1. Intro to Physics Units

The magnetic field in a cyclotron that accelerates protons is $1.70$ T. How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)

Rewrite 3.41 × 10⁻⁴ in standard form:

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?

An alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for $0.150$ s. The first officer on the spacecraft measures that the searchlight is on for $12.0$ ms.

(a) Which of these two measured times is the proper time?

(b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light $c$?

Table $44.3$ shows that a $Σ^0$ decays into a ${\Lambda }^0$ and a photon. What is the magnitude of the momentum of the photon? Is it reasonable to ignore the final momentum and kinetic energy of the ${\Lambda }^0$? Explain.

One mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?

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?

The common isotope of uranium, ${}^{238}U$, has a half-life of $4.47\times {10}^9$ years, decaying to ${}^{234}Th$ by alpha emission.

(a) What is the decay constant?

(b) What mass of uranium is required for an activity of $1.00$ curie?

(c) How many alpha particles are emitted per second by $10.0$ g of uranium?

An electron with a total energy of $30.0$ GeV collides with a stationary positron. What is the available energy?

Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–14, where h = 1.5 m , estimate the radius R of the Earth.

If a ${\Sigma }^{+}$ at rest decays into a proton and a ${\pi }^0$, what is the total kinetic energy of the decay products?

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

The unstable isotope ${}^{40}K$ is used for dating rock samples. Its half-life is $1.28\times {10}^9$ y.

(a) How many decays occur per second in a sample containing $1.63\times {10}^{-6}$ g of ${}^{40}K$?

(b) What is the activity of the sample in curies?

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.

The positive muon (µ⁺), an unstable particle, lives on average 2.20 × 10^-6 s (measured in its own frame of reference) before decaying. What average distance, measured in the laboratory, does the particle move before decaying?