The ionization energy is the energy required to completely remove an electron from the ground state of an atom or ion. Calculate the ionization energies (in KJ $mol^{-1} )$ of the $He^+$ and $Li^{2+}$ ions.

Use the Bohr theory to find the series wavelength limits of the Lyman and Paschen series of hydrogen.

(a) Calculate the ionization energy for He+ . (b) What is the minimum frequency of a photon capable of ionizing He+ ?

In the n = 3 state of hydrogen, find the electron’s velocity, kinetic energy, and potential energy.

Gamma rays of energy 0.662 MeV are Compton scattered. (a) What is the energy of the scattered photon observed at a scattering angle of $60.0^{\circ}$? (b) What is the kinetic energy of the scattered electrons?

Which of the following statements correctly describe hybrid orbitals? (Select all that apply)

A. Hybrid orbitals are formed from the hybridization of atomic orbitals. The hybrid orbitals all have the same shape and energy.

B. A hybrid orbital is formed by the combination of atomic orbitals from both the bonding atoms.

C. Several atomic orbitals can be combined to form a single hybrid orbital.

D. The type if hybrid orbital varies depending on the specific combination of atomic orbitals.

Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 252 g of water is heated in a microwave oven from $20 . ^ { \circ } \mathrm { C }$ to $98 ^ { \circ } \mathrm { C } ,$ with radiation of wavelength $1.55 \times 10 ? 2$ m. How many photons are absorbed by the water in the soup?

X-ray photons of wavelength 0.02480 nm are incident on a target and the Compton-scattered photons are observed at $90.0^{\circ}$. (a) What is the wavelength of the scattered photons? (b) What is the momentum of the incident photons? Of the scattered photons? (c) What is the kinetic energy of the scattered electrons? (d) What is the momentum (magnitude and direction) of the scattered electrons?

You have three metal samples- $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ - that are tantalum (Ta), barium (Ba), and tungsten (W), but you don't know which is which. Metal A emits electrons in response to visible light; metals $\mathrm{B}$ and $\mathrm{C}$ require UV light.
(b) What range of wavelengths would distinguish $\mathrm{B}$ and $\mathrm{C}$ ? [The work functions are Ta $\left(6.81 \times 10^{-19} \mathrm{~J}\right)$, $\mathrm{Ba}\left(4.30 \times 10^{-19} \mathrm{~J}\right)$, and W $\left(7.16 \times 10^{-19} \mathrm{~J}\right)$; work function is explained .

You have three metal samples- $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ - that are tantalum (Ta), barium (Ba), and tungsten (W), but you don't know which is which. Metal A emits electrons in response to visible light; metals $\mathrm{B}$ and $\mathrm{C}$ require UV light.
(a) Identify metal A, and find the longest wavelength that removes an electron.

Elements in the same group (column) of the periodic table tend to have similar chemical properties. Explain the reason for this pattern in terms of the element's electrons.

The polarizing (Brewster) angle for a certain media boundary is $33^{\circ}.$ What is the critical angle for total internal reflection for the same boundary?

The removal of an electron from the hydrogen atom corresponds to raising the electron to the Bohr orbit that has $n=\infty$. On the basis of this statement, calculate the ionization energy of hydrogen in units of (a) joules per atom and (b) kilojoules per mole.

The ionization energy of a hydrogen atom is $13.6 \mathrm{eV}$. When a hydrogen atom absorbs a photon with this energy, the electron is ejected from the atom.

(a) What are the frequency and wavelength of a photon with this energy? Where does this photon lie in the electromagnetic spectrum? Could you see light with this frequency?

(b) When a photon has an energy greater than $13.6 \mathrm{eV}$, the "extra" energy (the energy in excess of $13.6 \mathrm{eV}$ ) goes into kinetic energy of the ejected electron. If a hydrogen atom absorbs a photon with an energy of $15.0 \mathrm{eV}$, what are the kinetic energy and speed of the ejected electron?

(c) When the light intensity is very high, it is possible for a hydrogen atom to absorb two photons simultaneously. If a hydrogen atom absorbs two photons of equal energy and the atom is just barely ionized, what are the frequency and wavelength of these photons? Could you see this light?