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CHAPTER 7 HW

Name: Lab: MW 11-2 MW 2-5

WAVE PROPERTIES OF EM RADIATION1

1.) In 1997, the spacecraft Pathfinder landed on Mars, where it delivered the Sojourner Mars rover. At this time Mars was approximately 7.8 × 107 km from Earth. How long (in minutes) did it take a radio signal sent from Pathfinder to reach Earth?

2.) Microwave ovens sold in the United States operate on a frequency of 2450 MHz. What is the wavelength of these microwaves in centimeters?

3.) Data encoded on DVD and Blu-Ray discs are read by lasers. DVDs use a 650 nm laser and Blu-Rays use a 405 nm laser (technically in the violet range, not blue). What is the frequency of each laser?

4.) Draw the following, compared to the wave shown below.

Draw another wave with a longer wavelength.

Draw another wave with a higher frequency.

1 Q1) 4.3 min; Q2) 12.2 cm; Q3) 4.6 × 1014 s–1 (DVD), 7.40 × 1014 s–1 (Blu-Ray); Q4a) Stretched out, b) Closer together.

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5.) Wintergreen-flavored candies (like Lifesavers) containing methyl salicylate are triboluminescent, meaning they emit flashes of light when crushed. The strongest emission of light is at 450 nm (it appears blue). What is the energy of each photon of light emitted?

6.) Magnetic resonance imaging (MRI) body scanners used in hospitals typically operate on a 400. MHz frequency. What is the energy and wavelength of each photon of EM radiation used in an MRI?

7.) Cobalt-60 is a radioactive isotope used in medicine for the treatment of certain cancers. It is also used in food irradiation to prevent spoilage. It produces beta particles and gamma rays, the latter having energies of 1.173 MeV and 1.332 MeV (1 MeV = 106 electron volts, and 1 eV = 1.602 × 10–19 J/photon). What is the wavelength of a gamma ray photon with an energy of 1.173 MeV?

8.) Order the following four types of electromagnetic radiation…2

Gamma rays from nuclear reactor FM radio signal Yellow light Dental X-rays

a. From low to high energy:

b. From short to long wavelength

c. From low to high frequency

2 Q5) 4.4 × 10–19 J; Q6) E=2.65 × 10–25 J, l = 0.750 m; Q7) 1.057 × 10–12 m; Q8a) Low energy Radio < Yellow < X-rays < Gamma, b) Short wavelength Gamma < X-rays < Yellow < Radio, c) Low frequency Radio < Yellow < X-rays < Gamma.

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PHOTOELECTRIC EFFECT3

9.) Multiple choice:

According to the photoelectric effect, if you shine light on a metal it will give off a(n) ____________ if the light has a high enough ____________.

a. Proton; Intensity b. Electron; Intensity c. Photon; Intensity d. Electron; Frequency e. Photon; Frequency

Which is NOT an interpretation of the photoelectric effect?

a. Light can be described by E=mc2. b. Light has particle-like properties. c. Light is quantized in photons. d. Light’s energy is not related to its intensity.

EMISSION SPECTRA, BOHR MODEL

10.) Fireworks are created by reacting an oxidizer (KClO4, KClO3, or KNO3) with black powder, and including various salts to produce a desired color. For example, sodium produces a yellow color, strontium produces red, and barium produces green.

The explosion of the oxidizer and black powder provides energy that is transferred to the salts in the fireworks shell. Explain how an element converts this energy into colored light.

11.) The emission spectrum of hydrogen has only four lines (colors). This tells us that… (multiple choice).

a. The electron in hydrogen has quantized energies. b. The hydrogen atom produces dim light. c. There are four electrons in a hydrogen atom. d. The spectrum is continuous.

