An electron is trapped in a 1.00-nm-wide rigid box. Determine the probability of finding the electron within $0.15 \mathrm{~nm}$ of the center of the box (on either side of center) for $(c) n=20$

Which microscopic technique provides sharp pictures of threedimensional structures at high magnification?(a) light microscopy, (b) X-ray microscopy, (c) scanning electron microscopy, (d) transmission electron microscopy

We saw that there are 2N possible electron states in the 3s band of Na, where $N$ is the total number of atoms. How many possible electron states are there in the (a) $2s$ band, (b) $2p$ band, and (c) $3p$ band? (d) State a general formula for the total number of possible states in any given electron band.

If an electron is speeding down the two-mile-long Stanford Linear Accelerator at $99.98$ percent the speed of light, how many meters long is the trip as seen from the perspective of the electron?

In a typical electron microscope, the momentum of each electron is about $1.6 \times 10^{-\mathrm{zz}} \mathrm{kg}-\mathrm{m} / \mathrm{s}$. What is the de Broglie wavelength of the electrons?

An electron and a proton both start from rest and from the same point in a uniform electric field of 370.0 N/C. How far apart are they 1.00 $\mu \mathrm{s}$ after they are released? Ignore the attraction between the electron and the proton. (Hint: Imagine the experiment performed with the proton only, and then repeat with the electron only.)

An electron moves in a circular path perpendicular to a magnetic field of magnitude 0.235 T. If the kinetic energy of the electron is $3.30 \times 10 ^ { - 19 }$ J, find the radius of the circular path.

An electron approaches a 1.0-nm-wide potential-energy barrier of height $5.0 \mathrm{cV}$. What energy electron has a tunneling probability of (a) $10 \%$, (b) $1.0 \%$, and (c) $0.10 \%$ ?

A long, straight wire carries a current of $48.8 \mathrm{~A}$. An electron, traveling at $1.08 \times 10^7 \mathrm{~m} / \mathrm{s}$, is $5.20 \mathrm{~cm}$ from the wire. Calculate the force that acts on the electron if the electron voltage is directed $(a)$ toward the wire, $(b)$ parallel to the current (c) at right angles to the directions defined by $(a)$ and $(b)$.

An electron starts from rest $34.5 \mathrm{~cm}$ from a fixed point charge with $Q=-0.125 \mathrm{nC}$. How fast will the electron be moving when it is very far away?

An electron starts from rest 32.5 cm from a fixed point charge with $Q=-0.125 \mu \mathrm{C}$. How fast will the electron be moving when it is very far away?

Absorptions in the $v=1 \leftarrow 0$ vibration-rotation spectrum of $^{1}\mathrm{H}^{33} \mathrm{Cl}$ were observed at the following wavenumbers (in $\mathrm{cm}^{-2}).$

$$\begin{matrix} \text{2998.05} & \text{2981.05} & \text{2963.35} & \text{2944.99} & \text{2925.92}\\ \text{2906.25} & \text{2865.14} & \text{2843.63} & \text{2821.59} & \text{2799.00}\\ \end{matrix}$$

Assign the rotational quantum numbers and use the method of combination differences to calculate the rotational constants of the two vibrational levels.

An electron is trapped in a 1.00-nm-wide rigid box. Determine the probability of finding the electron within $0.15 \mathrm{~nm}$ of the center of the box (on either side of center) for (d) Compare to the classical prediction.

A measure of the density of the free-electron gas in a metal is the distance $r_s$, which is defined as the radius of the sphere whose volume equals the volume per conduction electron. (a) Show that $r_s=\left(3 / 4 \pi n_a\right)$, where $n_a$ is the free-electron number density. (b) Calculate $r_s$ for copper in nanometers.