?What does it mean to say that the energy of the electrons in an atom is quantized?

The light produced by a red neon sign is due to the emission of light by excited neon atoms. Qualitatively describe the spectrum produced by passing light from a neon lamp through a prism.

An FM radio station found at \(103.1\) on the FM dial broadcasts at a frequency of \(1.031 \times 10^{8} \mathrm{~s}^{-1}(103.1 \mathrm{MHz})\). What is the wavelength of these radio waves in meters? Equation Transcription: Text Transcription: 103.1 1.031 times 10^8 s^-1 (103.1 MHz)

\(FM-95\), an FM radio station, broadcasts at a frequency of \(9.51 \times 10^{7} \mathrm{~s}^{-1}(95.1 \mathrm{MHz})\). What is the wavelength of these radio waves in meters? Equation Transcription: Text Transcription: FM-95 9.51 times 10^7 s^-1 (95.1 MHz)

A bright violet line occurs at \(435.8 nm\) in the emission spectrum of mercury vapor. What amount of energy, in joules, must be released by an electron in a mercury atom to produce a photon of this light Equation Transcription: Text Transcription: 435.8 nm

Light with a wavelength of \(614.5 nm\) looks orange. What is the energy, in joules, per photon of this orange light? What is the energy in \(\mathrm{eV}\left(1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}\right)\)? Equation Transcription: Text Transcription: 614.5 nm eV (1 eV = 1.602 times 10^-19 J)

Heated lithium atoms emit photons of light with an energy of \(2.961 \times 10^{-19} \mathrm{~J}\). Calculate the frequency and wavelength of one of these photons. What is the total energy in \(1\) mole of these photons? What is the color of the emitted light? Equation Transcription: Text Transcription: 2.961 times 10^-19 J 1

A photon of light produced by a surgical laser has an energy of \(3.027 \times 10^{-19} \mathrm{~J}\). Calculate the frequency and wavelength of the photon. What is the total energy in \(1\) mole of photons? What is the color of the emitted light? Equation Transcription: Text Transcription: 3.027 times 10^-19 J 1

When rubidium ions are heated to a high temperature, two lines are observed in its line spectrum at wavelengths (a) \(7.9 \times 10^{-7} \mathrm{~m}\) and (b) \(4.2 \times 10^{-7} \mathrm{~m}\). What are the frequencies of the two lines? What color do we see when we heat a rubidium compound? Equation Transcription: Text Transcription: 7.9 times 10^-7 m 4.2 times 10^-7 m

The emission spectrum of cesium contains two lines whose frequencies are (a) \(3.45 \times 10^{14} \mathrm{~Hz}\) and (b) \(6.53 \times 10^{14} \mathrm{~Hz}\). What are the wavelengths and energies per photon of the two lines? What color are the lines? Equation Transcription: Text Transcription: 3.45 times 10^14 Hz 6.53 times 10^14 Hz

Photons of infrared radiation are responsible for much of the warmth we feel when holding our hands before a fire. These photons will also warm other objects. How many infrared photons with a wavelength of \(1.5 \times 10^{-6} \mathrm{~m}\) must be absorbed by the water to warm a cup of water \((175 g)\) from \(25.0^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\)? Equation Transcription: Text Transcription: 1.5 times 10^-6 m (175 g) 25.0 ^circ C 40 ^circ C

One of the radiographic devices used in a dentist's office emits an X-ray of wavelength \(2.090 \times 10^{-11} \mathrm{~m}\). What is the energy, in joules, and frequency of this X-ray? Equation Transcription: Text Transcription: 2.090 times 10^-11 m

The eyes of certain reptiles pass a single visual signal to the brain when the visual receptors are struck by photons of a wavelength of \(850 nm\). If a total energy of \(3.15 \times 10^{-14} \mathrm{~J}\) is required to trip the signal, what is the minimum number of photons that must strike the receptor? Equation Transcription: Text Transcription: 850 nm 3.15 times 10^-14 J

RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?