3 Q9a) d, electron/frequency, b) a, E=mc2; Q10) See complete solutions; Q11) a, Quantized energies.

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12.) Consider the following four electronic transitions in the hydrogen atom (A–D).

a. Which transition(s) cause emission of a photon? __________

b. In which transition(s) is energy absorbed? __________

c. Which transition(s) have a negative DE? __________

d. Which transition releases a photon with the longest l? __________

e. Is the change in energy equal or unequal in transitions A (n = 4→2) and B (n = 5→3)? _________

f. When an electron is in the n=2 energy level, is the hydrogen atom in the ground state or an excited state?

13.) Calculate the wavelength (in m) associated with the electronic transition (n = 7→2) in the H atom.

14.) Calculate the wavelength (in nm) associated with an electronic transition between n = 4 and n = 3 in the hydrogen atom.

15.) Does the electronic transition in the previous problem (n = 4→3) produce visible light (380–740 nm)? If it does not, is the light produced of higher or lower energy than visible light? Briefly explain.4

4 Q12a) A,B,D, b) C, c) A,B,D, d) Lowest E, D, e) Unequal, f) Excited state; Q13) 3.970 × 10–7 m; Q14) 1875 nm; Q15) Not visible, lower energy, see complete solutions for explanation.

n = 2

n = 3

n = 4n = 5n = 6

A B C D

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16.) Calculate the energy of an electron in the n = 5 state of the hydrogen atom.

17.) Calculate the change in energy associated with the electronic transition n = 5→1 in the hydrogen atom, and the frequency of light either absorbed or produced.

18.) A hydrogen atom in the ground state absorbs 93.8 nm of EM radiation. What n energy level does the electron reside in after absorption of the radiation?5

5 Q16) E= –8.716 × 10–20 J, note negative energy; Q17) E= –2.092 × 10–18 J, v = 3.157 × 1015 s–1; Q18) n=6.

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QUANTUM MECHANICS / QUANTUM NUMBERS6

19.) An orbital is… (multiple choice)

a. The path an electron takes around the nucleus. b. A region of space where the electron is found 90% of the time. c. The most probable location of an electron. d. The shape of an electron.

20.) Give the physical meaning of each quantum number, used to describe an electron.

n = _______________ l = _______________ ml = _______________ ms = _______________

21.) Sketch the general shape of each orbital.

3p orbital Orbital described by n = 3, l = 2

Orbital described by n = 4, l = 0

22.) Fill in the blanks, or choose the correct answer.

a. When n = 2, the numerical values of l can be

b. When n = 2, which of the following orbitals exist? 2s, 2p, 2d, 2f, 2g

c. The lowest n value which contains a “g” orbital is

d. When an electron is in a 4f orbital, the numerical value(s) of ml can be

e. When an electron is in a 3p orbital, the numerical value(s) of ms can be

f. The quantum numbers (4, 1, 0, +½) in the order of (n, l, ml, ms) describe an electron in which orbital? 4s, 4p, 4d, 4f

g. The quantum numbers (6, 0, 0, –½) in the order of (n, l, ml, ms) describe an electron in which orbital? 6s, 6p, 6d, 6f

h. In a certain multi-electron atom, how many different electrons can be in a 5p orbital?

23.) How do the three 2p orbitals differ, with values of ml = –1, 0, +1?

6 Q19) b; Q20) n = energy / size, l = shape of orbital, ml = orientation, ms = electron spin; Q21) See complete solutions, a) dumbbell, b) cloverleaf, c) sphere; Q22a) 0,1, b) 2s, 2p, c) 5, d) –3, –2, –1, 0, 1, 2, 3, e) +½, –½, f) 4p, g) 6s, h) 6, Q23) Orientation.

