Download PH469 Fall 2002

CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
1) Show that the radial probability density of the 1s level has its maximum value at
r=a0.
2) Prove that the most likely distance from the origin of an electron in the n=2, l=1
state is 4a0.
3) In what state is an electron of an hydrogen atom in terms of the principle, angular
momentum and magnetic quantum numbers (n, l, ml ) when the energy level E =
0.25E0, L2 = 2 ħ2, Lz= ħ, where E0 is the ground state energy, L is the magnitude
of the angular momentum and Lz the z component of the angular momentum.
4) An electron is in the ground state of a hydrogen atom. What is
(a) the orbital angular momentum?
(b) the spin angular momentum?
5) Calculate the possible magnetic moments for an n = 3 electron.
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CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
6) Determine the maximum separation of a beam of hydrogen atoms that moves a
distance of 20cm with a speed of 2  105 m/s perpendicular to a magnetic field
whose gradient is 2  102 T/m. The mass of hydrogen is 1.67  10-27 kg, and its
magnetic moment is about 1 Bohr magneton.
7) In a Stern-Gerlach type of experiment, the magnetic field varies with distance in
the z direction according to dBz/dz = 1.4 T/m. The silver atoms travel a distance x
= 3.5 cm. The most probable speed of the atoms emerging from the oven is v =
750 m/s. Find the separation of the two beams as they lave the magnet. The mass
of a silver atom is 1.8  10-25 kg, and its magnetic moment is about 1 Bohr
magneton.
8) Which of the following state transition of an hydrogen atom in energy level is
allowed.
(a) 5g
4g
(b) 4f
3d
(c) 3p
1s
(d) 4s
3p
(e) 4f
3p
9) Find the maximum number of electrons that can occupy a
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
s subshell
p subshell
d subshell
f subshell
g subshell
K shell
L shell
M shell
N shell
O shell
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CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
10) Give the electronic configuration of
(a) P (Z=15)
(b) V (Z=23)
11) The inert gases have only filled subshells. What is their outer-most subshell?
12) Write the expressions for
(a) the ground state average orbital radius and binding energy of a hydrogen
atom.
(b) the ground state average orbital radius and binding energy of a higher
charge atom as a function the the atomic number Z.
(c) the excited state binding energy of a higher charge atom as a function the
the atomic number Z.
13) Moseley’s work was important in determining the correct order of the periodic
table. Ni, having a lower atomic weight, was listed before Co. In an experiment,
the Kα X-ray lines was found to be 1.79Å Co and 1.66Å for Ni. Determine their
atomic number and correct ordering in the periodic table.
(10 pts)
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CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
14) The following diagram depicts the composition of acetic acid.
O
H3C-C
OH
(a) What type of sp-hybrid covalent bond is formed between the carbon atom
on the left and hydrogen atoms?
(b) What type of sp-hybrid covalent bond is formed between the two carbon
atoms?
(c) What type of sp-hybrid covalent bond is formed between the carbon atom
on the right and the oxygen atom in OH
(d) What two different types of sp-hybrid covalent bonds are formed between
the carbon atom on the right and the single oxygen atom?
15) The following diagram depicts the electronic configuration of a carbon atom
(Z=6).
1s
2s
2px 2py 2pz
What is the sp-hybridization (spn where n = 1, 2, 3) of the following molecules?
Show how the electrons are distributed, and indicate the states (2s, 2px, 2py, etc)
that are included in the hybrid bonds
(a) C2H2 - ethene
1s
2s
2px 2py 2pz
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CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
(b) C2H4 - ethylene
1s
2s
2px 2py 2pz
(c) C2H6 - ethane
1s
2s
2px 2py 2pz
16) From the following data of the atoms K and Cl, and the molecule KCl:
Cl electron affinity energy = 3.62 eV
K ionization energy = 4.34 eV
KCl bond length = 2.79 Å
(a) Estimate the dissociation energy of KCl. (Hint: ignore the Pauli repulsion
energy; (e2/4πεo) = 14.40 eV- Å).
(b) Estimate the dipole moment for KCl. Assume charge separation to be the
atomic separation.
17) The N2 molecule’s natural vibrational frequency is 7  1013 Hz. What is the
difference in energy between its allowed state of vibration?
18) Molecules of N2 are excited into the n = 1 vibrational levels and deexcite through
the emission of photons. What are the energies of the emitted photons? For N2,
ħ/2I = 2.510-4eV, ħω = 0.29eV.
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CAPITOL COLLEGE
Introduction to Modern Physics
PH469 Fall 2002
Review 3
19) Determine the first 2 non-zero rotational energy levels for H2, whose equilibrium
spacing is 0.74 Å. (Hint: the mass of the proton in energy form is
(1.008u)(931.5106 eV/u); ħ=1973 eV- Å).
20) The electrical conductivity of copper is 5.88 107 Ω-1 m-1. What is its thermal
conductivity of copper at room temperature (20°C)?
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