Answer the following questions about a Blu-ray laser: 1. The laser on a Blu-ray player has a wavelength of \(405 nm\). In what region of the electromagnetic spectrum is this radiation? What is its frequency? 2. A Blu-ray laser has a power of \(5 \text { milliwatts }\left(1 \text { watt }=1 \mathrm{~J} \mathrm{~s}^{-1}\right. \text { ). }\). How many photons of light are produced by the laser in \(1 hour\)? 3. The ideal resolution of a player using a laser (such as a Blu-ray player), which determines how close together data can be stored on a compact disk, is determined using the following formula: \(\text { Resolution }=0.60(\lambda / \mathrm{NA})\), where \(\lambda\) is the wavelength of the laser and \(NA\) is the numerical aperture. Numerical aperture is a measure of the size of the spot of light on the disk; the larger the \(NA\), the smaller the spot. In a typical Blu-ray system, \(NA = 0.95\). If the \(405-nm\) laser is used in a Blu-ray player, what is the closest that information can be stored on a Blu-ray disk? 4. The data density of a Blu-ray disk using a \(405-nm\) laser is \(1.5 \times 10^{7} \text { bits } \mathrm{mm}^{-2}\). Disks have an outside diameter of \(120 mm\) and a hole of \(15-mm\) diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold \(9,400,000\) pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by \(A=\pi r^{2}\), where the radius \(r\) is one-half of the diameter.) Equation Transcription: Text Transcription: 405 nm 5 milliwatts (1 watt=1 J s^-1 1 hour Resolution=0.60(lambda/NA) lambda NA NA=0.95 1.5 times 10^7 bits mm^-2 120 mm 15-mm 9,400,000 A=pi r^2 r

What is the threshold frequency for sodium metal if a photon with frequency \(6.66 \times 10^{14} \mathrm{~s}^{-1}\) ejects an electron with \(7.74 \times 10^{-20} \mathrm{~J}\) kinetic energy? Will the photoelectric effect be observed if sodium is exposed to orange light? Equation Transcription: Text Transcription: 6.66 times 10^14 s^-1 7.74 times 10^-20 J

Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of \(3\) than when it has a quantum number of \(1\)? Equation Transcription: Text Transcription: 3 1

What does it mean to say that the energy of the electrons in an atom is quantized?

Using the Bohr model, determine the energy, in joules, necessary to ionize a ground-state hydrogen atom. Show your calculations

The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the amount of energy that an electron gains when subjected to a potential of \(1 volt\); \(1 \mathrm{eV}=1.602 \times 10^{-19} \mathrm{~J}\). Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with \(n=5\) to the orbit with \(n=2\). Show your calculations. Equation Transcription: Text Transcription: 1 volt 1 eV = 1.602 times 10^-19 J n = 5 n = 2

Using the Bohr model, determine the lowest possible energy, in joules, for the electron in the \(\mathrm{Li}^{2+}\) ion. Equation Transcription: Text Transcription: Li^2+

Using the Bohr model, determine the lowest possible energy for the electron in the \(\mathrm{He}^{+}\) ion. Equation Transcription: Text Transcription: He^+

Using the Bohr model, determine the energy of an electron with \(n=6\) in a hydrogen atom. Equation Transcription: Text Transcription: n=6

Using the Bohr model, determine the energy of an electron with \(n=8\) in a hydrogen atom. Equation Transcription: Text Transcription: n=8

How far from the nucleus in angstroms \(\text { (1 angstrom }=1 \times 10^{-10} \mathrm{~m} \text { ) }\) is the electron in a hydrogen atom if it has an energy of \(-8.72 \times 10^{-20} \mathrm{~J}\)? Equation Transcription: Text Transcription: (1 angstrom = 1 times 10^-10 m) -8.72 times 10^-20 J

What is the radius, in angstroms, of the orbital of an electron with \(n=8\) in a hydrogen atom? Equation Transcription: Text Transcription: n=8

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a \(\mathrm{He}^{+}\) ion moves from the orbit with \(n=5\) to the orbit with \(n=2\). Equation Transcription: Text Transcription: He^+ n=5 n=2

Using the Bohr model, determine the energy in joules of the photon produced when an electron in a \(\mathrm{Li}^{2+}\) ion moves from the orbit with \(n=2\) to the orbit with \(n=1\). Equation Transcription: Text Transcription: Li^2+ n=2 n=1

Consider a large number of hydrogen atoms with electrons randomly distributed in the \(n = 1, 2, 3, and 4\) orbits. 1. How many different wavelengths of light are emitted by these atoms as the electrons fall into lower-energy orbitals? 2. Calculate the lowest and highest energies of light produced by the transitions described in part (a). 3. Calculate the frequencies and wavelengths of the light produced by the transitions described in part (b). Equation Transcription: Text Transcription: n=1,2,3 and 4

How are the Bohr model and the Rutherford model of the atom similar? How are they different?