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24.) Could the following quantum numbers describe an electron in the hydrogen atom? Briefly explain why or why not.

a. n = 3, l = 2, ml = 2

b. n = 4, l = 3, ml = 4

c. n = 0, l = 0, ml = 0

d. n = 2, l = –1, ml = 1

25.) Explain why each set of quantum numbers, in the order of (n, l, ml, ms), does not describe an electron. In other words, why are these quantum numbers not allowed?

a. (1, 0, 0, 0)

b. (2, 2, 0, +½)

c. (6, 0, 1, –½)

d. (3, 1, –2, –½)

26.) In a poly-electronic atom such as uranium (Z = 92), what are the maximum number of electrons that could have these quantum numbers? Briefly explain.7

a. n = 2

b. n = 3, ms = +½

c. n = 5, ml = +1

7 Q24a) Yes, 3d electron, b) No, ml can’t be 4 with 4f electron, c) No, n can’t be zero, d) No, l can’t be negative; Q25a) ms must be +½ or –½, b) 2d doesn’t exist, c) ml can’t be 1 if l=0, s orbital, d) ml can’t be –2 if l=1, p orbital; Q26a) 8 e–, b) 9 e–, c) 8 e–.

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ELECTRON CONFIGURATIONS8

27.) For each element, draw the orbital energy diagram and write the complete (not condensed) ground state electron configuration.

Carbon Neon Sulfur

Orbital diagram

e– config

28.) Write the condensed electron configuration for each element, using noble gas abbreviations.

a. Boron, B d. Gallium, Ga (Z=31)

b. Aluminum, Al e. Cadmium, Cd (Z=48)

c. Scandium, Sc, (Z=21) f. Selenium, Se, (Z=34)

29.) Write the condensed electron configuration for each element.

Silicon (Si) Arsenic (As) Zirconium (Zr)

>90% of Earth’s crust are silicon compounds. Clay,

stone + cement are silicates.

Poisonous in large amounts but needed in small amounts

by rats and goats.

Cubic zirconia (ZrO2) can be cut into inexpensive

gemstones.

e– config

Tungsten (W) Lead (Pb) Meitnerium (Mt)

Robust metal with highest melting point of all elements

(3422 ˚C). Used in incandescent light bulbs.

Used in bullets and ammunition as its low melting point (327 ˚C)

makes lead easy to cast.

First created in 1982, named in honor of Lisa Meitner for

her contributions in radioactivity and nuclear

physics.

e– config

8 Q27) See complete solutions for drawings, C=1s22s22p2, Ne=1s22s22p6, S=1s22s22p63s23p4; Q28a) [He] 2s22p1, b) [Ne] 3s23p1, c) [Ar] 4s23d1, d) [Ar] 4s23d104p1, e) [Kr] 5s24d10, f) [Ar] 4s23d104p4; Q29) Si=[Ne] 3s23p2, As=[Ar] 4s23d104p3, Zr=[Kr] 5s24d2, W=[Xe] 6s24f145d4, Pb=[Xe] 6s24f145d106p2, Mt=[Rn] 7s25f146d7.

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30.) Answer the following, assuming ground state electron configurations.

a. How many paired electrons are present in a fluorine atom?

b. How many unpaired electrons are in a selenium (Se) atom?

c. Which element has three unpaired 6p electrons?

d. Which element has 18 core electrons and 2 valence electrons?

ORBITAL ENERGIES9

31.) Multiple choice:

Which is NOT true about a 3s orbital compared to a 2s orbital? (Assume they are in the same atom.)

a. 3s orbital e– are on average further from the nucleus than 2s orbital e–. b. A 3s orbital has fewer nodes than a 2s orbital. c. A 3s orbital is larger than a 2s orbital. d. 3s orbital e– are higher energy than 2s orbital e–.

Which is true about the orbitals in a hydrogen atom?

a. The 4s, 4p, 4d, and 4f orbitals are equal in energy. b. The electronic transition n = 1→3 causes emission of a photon. c. The exact position of the electron can be determined with accurate experiments. d. The difference in energy between the 3s and 4s orbital is the same as the difference in

energy between the 4s and 5s orbital.

The presence of core electrons closer to the nucleus than an outer electron cause the outer electron to be _____________ attracted to the nucleus.

a. More b. Less

32.) Use a discussion of shielding to explain why the 2s electron is lower in energy than the 2p electron in a helium atom.

