Question 1

An LED emits light of wavelength 600 nm.What is its band gap?

Accepted Answer

A) 1.11 eV 
B) 1.54 eV 
C) 1.99 eV 
D) 2.07 eV 
E) 2.33 eV 
A) 1.11 eV 
B) 1.54 eV 
C) 1.99 eV 
D) 2.07 eV 
E) 2.33 eV D

Question 2

The diagram below shows the distance between the nuclei,pA and pB,and the electrons,e1 and e2,in a hydrogen molecule.We would expect the electrostatic potential energy of this molecule to be

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    . E

Question 3

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J − 1,the difference in energy of levels J and J − 1,EJ − EJ − 1,is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    . D

Question 4

The rotation spectrum of the HCl molecule suggests a photon in the far infrared (around 5.0 × 10−6 m)can excite the first rotational level.From this data,the moment of inertia of the HCl molecule (in kg ⋅ m2)is

Accepted Answer

A) 2.8 × 10−48 
B) 2.8 × 10−49 
C) 2.8 × 10−47 
D) 2.8 × 10−46 
E) 2.8 × 10−45 
A) 2.8 × 10−48 
B) 2.8 × 10−49 
C) 2.8 × 10−47 
D) 2.8 × 10−46 
E) 2.8 × 10−45

Question 5

What is the energy of the first rotational state of the hydrogen (H2)molecule? The separation between the protons is 10−10 m and the mass of each proton is 1.67 × 10−27 kg.(h = 6.626 × 10−34 J ⋅ s and 1 eV = 1.6 × 10−19 J. )

Accepted Answer

Question 6

The Fermi temperature of copper is 80 000 K.The corresponding Fermi energy (in eV)is

Accepted Answer

A) 7 
B) 5 
C) 3 
D) 1 
E) 4 
A) 7 
B) 5 
C) 3 
D) 1 
E) 4

Question 7

An experiment determines that there are 49 allowed rotational energies for a diatomic molecule whose moment of inertia is 2 × 10−46 kg ⋅ m2.The maximum rotational kinetic energy (in eV)is

Accepted Answer

A) 0.6 
B) 0.2 
C) 0.4 
D) 0.8 
E) 1.0 
A) 0.6 
B) 0.2 
C) 0.4 
D) 0.8 
E) 1.0

Question 8

Which of the following refer to the basic categories associated with the energy of a single molecule in a gaseous phase?

Accepted Answer

A) nuclear,electronic,interval 
B) electronic,translation,rotation,vibration 
C) ionic,covalent,hydrogen,Van der Waals 
D) translation,rotation,vibration 
E) dipole-dipole,covalent,ionic,translation 
A) nuclear,electronic,interval 
B) electronic,translation,rotation,vibration 
C) ionic,covalent,hydrogen,Van der Waals 
D) translation,rotation,vibration 
E) dipole-dipole,covalent,ionic,translation

Question 9

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by

Accepted Answer

A) the probability that a state is unoccupied,   . 
B) the probability that a state is occupied,   . 
C) the probability that a state is unoccupied,   . 
D) the probability that a state is occupied,   . 
E) dE alone. 
A) the probability that a state is unoccupied,   . 
B) the probability that a state is occupied,   . 
C) the probability that a state is unoccupied,   . 
D) the probability that a state is occupied,   . 
E) dE alone.

Question 10

Solid argon has a density of 1650 kg/m3.The atomic weight of argon is 40.0.Assuming each atom occupies a cubical volume,what is the distance between the argon atoms?

Accepted Answer

Question 11

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1,the change in energy,EJ + 1 − EJ,is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 12

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.Find the moment of inertia through the center of mass about an axis perpendicular to the molecular axis.

Accepted Answer

A) m1m2r2/(m1 + m2) 
B) [(m1m2/m1)+ m2]r2 
C) (m1 + m2)/m1m2r2 
D) (m1 + m1)r2 /m1m2 
E) m1m2r2/m1 
A) m1m2r2/(m1 + m2) 
B) [(m1m2/m1)+ m2]r2 
C) (m1 + m2)/m1m2r2 
D) (m1 + m1)r2 /m1m2 
E) m1m2r2/m1

Question 13

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 1011 Hz.The moment of inertia of the molecule (in kg ⋅ m2)is

Accepted Answer

A) 5.70 × 10−45 
B) 1.45 × 10−46 
C) 1.12 × 10−44 
D) 2.91 × 10−46 
E) 9.11 × 10−46 
A) 5.70 × 10−45 
B) 1.45 × 10−46 
C) 1.12 × 10−44 
D) 2.91 × 10−46 
E) 9.11 × 10−46

Question 14

Assume the angular momentum of a diatomic molecule is quantized according to the relation  
)What are the allowed rotational kinetic energies?

