Question 1

Must all physically reasonable wavefunctions remain finite as $|x| \rightarrow \infty(A)$, or does this apply only to solutions to the Schrödinger equation (B)?

Accepted Answer

A)  $|x| \rightarrow \infty$ 
B)  Does this apply only to solutions to the Schrödinger equation

Question 2

Consider the experimental evidence we have discussed in the past few chapters. Classify the following experimental results according to the following scheme: For the quantons in question, the results:
- The number of electrons ejected from a metal surface depends directly on the intensity of the light shining on that metal surface.

Accepted Answer

The answer of Consider the experimental evidence we have discussed...

Question 3

Two electrons are placed into separate (very tiny) one-dimensional boxes $A$ and $B$. When the electrons are excited to higher energy levels and then decay to lower levels, they emit photons. The longest-wavelength spectral line from the electron in box $A$ is observed to have the same wavelength as the third-longest spectral line from the electron in box
$B$. The ratio of the box lengths $L_{A} / L_{B}$ is equal to

Accepted Answer

A)  $3 / 7$ 
B)  $7 / 3$ 
C)  $\sqrt{3 / 7}$ 
D)  $\sqrt{7 / 3}$ 
E)  $9 / 49$

Question 4

The ground-state energy of an electron in a hydrogen atom is $-13.6 \mathrm{eV}$. This means that the binding energy of that electron is

Accepted Answer

A)  $-13.6 \mathrm{eV}$. 
B)  $+13.6 \mathrm{eV}$. 
C)  Some other value (specify).

Question 5

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen
- The wavelength of the light increases.

Accepted Answer

A)  increases 
B)  decreases 
C)  remains the same

Question 6

Quantum issues often constrain transitions in quantum harmonic oscillators to those where $\Delta n=1$. Consider a spectrum chart (like the one shown in figure Q11.2) for such a system. What would this chart look like?

Accepted Answer

A)  There would be only one emission line.} 
B)  The emission lines would be evenly spaced in energy. 
C)  The emission lines would become more closely spaced (in energy) as we go to the right. 
D)  The emission lines would become farther apart (in energy) as we go to the right.

Question 7

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?

Accepted Answer

A)  Transverse wave 
B)  Longitudinal wave

Question 8

Suppose we measure the wavelengths of the absorption lines of a vibrating diatomic molecule involving atoms whose masses we know. From this data, we can deduce the effective spring constant $k_{s}$ of the bond holding these atoms together.

Accepted Answer

A) True 
 B)False

Question 9

Consider a two-component complex vector
$$|\psi\rangle=\left[\begin{array}{c}
A \
I b
\end{array}\right]$$
Where $a$ and $b$ are real numbers. Which of the following vectors are orthogonal to this vector?

Accepted Answer

A)  $\left[\begin{array}{c}a \ i b\end{array}\right]$ 
B)  $\left[\begin{array}{c}i a \ b\end{array}\right]$ 
C)  $\left[\begin{array}{c}i b \ a\end{array}\right]$ 
D)  $\left[\begin{array}{c}b \ -i a\end{array}\right]$ 
E)  $\left[\begin{array}{c}i b \ -a\end{array}\right]$
F) C and D
G) None of the above.

Question 10

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen
-We look at fringes farther from the central maximum.

Accepted Answer

A)  increases 
B)  decreases 
C)  remains the same

Question 11

Imagine that in a Davisson-Germer-type experiment we shine a beam of electrons on a nickel crystal perpendicular to the crystal face and find that we get enhanced scattering at an angle of $50^{\circ}$. If we double the electrons' kinetic energy,
-(c) (A) 1 (B) $2^{1 / 2}$, or (C) 2

Accepted Answer

The answer of Imagine that in a Davisson-Germer-type experiment we...

Question 12

Consider the experimental evidence we have discussed in the past few chapters. Classify the following experimental results according to the following scheme: For the quantons in question, the results:
- When dim light falls on a photomultiplier, the latter produces discrete electric pulses at random times.

Accepted Answer

The answer of Consider the experimental evidence we have discussed...

Question 13

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

Accepted Answer

A)  Upward. 
B)  Downward. 
C)  There is zero net force. 
D)  None of the above (explain).

Question 14

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is

Accepted Answer

A)  2 times greater. 
B)  20 times greater. 
C)  100 times greater. 
D)  200 times greater. 
E)  We need to know the actual sound level: $30 \mathrm{db}$ to $50 \mathrm{db}$ represents a different factor of intensity increase than 60 $\mathrm{db}$ to $80 \mathrm{db}$ (for example).

Question 15

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?

Accepted Answer

A)  Inverted 
B)  Upright

Question 16

We can define the local wavelength of any continuous and doubly differentiable function.

Accepted Answer

A) True 
 B)False

Question 17

Note: Each problem in this column concerns a quanton moving in one dimension in response to the potential energy function $V(x)$ shown. The graph below the potential energy graph shows the energy eigen function (EEF) $\psi_{n}(x)$ corresponding to the energy shown as a horizontal line on the potential energy graph ( $E_{n}$ means the $n$th energy level, where $n=1$ is the ground state). In each case, there is something wrong with the energy eigen function shown. Select from the following responses to indicate what is wrong:
The EEF shown is incorrectly drawn because

Accepted Answer

A)  It curves toward the axis in a forbidden region or away from the axis in an allowed region. 
B)  Its wavy part doesn't have the right number of bumps. 
C)  The amplitude of the wavy part varies incorrectly. 
D)  The wavelength of the wavy part varies incorrectly. 
E)  One of the exponential-like tails has the wrong length.

Question 18

Consider two $q$-vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. Their inner product $\langle u \mid w\rangle$ obeys the relation $\langle u \mid w\rangle=\langle w \mid u\rangle^{*}$.