The spectra of hydrogen and of calcium are shown here. What causes the lines in these spectra? Why are the colors of the lines different? Suggest a reason for the observation that the spectrum of calcium is more complicated than the spectrum of hydrogen.

How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?

What are the allowed values for each of the four quantum numbers: \(\mathrm{n}, \mathrm{l}, m_{l}, \text { and } m_{s}\)? Equation Transcription: Text Transcription: n, l, m_l, and m_s

Describe the properties of an electron associated with each of the following four quantum numbers: \(\mathrm{n}, \mathrm{l}, m_{l}, \text { and } m_{s}\). Equation Transcription: Text Transcription: n, l, m_l, and m_s

Answer the following questions: 1. Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom. 2. How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?

Identify the subshell in which electrons with the following quantum numbers are found: (a) \(n=2, l=1\) (b) \(n=4, I=2\) (c) \(n=6, I=0\) Equation Transcription: Text Transcription: n=2, l=1 n=4, l=2 n=6, l=0

Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?

Identify the subshell in which electrons with the following quantum numbers are found: (a) \(n=3, I=2\) (b) \(n=1,1=0\) (c) \(n=4, I=3\) Equation Transcription: Text Transcription: n=3, l=2 n=1, l=0 n=4, l=3

Which of the subshells described in the previous question contain degenerate orbitals? How many degenerate orbitals are in each?

Sketch the boundary surface of a \(d_{x^{2}-y^{2}}\) and a \(p_{y}\) orbital. Be sure to show and label the axes. Equation Transcription: Text Transcription: d_x^2-y^2 p_y

Sketch the \(\mathrm{p}_{\mathrm{x}}\) and \(\mathrm{d}_{\mathrm{xz}}\) orbitals. Be sure to show and label the coordinates. Equation Transcription: Text Transcription: p_x d_xz

Consider the orbitals shown here in outline. 1. What is the maximum number of electrons contained in an orbital of type \((x)\)? Of type \((y)\)? Of type \((z)\)? 2. How many orbitals of type \((x)\) are found in a shell with \(n=2\)? How many of type \((y)\)? How many of type \((z)\)? 3. Write a set of quantum numbers for an electron in an orbital of type \((x)\) in a shell with \(n=4\). Of an orbital of type \((y)\) in a shell with \(n=2\). Of an orbital of type \((z)\) in a shell with \(n=3\). 4. What is the smallest possible \(n\) value for an orbital of type \((x)\)? Of type \((y)\)? Of type \((z)\)? 5. What are the possible \(l\) and \(m_{l}\) values for an orbital of type \((x)\)? Of type \((y)\)? Of type \((z)\)? Equation Transcription: Text Transcription: (x) (y) (z) n=2 n=4 n=3 n l m_l

State the Heisenberg uncertainty principle. Describe briefly what the principle implies.

How many electrons could be held in the second shell of an atom if the spin quantum number \(\mathrm{m}_{\mathrm{s}}\) could have three values instead of just two? (Hint: Consider the Pauli exclusion principle.) Equation Transcription: Text Transcription: m_s

Which of the following equations describe particle-like behavior? Which describe wavelike behavior? Do any involve both types of behavior? Describe the reasons for your choices. 1. \(\mathrm{c}=\lambda \mathrm{V}\) 2. \(E=\frac{m v^{2}}{2}\) 3. \(r=\frac{n^{2} a_{0}}{Z}\) 4. \(E=h v\) 5. \(\lambda=\frac{h}{m v}\) Equation Transcription: Text Transcription: c = lambda v E = m nu^2 /2 r = n^2 a_0 /Z E = hv lambda = h/m nu

Write a set of quantum numbers for each of the electrons with an \(n\) of \(4\) in a \(Se\) atom. Equation Transcription: Text Transcription: n 4 Se

Read the labels of several commercial products and identify monatomic ions of at least four transition elements contained in the products. Write the complete electron configurations of these cations.

Read the labels of several commercial products and identify monatomic ions of at least six main group elements contained in the products. Write the complete electron configurations of these cations and anions.