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Ellis and Randy are looking at a molecular absorption spectrum.The spectral lines appear to fall into two groups with a gap in the middle.Ellis says that this must be an absorption spectrum for transitions between the v = 0 and v = 1 vibrational states of a diatomic molecule.Randy says the gap in the middle must occur because a ΔJ = 0 transition is forbidden.Which one,if either,is correct,and why?

Accepted Answer

A) Ellis,because rotational levels are separated by greater energy differences than vibrational levels. 
B) Randy,because rotational levels are separated by greater energy differences than vibrational levels. 
C) Ellis,because the ΔJ = 0 transition is the most prominent spectral line in transitions between vibrational levels. 
D) Neither,because rotational levels are separated by greater energies that vibrational levels and ΔJ = 0 transitions are not forbidden. 
E) Both,because vibrational levels are separated by greater energy differences than rotational levels and ΔJ = 0 transitions are forbidden. 
A) Ellis,because rotational levels are separated by greater energy differences than vibrational levels. 
B) Randy,because rotational levels are separated by greater energy differences than vibrational levels. 
C) Ellis,because the ΔJ = 0 transition is the most prominent spectral line in transitions between vibrational levels. 
D) Neither,because rotational levels are separated by greater energies that vibrational levels and ΔJ = 0 transitions are not forbidden. 
E) Both,because vibrational levels are separated by greater energy differences than rotational levels and ΔJ = 0 transitions are forbidden.

Question 16

In the hydrogen molecule,H2,the separation between the protons is 10−10 m.If the molecule is in its first rotational energy state,what is the angular velocity of the molecule about its center of mass?

Accepted Answer

Question 17

The Fermi temperature is

Accepted Answer

A) a characteristic temperature of an electron gas at a physical temperature of absolute zero. 
B) a characteristic temperature of an electron gas at a physical temperature of 0° Celsius. 
C) the temperature of the electron gas in absolute degrees. 
D) related to the Fermi energy by the relation EF = (3/2)kT. 
E) independent of the Fermi energy. 
A) a characteristic temperature of an electron gas at a physical temperature of absolute zero. 
B) a characteristic temperature of an electron gas at a physical temperature of 0° Celsius. 
C) the temperature of the electron gas in absolute degrees. 
D) related to the Fermi energy by the relation EF = (3/2)kT. 
E) independent of the Fermi energy.

Question 18

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.If x is the distance from m1 to the center of mass,find the moment of inertia in terms of x about an axis parallel to the molecular axis through the center of mass.

Accepted Answer

A) 0 
B) m1x2 + m2(r − x)2 
C) m1m2 r2(m1m2) 
D) m1(r − x)2 + m2x2 
E) m1x2 + m2r2 
A) 0 
B) m1x2 + m2(r − x)2 
C) m1m2 r2(m1m2) 
D) m1(r − x)2 + m2x2 
E) m1x2 + m2r2

Question 19

The energy gap for germanium is 0.670 eV at room temperature.What wavelength must a photon have (in nm)to excite the electron to the conduction band?

Accepted Answer

A) 640 
B) 1 090 
C) 1 850 
D) 2 200 
E) 925 
A) 640 
B) 1 090 
C) 1 850 
D) 2 200 
E) 925

Question 20

The fundamental frequency of CO is 6.42 × 1013 Hz.If the atomic masses are 12 u and 16 u (1 u = 1.66 × 10−27 kg),find the force constant (in N/m)for the diatomic molecule.

Accepted Answer

A) 970 
B) 1 530 
C) 1 850 
D) 480 
E) 47 
A) 970 
B) 1 530 
C) 1 850 
D) 480 
E) 47

Exam 43: Molecules and Solids

An LED emits light of wavelength 600 nm.What is its band gap?

The diagram below shows the distance between the nuclei,pA and pB,and the electrons,e1 and e2,in a hydrogen molecule.We would expect the electrostatic potential energy of this molecule to be

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J − 1,the difference in energy of levels J and J − 1,EJ − EJ − 1,is

The rotation spectrum of the HCl molecule suggests a photon in the far infrared (around 5.0 × 10−6 m)can excite the first rotational level.From this data,the moment of inertia of the HCl molecule (in kg ⋅ m2)is

What is the energy of the first rotational state of the hydrogen (H2)molecule? The separation between the protons is 10−10 m and the mass of each proton is 1.67 × 10−27 kg.(h = 6.626 × 10−34 J ⋅ s and 1 eV = 1.6 × 10−19 J. )

The Fermi temperature of copper is 80 000 K.The corresponding Fermi energy (in eV)is

An experiment determines that there are 49 allowed rotational energies for a diatomic molecule whose moment of inertia is 2 × 10−46 kg ⋅ m2.The maximum rotational kinetic energy (in eV)is

Which of the following refer to the basic categories associated with the energy of a single molecule in a gaseous phase?