Accepted Answer

A) True 
 B)False

Question 19

Suppose we have a vial of quantum systems that could either be boxes or harmonic oscillators. When we excite these systems and look at their emission spectra, we see two visible lines, whose wavelengths we measure. From this data, we can determine which kind of system we have.

Accepted Answer

A) True 
 B)False

Question 20

The work function $W$ for copper is $4.65 \mathrm{eV}$. Visible light will dislodge electrons from a copper surface.

Accepted Answer

A) True 
 B)False

Exam 5: Matter Behaves Like Waves Quantum Physics

Must all physically reasonable wavefunctions remain finite as $|x| \rightarrow \infty(A)$ , or does this apply only to solutions to the Schrödinger equation (B) ?

The ground-state energy of an electron in a hydrogen atom is $-13.6 \mathrm{eV}$ . This means that the binding energy of that electron is

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen - The wavelength of the light increases.

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?

Suppose we measure the wavelengths of the absorption lines of a vibrating diatomic molecule involving atoms whose masses we know. From this data, we can deduce the effective spring constant $k_{s}$ of the bond holding these atoms together.

Consider a two-component complex vector $|\psi\rangle=\left[\begin{array}{c}A \\I b\end{array}\right]$ Where $a$ and $b$ are real numbers. Which of the following vectors are orthogonal to this vector?

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen -We look at fringes farther from the central maximum.

Imagine that in a Davisson-Germer-type experiment we shine a beam of electrons on a nickel crystal perpendicular to the crystal face and find that we get enhanced scattering at an angle of $50^{\circ}$ . If we double the electrons' kinetic energy, -(c) (A) 1 (B) $2^{1 / 2}$ , or (C) 2

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?

We can define the local wavelength of any continuous and doubly differentiable function.

Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. Their inner product $\langle u \mid w\rangle$ obeys the relation $\langle u \mid w\rangle=\langle w \mid u\rangle^{*}$ .

Suppose we have a vial of quantum systems that could either be boxes or harmonic oscillators. When we excite these systems and look at their emission spectra, we see two visible lines, whose wavelengths we measure. From this data, we can determine which kind of system we have.

The work function $W$ for copper is $4.65 \mathrm{eV}$ . Visible light will dislodge electrons from a copper surface.

Exam 5: Matter Behaves Like Waves Quantum Physics

Must all physically reasonable wavefunctions remain finite as ∣x∣→∞(A) |x| \rightarrow \infty(A) ∣x∣→∞(A) , or does this apply only to solutions to the Schrödinger equation (B) ?

The ground-state energy of an electron in a hydrogen atom is −13.6eV-13.6 \mathrm{eV}−13.6eV . This means that the binding energy of that electron is

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen - The wavelength of the light increases.

Quantum issues often constrain transitions in quantum harmonic oscillators to those where Δn=1\Delta n=1Δn=1 . Consider a spectrum chart (like the one shown in figure Q11.2) for such a system. What would this chart look like?

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?

Suppose we measure the wavelengths of the absorption lines of a vibrating diatomic molecule involving atoms whose masses we know. From this data, we can deduce the effective spring constant ksk_{s}ks​ of the bond holding these atoms together.

Consider a two-component complex vector ∣ψ⟩=[AIb]|\psi\rangle=\left[\begin{array}{c}A \\I b\end{array}\right]∣ψ⟩=[AIb​] Where aaa and bbb are real numbers. Which of the following vectors are orthogonal to this vector?

Consider an experiment where we send monochromatic light to a distant screen through a single narrow slit. The distance between adjacent dark fringes in the diffraction pattern displayed on the screen -We look at fringes farther from the central maximum.

Imagine that in a Davisson-Germer-type experiment we shine a beam of electrons on a nickel crystal perpendicular to the crystal face and find that we get enhanced scattering at an angle of 50∘50^{\circ}50∘ . If we double the electrons' kinetic energy, -(c) (A) 1 (B) 21/22^{1 / 2}21/2 , or (C) 2

Imagine a small magnet (with its north pole vertically upward) passing near the north pole of an external magnet that is below the small magnet. In what direction does the net force acting on the magnet point?

If one sound is 20 dB20 \mathrm{~dB}20 dB louder than another sound, its intensity is

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?

We can define the local wavelength of any continuous and doubly differentiable function.

Suppose we have a vial of quantum systems that could either be boxes or harmonic oscillators. When we excite these systems and look at their emission spectra, we see two visible lines, whose wavelengths we measure. From this data, we can determine which kind of system we have.

The work function WWW for copper is 4.65eV4.65 \mathrm{eV}4.65eV . Visible light will dislodge electrons from a copper surface.

Must all physically reasonable wavefunctions remain finite as $|x| \rightarrow \infty(A)$ , or does this apply only to solutions to the Schrödinger equation (B) ?

The ground-state energy of an electron in a hydrogen atom is $-13.6 \mathrm{eV}$ . This means that the binding energy of that electron is

Suppose we measure the wavelengths of the absorption lines of a vibrating diatomic molecule involving atoms whose masses we know. From this data, we can deduce the effective spring constant $k_{s}$ of the bond holding these atoms together.

Consider a two-component complex vector $|\psi\rangle=\left[\begin{array}{c}A \\I b\end{array}\right]$ Where $a$ and $b$ are real numbers. Which of the following vectors are orthogonal to this vector?

Imagine that in a Davisson-Germer-type experiment we shine a beam of electrons on a nickel crystal perpendicular to the crystal face and find that we get enhanced scattering at an angle of $50^{\circ}$ . If we double the electrons' kinetic energy, -(c) (A) 1 (B) $2^{1 / 2}$ , or (C) 2

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is

The work function $W$ for copper is $4.65 \mathrm{eV}$ . Visible light will dislodge electrons from a copper surface.