1. Intro to Physics Units

A laser used to weld detached retinas emits light with a wavelength of $652$ nm in pulses that are $20.0$ ms in duration. The average power during each pulse is $0.600$ W. How much energy is in each pulse in joules? In electron volts?

A photon of green light has a wavelength of $520$ nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

The energy of the $2s$ state of lithium is $-5.391$ eV. Calculate the value of $Z_{eff}$ for this state.

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

The doubly charged ion N²⁺ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N²⁺ ion?

The energies of the $4s$, $4p$, and $4d$ states of potassium are given in Example $41.10$. Calculate $Z_{eff}$ for each state. What trend do your results show? How can you explain this trend?

The $5s$ electron in rubidium (Rb) sees an effective charge of $2.771e$. Calculate the ionization energy of this electron.

A hydrogen atom in a particular orbital angular momentum state is found to have $j$ quantum numbers $\frac{7}{2}$ and $\frac{9}{2}$. If $n=5$, what is the energy difference between the $j=\frac{7}{2}$ and $j=\frac{9}{2}$ levels?

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?

The hyperfine interaction in a hydrogen atom between the magnetic dipole moment of the proton and the spin magnetic dipole moment of the electron splits the ground level into two levels separated by $5.9\times {10}^{-6}$ eV. Calculate the wavelength and frequency of the photon emitted when the atom makes a transition between these states, and compare your answer to the value given at the end of Section $41.5$. In what part of the electromagnetic spectrum does this lie? Such photons are emitted by cold hydrogen clouds in interstellar space; by detecting these photons, astronomers can learn about the number and density of such clouds.

(a) If you treat an electron as a classical spherical object with a radius of $1.0\times {10}^{-17}$ m, what angular speed is necessary to produce a spin angular momentum of magnitude $\sqrt{\frac{3}{4}}h$?

(b) Use $v=r\omega$ and the result of part (a) to calculate the speed $v$ of a point at the electron's equator. What does your result suggest about the validity of this model?

A hydrogen atom in the $5g$ state is placed in a magnetic field of $0.600$ T that is in the $z$-direction. Into how many levels is this state split by the interaction of the atom's orbital magnetic dipole moment with the magnetic field?

A hydrogen atom in a $3p$ state is placed in a uniform external magnetic field $\overrightarrow{B}$. Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. What field magnitude $B$ is required to split the $3p$ state into multiple levels with an energy difference of $2.71\times {10}^{-5}$ eV between adjacent levels?

Pure germanium has a band gap of $0.67$ eV. The Fermi energy is in the middle of the gap. For temperatures of $250$ K, $300$ K, and $350$ K, calculate the probability $f\left(E\right)$ that a state at the bottom of the conduction band is occupied.

At the Fermi temperature $T_F$, $E_F=k{T}_F$ (see Exercise $42.22$). When $T=T_F$, what is the probability that a state with energy $E=2E_F$ is occupied?