1. Intro to Physics Units

The orbital angular momentum of an electron has a magnitude of $4.716\times {10}^{-34}$ kg-m²/s. What is the angular momentum quantum number $l$ for this electron?

Calculate, in units of $U$, the magnitude of the maximum orbital angular momentum for an electron in a hydrogen atom for states with a principal quantum number of $2$, $20$, and $200$. Compare each with the value of $nh$ postulated in the Bohr model. What trend do you see?

A hydrogen atom is in a $d$ state. In the absence of an external magnetic field, the states with different $m_l$ values have (approximately) the same energy. Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. Calculate the splitting (in electron volts) of the ml levels when the atom is put in a $0.800$ T magnetic field that is in the $+z$-direction

A hydrogen atom undergoes a transition from a $2p$ state to the $1s$ ground state. In the absence of a magnetic field, the energy of the photon emitted is $122$ nm. The atom is then placed in a strong magnetic field in the $z$-direction. Ignore spin effects; consider only the interaction of the magnetic field with the atom's orbital magnetic moment. How many different photon wavelengths are observed for the $2p\to 1s$ transition? What are the $m_l$ values for the initial and final states for the transition that leads to each photon wavelength?

Estimate the energy of the highest-$l$ state for (a) the $L$ shell of Be⁺ and (b) the $N$ shell of Ca⁺.

The energies for an electron in the $K$, $L$, and $M$ shells of the tungsten atom are $-69,500$ eV, $-12,000$ eV, and $-2,200$ eV, respectively. Calculate the wavelengths of the $K_{\alpha }$ and $K_{\beta }$ x rays of tungsten.

For the H₂ molecule the equilibrium spacing of the two protons is $0.074$ nm. The mass of a hydrogen atom is $1.67\times {10}^{-27}$ kg. Calculate the wavelength of the photon emitted in the rotational transition $l=2$ to $l=1$.

During each of these processes, a photon of light is given up. In each process, what wavelength of light is given up, and in what part of the electromagnetic spectrum is that wavelength? A molecule decreases its vibrational energy by $0.198$ eV.

The H₂ molecule has a moment of inertia of $4.6\times {10}^{-48}$ kg-m². What is the wavelength $l$ of the photon absorbed when H₂ makes a transition from the $l=3$ to the $l=4$ rotational level?

Two atoms of cesium (Cs) can form a $C{s}_2$ molecule. The equilibrium distance between the nuclei in a $C{s}_2$ molecule is $0.447$ nm. Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is $2.21\times {10}^{-25}$ kg.

The rotational energy levels of CO are calculated in Example $42.2$. If the energy of the rotating molecule is described by the classical expression $K=(\frac12)I\omega^2$, for the $l = 1$ level, what is the angular speed of the rotating molecule?

Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires $0.67$ eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie?

At a temperature of $290$ K, a certain $p-n$ junction has a saturation current $I_S=0.500$ mA. Find the current at this temperature when the voltage is (i) $1.00$ mV, (ii) $-1.00$ mV, (iii) $100$ mV, and (iv) $-100$ mV.

How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, ${}_{\phantom{0}14}^{28}Si$; (b) rubidium, ${}_{\phantom{0}37}^{85}Rb$; (c) thallium, ${}_{\phantom{0}81}^{205}Tl$?

It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans) using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of $12$ mSv, applied to the whole body. By contrast, a chest x ray typically administers $0.20$ mSv to only $5.0$ kg of tissue. How many chest x rays would deliver the same total amount of energy to the body of a $75$-kg person as one whole-body scan?