Exam 5: Matter Behaves Like Waves Quantum Physics

Consider a two-slit interference experiment like the one shown in figure Q3.7b. The distance between adjacent bright spots in the interference pattern on the screen , - The intensity of the light increases.

Suppose we have a box containing an electron with the lowest possible energy $E_{1}$ . Imagine that we slowly squeeze the box, making its length $L$ smaller. What will happen to the electron's energy? The electron's energy will

Why (experimentally) is a set of quantons prepared in a superposition of a given observable's eigenvectors different from a classical mixture of quantons that have "already collapsed" to the different eigenvectors (with the same probabilities as predicted by the superposition)?

A certain organ pipe is open at both ends. Another pipe of the same length is open at one end and closed at the other. Which will have the lower pitch?

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

Nuclei with the highest binding energy per nucleon $e_{b}$ have $Z$ most closely equal to what?

The earth's rotation (A) increases, (B) decreases, or (C) does not affect its gravitational binding energy.

Consider a two-slit interference experiment like the one shown in figure Q3.7b. The distance between adjacent bright spots in the interference pattern on the screen , -The value of $n$ increases (careful!).

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: -Light that goes through two narrow, closely spaced slits in an opaque barrier and then falls on a screen creates a pattern of multiple bright spots on the screen.

Consider a set of electrons with an initial spin state $|\psi\rangle=\left[\begin{array}{c}\sqrt{1 / 2} \\\sqrt{1 / 2}\end{array}\right]$ If we send these electrons into an SGx device, what is the probability that a given electron will be determined to have its spin anti aligned with the $+x$ direction?

A linear traveling wave can be partially reflected when it encounters another linear traveling wave.

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

According to the chart shown in figure Q13.6, how many stable isotopes of ${ }_{30} \mathrm{Zn}$ exist?

Consider the sequence of SG devices shown in figure Q7.7. Which of the expressions below gives the proper quantum amplitude that an electron emerging from the first SG device leaves via the - channel of the final device? (Do not assume that the inner product is commutative.) Figure 07.7

As a sinusoidal wave's wavenumber increases, the wave's wavelength (in a non-dispersive medium)

An electron moving near a proton can never be unbound, no matter what its energy might be.

Suppose the energy of the longest-wavelength photon emitted by an electron in a box of length $L$ is $E_{\mathrm{ph}}$ . What is the energy of the photon with the fourth-longest wavelength that might be emitted?

A free quanton with a well-defined position can also have a well-defined energy.

The amount of ${ }_{18}^{40} \mathrm{Ar}$ is one-ninth the amount of ${ }_{19}^{40} \mathrm{~K}$ . If the half-life of the latter is $T$ , what is the rock's age?

A quanton really has a position at all times, but quantum mechanics does not allow us to predict that position with certainty at future times as we could in Newtonian mechanics.