allowed quan-
tum numbers forn=1 andn=2 and specify fully the electronic quantum
numbers for the ground state of the Carbon atom (atomic numberZ=6)
[Adapted from University of London 2002]2.8 Estimate the total ground state energy in eV of the system obtained if all the
electrons in the Carbon atom were replaced byπ−particles. (You are given
that the ground state energy of the hydrogen atom is− 13 .6 eV and that theπ−
is a particle with charge−1, spin 0 and mass 270me
[University of London]2.9 What are atomic units? In this system what are the units of (a) length (b) energy
(c)^2 (d)e^2 (e)me? (f) Write down Schrodinger’s equation for H-atom in
atomic units
2.10 (a) Two positive nuclei each having a charge q approach each other and elec-
trons concentrate between the nuclei to create a bond. Assume that the
electrons can be represented by a single point charge at the mid-point
between the nuclei. Calculate the magnitude this charge must have to
ensure that the potential energy is negative.
(b) A positive ion of kinetic energy 1× 10 −^19 J collides with a stationary
molecule of the same mass and forms a single excited composite molecule.
Assuming the initial internal energies of the ion and neutral molecule were
zero, calculate the internal energy of the molecule.
[Adapted from University of Wales, Aberystwyth 2008]2.11 (a) By using the deBroglie relation, derive the Bohr conditionmvr=nfor
the angular momentum of an electron in a hydrogen atom.
(b) Use this expression to show that the allowed electron energy states in
hydrogen atom can be written
En=−me^4
8 ε^20 h^2 n^2
(c) How would this expression be modified for the case of a triply ionized
beryllium atomBe(Z=4)?
(d) Calculate the ionization energy in eV ofBe+^3 (ionization energy of hydro-
gen= 13 .6eV)
[Adapted from the University of Wales, Aberystwyth 2007]2.12 When a negatively charged muon (mass 207meis captured in a Bohr’s orbit
of high principal quantum number (n) to form a mesic atom, it cascades
down to lower orbits emitting X-rays and the radii of the mesic atom are
shrunk by a factor of about 200 compared with the corresponding Bohr’s atom.
Explain.
2.13 In which mu-mesic atom would the orbit withn=1 just touch the nuclear
surface. TakeZ=A/2 andR= 1. 3 A^1 /^3 fm.