PROBLEMS
9.1 Calculate the velocity of an electron if it has a wavelength of (a) 2.0 Å, (b) 1.0 Å, and
(c) 10.0 Å.
9.2 Calculate the velocity of a proton if it has a wavelength of (a) 2.0 Å, (b) 1.0 Å, and (c) 10.0 Å.
9.3 Calculate the wavelength of an electron moving at a velocity of (a) 2 × 10
5 m s
−1
, (b) 1.0
× 10
7 m s
−1
, and (c) 1.5 × 10
8 m s
−1
.
9.4 Calculate the wavelength of a proton moving at a velocity of (a) 2 × 10
5 m s
−1
, (b) 1.0 ×
10
7 m s
−1
, and (c) 1.5 × 10
8 m s
−1
.
9.5 Calculate the wavelength of a 5-g snail moving at a speed of (a) 1 mm h
−1
, (b) 1 μm h
−1
,
and (c) 100 mm h
−1
.
9.6 Calculate the wavelength of an object that is moving at a speed of 100 km h
−1 and has a
mass of (a) 5 μg, (b) 1 g, and (c) 5 kg.
9.7 Why is the observed blackbody radiation in conflict with classical physics?
9.8 Qualitatively, why does quantum theory give the correct expression for blackbody radiation?
9.9 Why does the presence of discrete lines in the emission spectra of atoms support the ideas
of quantum theory?
9.10 For each of the following experimental results, write whether classical theory can explain
the result or whether quantum theory is required: (a) light can diffract; (b) electrons can
diffract; (c) for blackbody radiation, the energy density is small at small wavelengths; (d)
for blackbody radiation, the energy density is small at long wavelengths; (e) light has wavelength; (f) electrons are in atomic orbitals; (g) electrons have mass; and (h) electrons have
a wavelength.
9.11 For the photoelectric effect, what does the classical theory predict for the dependence of
the kinetic energy of the emitted electron on the frequency of the light? Does this agree
with the observed dependence?
9.12 For the photoelectric effect, what does the quantum theory predict for the dependence of
the kinetic energy of the emitted electron on the frequency of the light? Does this agree
with the observed dependence?
9.13 For the photoelectric effect with a metal that has a work function of 2.0 eV, what is the
kinetic energy of the ejected electron if the light has a wavelength of (a) 200 nm, (b) 250 nm,
and (c) 350 nm?
9.14 For the photoelectric effect with a metal that has a work function of 2.3 eV, what is the
kinetic energy of the ejected electron if the light has a wavelength of (a) 200 nm, (b) 250 nm,
and (c) 350 nm?
9.15 For the photoelectric effect, what is the maximal wavelength of light that will still result in
ejection of an electron from a metal that has a work function with the value of (a) 2.25 eV,
(b) 2.0 eV, and (c) 2.5 eV?
9.16 Why is there a minimal frequency needed to cause the photoelectric effect?
9.17 What is the probability of finding a particle within a volume V 0 ?
9.18 What frequency dependence does classical theory predict for the energy, E, of light? What
dependence is predicted using quantum theory?
9.19 If the classical term for kinetic energy was 4 m
3
9 instead of m9
2
/2 what would Schrödinger’s
equation be? What if the classical term for kinetic energy was m9
4
?
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PART 2
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9.1 Calculate the velocity of an electron if it has a wavelength of (a) 2.0 Å, (b) 1.0 Å, and
(c) 10.0 Å.
9.2 Calculate the velocity of a proton if it has a wavelength of (a) 2.0 Å, (b) 1.0 Å, and (c) 10.0 Å.
9.3 Calculate the wavelength of an electron moving at a velocity of (a) 2 × 10
5 m s
−1
, (b) 1.0
× 10
7 m s
−1
, and (c) 1.5 × 10
8 m s
−1
.
9.4 Calculate the wavelength of a proton moving at a velocity of (a) 2 × 10
5 m s
−1
, (b) 1.0 ×
10
7 m s
−1
, and (c) 1.5 × 10
8 m s
−1
.
9.5 Calculate the wavelength of a 5-g snail moving at a speed of (a) 1 mm h
−1
, (b) 1 μm h
−1
,
and (c) 100 mm h
−1
.
9.6 Calculate the wavelength of an object that is moving at a speed of 100 km h
−1 and has a
mass of (a) 5 μg, (b) 1 g, and (c) 5 kg.
9.7 Why is the observed blackbody radiation in conflict with classical physics?
9.8 Qualitatively, why does quantum theory give the correct expression for blackbody radiation?
9.9 Why does the presence of discrete lines in the emission spectra of atoms support the ideas
of quantum theory?
9.10 For each of the following experimental results, write whether classical theory can explain
the result or whether quantum theory is required: (a) light can diffract; (b) electrons can
diffract; (c) for blackbody radiation, the energy density is small at small wavelengths; (d)
for blackbody radiation, the energy density is small at long wavelengths; (e) light has wavelength; (f) electrons are in atomic orbitals; (g) electrons have mass; and (h) electrons have
a wavelength.
9.11 For the photoelectric effect, what does the classical theory predict for the dependence of
the kinetic energy of the emitted electron on the frequency of the light? Does this agree
with the observed dependence?
9.12 For the photoelectric effect, what does the quantum theory predict for the dependence of
the kinetic energy of the emitted electron on the frequency of the light? Does this agree
with the observed dependence?
9.13 For the photoelectric effect with a metal that has a work function of 2.0 eV, what is the
kinetic energy of the ejected electron if the light has a wavelength of (a) 200 nm, (b) 250 nm,
and (c) 350 nm?
9.14 For the photoelectric effect with a metal that has a work function of 2.3 eV, what is the
kinetic energy of the ejected electron if the light has a wavelength of (a) 200 nm, (b) 250 nm,
and (c) 350 nm?
9.15 For the photoelectric effect, what is the maximal wavelength of light that will still result in
ejection of an electron from a metal that has a work function with the value of (a) 2.25 eV,
(b) 2.0 eV, and (c) 2.5 eV?
9.16 Why is there a minimal frequency needed to cause the photoelectric effect?
9.17 What is the probability of finding a particle within a volume V 0 ?
9.18 What frequency dependence does classical theory predict for the energy, E, of light? What
dependence is predicted using quantum theory?
9.19 If the classical term for kinetic energy was 4 m
3
9 instead of m9
2
/2 what would Schrödinger’s
equation be? What if the classical term for kinetic energy was m9
4
?
196
PART 2
QUANTUM MECHANICS AND SPECTROSCOPY
9781405124362_4_009.qxd 4/29/08 10:42 Page 196