Using complete subshell notation (not abbreviations, \(1 s^{2} 2 s^{2} 2 p^{6}\), and so forth), predict the electron configuration of each of the following atoms: (a) \(C\) (b) \(P\) (c) \(V\) (d) \(Sb\) (e) \(Sm\) Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 C P V Sb Sm

Using complete subshell notation (\(1 s^{2} 2 s^{2} 2 p^{6}\), and so forth), predict the electron configuration of each of the following atoms: (a) \(N\) (b) \(Si\) (c) \(Fe\) (d) \(Te\) (e) \(Tb\) Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 N Si Fe Te Tb

Is \(1 s^{2} 2 s^{2} 2 p^{6}\) the symbol for a macroscopic property or a microscopic property of an element? Explain your answer. Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6

What additional information do we need to answer the question “Which ion has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6}\)”? Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 3s^2 3p^6

Draw the orbital diagram for the valence shell of each of the following atoms: (a) \(C\) (b) \(P\) (c) \(V\) (d) \(Sb\) (e) \(Ru\) Equation Transcription: Text Transcription: C P V Sb Ru

Use an orbital diagram to describe the electron configuration of the valence shell of each of the following atoms: (a) \(N\) (b) \(Si\) (c) \(Fe\) (d) \(Te\) (e) \(Mo\) Equation Transcription: Text Transcription: N Si Fe Te Mo

Using complete subshell notation (\(1 s^{2} 2 s^{2} 2 p^{6}\), and so forth), predict the electron configurations of the following ions. (a) \(N^{3-}\) (b) \(\mathrm{Ca}^{2+}\) (c) \(\mathrm{S}^{-}\) (d) \(\mathrm{Cs}^{2+}\) (e) \(\mathrm{Cr}^{2+}\) (f) \(\mathrm{Gd}^{3+}\) Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 N^3- Ca^2+ S^- Cs^2+ Cr^2+ Gd^3+

Which atom has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 4 s^{2} 3 d^{10} 4 p^{6} 5 s^{2} 4 d^{2}\)? Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^2

Which atom has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{7} 4 s^{2}\)? Equation Transcription: Text Transcription: 1s^2 2s^2 2p^6 3s^2 3p^6 3d^7 4s^2

Which ion with a \(+1\) charge has the electron configuration \(1 s^{2} 2 s^{2} 2 p^{6} 3 s^{2} 3 p^{6} 3 d^{10} 4 s^{2} 4 p^{6}\)? Which ion with a \(–2\) charge has this configuration? Equation Transcription: Text Transcription: a+1 1s^2 2s^2 2p^6 3s^2 3p^6 3d^10 4s^2 4p^6 -2

Which of the following atoms contains only three valence electrons: \(Li\), \(B\), \(N\), \(F\), \(Ne\)? Equation Transcription: Text Transcription: Li B N F Ne

Which of the following has two unpaired electrons? (a) \(Mg\) (b) \(Si\) (c) \(S\) (d) \(Both Mg and S\) (e) \(Both Si and S\). Equation Transcription: Text Transcription: Mg Si S Both Mg and S Both Si and S

Which atom would be expected to have a half-filled \(6p\) subshell? Equation Transcription: Text Transcription: 6p

Which atom would be expected to have a half-filled \(4s\) subshell? Equation Transcription: Text Transcription: 4s

In one area of Australia, the cattle did not thrive despite the presence of suitable forage. An investigation showed the cause to be the absence of sufficient cobalt in the soil. Cobalt forms cations in two oxidation states, \(\mathrm{Co}^{2+}\) and \(\mathrm{Co}^{3+}\). Write the electron structure of the two cations. Equation Transcription: Text Transcription: Co^2+ Co^3+

Thallium was used as a poison in the Agatha Christie mystery story "The Pale Horse." Thallium has two possible cationic forms, \(+1\) and \(+3\). The \(+1\) compounds are the more stable. Write the electron structure of the \(+1\) cation of thallium. Equation Transcription: Text Transcription: +1 +3

Write the electron configurations for the following atoms or ions: (a) \(B^{3+}\) (b) \(O^{-}\) (c) \(C l^{3+}\) (d) \(\mathrm{Ca}^{2+}\) (e) \(T i\) Equation Transcription: Text Transcription: B^3+ O^- Cl^3+ Ca^2+ Ti

\(Cobalt-60\) and \(iodine-131\) are radioactive isotopes commonly used in nuclear medicine. How many protons, neutrons, and electrons are in atoms of these isotopes? Write the complete electron configuration for each isotope. Equation Transcription: Text Transcription: Cobalt-60 iodine - 131

Write a set of quantum numbers for each of the electrons with an \(n\) of \(3\) in a \(Sc\) atom. Equation Transcription: Text Transcription: n 3 Sc

