1. Intro to Physics Units

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?

In a diagnostic x-ray procedure, $5.00\times {10}^{10}$ photons are absorbed by tissue with a mass of $0.600$ kg. The x-ray wavelength is $0.0200$ nm.

(a) What is the total energy absorbed by the tissue?

(b) What is the equivalent dose in rem?

Calculate the energy released in the fusion reaction: ${}_2^{3}He{+}_1^{2}H{\to }_2^{4}He{+}_1^{1}H$

A proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon if the $p$ and $\overline{p}$ collide head-on, each with an initial kinetic energy of $620$ MeV.

The starship Enterprise, of television and movie fame, is powered by combining matter and antimatter. If the entire $400$-kg antimatter fuel supply of the Enterprise combines with matter, how much energy is released? How does this compare to the U.S. yearly energy use, which is roughly $1.0\times {10}^{20}$ J?

In Example $44.3$, it was shown that a proton beam with an $800$-GeV beam energy gives an available energy of $38.7$ GeV for collisions with a stationary proton target. In a colliding-beam experiment, what total energy of each beam is needed to give an available energy of $2(38.7$ GeV$)=77.4$ GeV?