9 Q30a) 4, b) 2, c) Bi, d) Ca; Q31a) b, Fewer nodes, b) a, 4s, 4p equal in E, c) b, Less; Q32) See complete solutions.

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PERIODIC TRENDS10

33.) Explain why the outer electron in a carbon atom experiences a higher effective nuclear charge (Zeff) than the outer electron in a boron atom.

34.) Explain the following trends:

a. A cesium atom is roughly 1.5 times larger in diameter than a sodium atom.

b. A phosphorus atom is slightly smaller in diameter than a silicon atom.

35.) Write the condensed electron configuration for each ion. Note: these may not be the most common ion formed by each element.

a. Mg+ c. S2–

b. N2– d. Sr2+

36.) Explain why the Cl– ion is larger than the K+ ion. Use electron configurations with your answer.

37.) Rank each set from smallest to largest atomic or ionic radius.

a. Br, Ni, K c. Mg2+, O2–, Ne

b. N, F, Ba d. Ca, Ca2+, Sr

10 Q33) Carbon has an extra proton, so stronger nuclear attraction; Q34a) Cs has more shielding electrons, so more repulsive forces pushing out, b) P has higher Zeff which pulls inward; Q35a) [Ne] 3s1, b) [He] 2s22p5, c) [Ar], or [Ne] 3s23p6, d) [Kr], or [Ar] 4s23d104p6; Q36) K+ has more protons, so higher Zeff; Q37a) Br <Ni <K, b) F < N < Ba, c) Mg2+ < Ne < O2–, d) Ca2+ < Ca < Sr.

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38.) Write the equation (including phases) associated with each ionization process.11

a. First ionization energy (IE1) of Rb

b. Second ionization energy (IE2) of Rb

c. IE1 of Nitrogen

d. IE4 of Sulfur

39.) Explain the following trends:

a. The first ionization energy of Cl is 1255 kJ/mol while the first ionization energy of Si is 780 kJ/mol.

b. All alkali metals (Li, Na, K, Rb, Cs) react with water as shown in the equation below with lithium. Since the reaction involves ionization, a more reactive metal has a lower ionization energy. When reacting water with equal quantities of metal, the reaction with lithium is mild while the reaction with potassium is violent (see picture). Explain why the IE1 of potassium is much lower than the IE1 of lithium.

Li (s) + H2O (l) → LiOH (aq) + H2 (g)

c. There is a dramatic increase in ionization energy between IE3 and IE4 for aluminum.

Aluminum (kJ/mol): IE1 = 580 IE2 = 1815 IE3 = 2740 IE4 = 11,600

11 Q38a) Rb(g)→Rb+(g)+ e–, b) Rb+(g)→Rb2+(g) + e–, c) N(g)→N+(g) + e–, d) S3+(g)→S4+(g) + e–; Q39a) Cl has a higher Zeff, so its outer electron is low in energy and harder to remove, b) K’s outer electron is in the n=4 shell, so high energy and easy to remove, c) Removing fourth electron in Al removes a low energy core electron in the n=2 shell.

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40.) Rank each set from smallest to largest ionization energy.12

a. Rank IE1: Cl, Al, Ar c. Rank IE2: Sr, Be, Li

b. Rank IE1: Be, Li, K d. Rank IE3: Sc, Ca, Ac

41.) The Na+ ion and Ne atom are isoelectronic. Explain why their ionization energies differ.

IE (Na+): 4652 kJ/mol IE (Ne): 2081 kJ/mol

42.) Write the equation (including phases) associated with each process.

a. First electron affinity (EA1) of O

b. First electron affinity (EA1) of Mg

43.) Rank O, F, and Li from least exothermic to most exothermic first electron affinity, and briefly explain.

12 Q40a) Al < Cl < Ar, b) K < Li < Be, c) Sr < Be < Li, d) Ac < Sc < Ca; Q41a) Na+ has more protons so a higher Zeff, thus low energy outer electron and higher IE; Q42a) O (g) + e– → O– (g), b) Mg (g) + e– → Mg– (g); Q43) Li < O < F, follows Zeff.