1. Intro to Physics Units

Table $44.3$ shows that a ${\Sigma }^0$ decays into a ${\Lambda }^0$ and a photon. Calculate the energy of the photon emitted in this decay, if the ${\Lambda }^0$ is at rest.

(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1–12). (State your assumptions, such as the mower moves with a 1-km/h speed, and has a 0.5-m width.) <IMAGE>

Rewrite 9.98 × 10⁷  in standard form.

Model a hydrogen atom as an electron in a cubical box with side length $L$. Set the value of $L$ so that the volume of the box equals the volume of a sphere of radius $a=5.29\times {10}^{-11}$ m, the Bohr radius. Calculate the energy separation between the ground and first excited levels, and compare the result to this energy separation calculated from the Bohr model.

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is $15.0$ kV, what are the shortest-wavelength x rays produced by the television?

Estimate the energy of the least strongly bound level in the $L$ shell of N²⁺.

The lowest and highest natural temperatures ever recorded on earth are −129°F in Antarctica and 134°F in Death Valley. What are these temperatures in °C and in K?

Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced by photons with frequency $22.7$ MHz?

(II) Estimate how many books can be shelved in a college library with 6500 m² of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average.

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?

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.

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R = 13.7 x 10⁹ light-years = 13.0 x 10²⁵ m with an average total mass density of about 1 x 10⁻^-26 kg/m³. Only about 4% of total mass is due to 'ordinary' matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 25.)

A photon has momentum of magnitude $8.24\(\times\)10^{-28}$ kg-m/s. What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

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?

Calculate the energy difference between the $m_s=\frac{1}{2}$ ('spin up') and $m_s=-\frac{1}{2}$ ('spin down') levels of a hydrogen atom in the $1s$ state when it is placed in a $1.45$ T magnetic field in the negative $z$-direction. Which level, $m_s=\frac{1}{2}$ or $m_s=-\frac{1}{2}$, has the lower energy?