Based on their positions in the periodic table, predict which has the smallest atomic radius: \(Mg\), \(Sr\), \(Si\), \(Cl\), \(I\). Equation Transcription: Text Transcription: Mg Sr Si Cl I

Based on their positions in the periodic table, predict which has the largest atomic radius: \(Li\), \(Rb\), \(N\), \(F\), \(I\). Equation Transcription: Text Transcription: Li Rb N F I

Based on their positions in the periodic table, predict which has the largest first ionization energy: \(Mg\), \(Ba\), \(B\),\(O\), \(Te\). Equation Transcription: Text Transcription: Mg Ba B O Te

Based on their positions in the periodic table, predict which has the smallest first ionization energy: \(Li\), \(Cs\), \(N\), \(F\), \(I\). Equation Transcription: Text Transcription: Li Cs N F I

Based on their positions in the periodic table, rank the following atoms in order of increasing first ionization energy: \(F\), \(Li\), \(N\), \(Rb\) Equation Transcription: Text Transcription: F Li N Rb

Based on their positions in the periodic table, rank the following atoms in order of increasing first ionization energy: \(Mg\), \(O\), \(S\), \(Si\). Equation Transcription: Text Transcription: Mg O S Si

Atoms of which group in the periodic table have a valence shell electron configuration of \(n s^{2} n p^{3}\)? Equation Transcription: Text Transcription: ns^2 np^3

Atoms of which group in the periodic table have a valence shell electron configuration of \(n s^{2}\)? Equation Transcription: Text Transcription: ns^2

Based on their positions in the periodic table, list the following atoms in order of increasing radius: \(Mg\), \(Ca\), \(Rb\), \(Cs\). Equation Transcription: Text Transcription: Mg Ca Rb Cs

Based on their positions in the periodic table, list the following atoms in order of increasing radius: \(Sr\), \(Ca\), \(Si\), \(Cl\). Equation Transcription: Text Transcription: Sr Ca Si Cl

Based on their positions in the periodic table, list the following ions in order of increasing radius: \(K^{+}\) , \(\mathrm{Ca}^{2+}\) , \(A l^{3+}\) , \(S i^{4+}\) Equation Transcription: Text Transcription: K^+ Ca^2+ Al^3+ Si^4+

List the following ions in order of increasing radius: \(\mathrm{Li}^{+}\), \(M g^{2+}\), \(B r^{-}\), \(T e^{2-}\). Equation Transcription: Text Transcription: Li^+ Mg^2+ Br^- Te^2-

Which atom and/or ion is (are) isoelectronic with \(B r^{+}: S e^{2+}, S e, A s^{-}, K r, G a^{3+}, C l^{-}\) ? Equation Transcription: Text Transcription: Br^+ : Se^2+, Se, As^-, Kr, Ga^3+, Cl^-

Which of the following atoms and ions is (are) isoelectronic with \(S^{2+}: S i^{4+}, C l^{3+}, A r, A s^{3+}, S i, A l^{3+}\)? Equation Transcription: Text Transcription: S^2+ : Si^4+, Cl^3+, Ar, As^3+, Si, Al^3+

Compare both the numbers of protons and electrons present in each to rank the following ions in order of increasing radius: \(A s^{3-}, B r^{-}, K^{+}, M g^{2+}\). Equation Transcription: Text Transcription: As^3-,Br^-,K^+,Mg^2+.

Of the five elements Al, Cl, I, Na, Rb, which has the most exothermic reaction? (E represents an atom.) What name is given to the energy for the reaction? Hint: Note the process depicted does not correspond to electron affinity.) \(E^{+}(g)+e^{-} \rightarrow E(g)\) Equation Transcription: Text Transcription: E^+(g)+e^- rightarrow E(g)

Of the five elements Sn, Si, Sb, O, Te, which has the most endothermic reaction? (E represents an atom.) What name is given to the energy for the reaction? \(E(g) \rightarrow E^{+}(g)+e^{-}\) Equation Transcription: Text Transcription: E(g) rightarrow E^+(g)+e^-

The ionic radii of the ions \(S^{2-}, C l^{-}\), and \(K^{+}\) are \(184,181,138 \mathrm{pm}\) respectively. Explain why these ions have different sizes even though they contain the same number of electrons. Equation Transcription: Text Transcription: S^2-,Cl^- K^+ 184,181,138pm

Which main group atom would be expected to have the lowest second ionization energy?

Explain why \(Al\) is a member of group 13 rather than group 3? Equation Transcription: Text Transcription: Al