To find the number of electrons per unit volume with energy between E and E + dE in a metal we must multiply the number of allowed states per unit volume with energy E by

Solid argon has a density of 1650 kg/m3.The atomic weight of argon is 40.0.Assuming each atom occupies a cubical volume,what is the distance between the argon atoms?

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1,the change in energy,EJ + 1 − EJ,is

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.Find the moment of inertia through the center of mass about an axis perpendicular to the molecular axis.

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 1011 Hz.The moment of inertia of the molecule (in kg ⋅ m2)is

Assume the angular momentum of a diatomic molecule is quantized according to the relation )What are the allowed rotational kinetic energies?

In the hydrogen molecule,H2,the separation between the protons is 10−10 m.If the molecule is in its first rotational energy state,what is the angular velocity of the molecule about its center of mass?

The Fermi temperature is

A diatomic molecule consists of two point masses,m1 and m2,separated by a distance r.If x is the distance from m1 to the center of mass,find the moment of inertia in terms of x about an axis parallel to the molecular axis through the center of mass.

The energy gap for germanium is 0.670 eV at room temperature.What wavelength must a photon have (in nm)to excite the electron to the conduction band?

The fundamental frequency of CO is 6.42 × 1013 Hz.If the atomic masses are 12 u and 16 u (1 u = 1.66 × 10−27 kg),find the force constant (in N/m)for the diatomic molecule.

Physics and Measurement

Motion in One Dimension

Vectors

Motion in Two Dimensions

The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

Angular Momentum

Static Equilibrium and Elasticity

Universal Gravitation

Fluid Mechanics

Oscillatory Motion

Wave Motion

Sound Waves

Superposition and Standing Waves

Temperature

The First Law of Thermodynamics

The Kinetic Theory of Gases

Heat Engines, entropy, and the Second Law of Thermodynamics

Electric Fields

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Sources of the Magnetic Field

Faradays Law

Inductance

Alternating-Current Circuits

Electromagnetic Waves

The Nature of Light and the Principles of Ray Optics

Image Formation

Wave Optics

Diffraction Patterns and Polarization

Relativity

Introduction to Quantum Physics

Quantum Mechanics

Atomic Physics

Nuclear Structure

Applications of Nuclear Physics

Particle Physics and Cosmology

Filters

The diagram below shows the distance between the nuclei,p_A and p_B,and the electrons,e₁ and e₂,in a hydrogen molecule.We would expect the electrostatic potential energy of this molecule to be

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J − 1,the difference in energy of levels J and J − 1,E_J − EJ₋₁,is

The rotation spectrum of the HCl molecule suggests a photon in the far infrared (around 5.0 × 10−⁶ m)can excite the first rotational level.From this data,the moment of inertia of the HCl molecule (in kg ⋅ m²)is

What is the energy of the first rotational state of the hydrogen (H₂)molecule? The separation between the protons is 10−¹⁰ m and the mass of each proton is 1.67 × 10−²⁷ kg.(h = 6.626 × 10−³⁴ J ⋅ s and 1 eV = 1.6 × 10−¹⁹ J. )

An experiment determines that there are 49 allowed rotational energies for a diatomic molecule whose moment of inertia is 2 × 10−⁴⁶ kg ⋅ m².The maximum rotational kinetic energy (in eV)is

Solid argon has a density of 1650 kg/m³.The atomic weight of argon is 40.0.Assuming each atom occupies a cubical volume,what is the distance between the argon atoms?

When a molecule jumps from a rotational energy level characterized by the rotational quantum number J to one characterized by J + 1,the change in energy,EJ_{+ 1} − E_J,is

A diatomic molecule consists of two point masses,m₁ and m₂,separated by a distance r.Find the moment of inertia through the center of mass about an axis perpendicular to the molecular axis.

The frequency of a microwave absorbed by a molecule when changing from the J = 3 to J = 4 rotation energy state is 4.61 × 10¹¹ Hz.The moment of inertia of the molecule (in kg ⋅ m²)is

In the hydrogen molecule,H₂,the separation between the protons is 10−¹⁰ m.If the molecule is in its first rotational energy state,what is the angular velocity of the molecule about its center of mass?

A diatomic molecule consists of two point masses,m₁ and m₂,separated by a distance r.If x is the distance from m₁ to the center of mass,find the moment of inertia in terms of x about an axis parallel to the molecular axis through the center of mass.

The fundamental frequency of CO is 6.42 × 10¹³ Hz.If the atomic masses are 12 u and 16 u (1 u = 1.66 × 10−²⁷ kg),find the force constant (in N/m)for the diatomic molecule.