HW7 sample problems key PDF

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lecture noes from professor and TA's...

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Key 1. Consider the following waves representing electromagnetic radiation.

Which wave has the longer wavelength?

wave a

Calculate the wavelengths. wave a

0.00040 m

wave b

0.00020 m

Which wave has the higher frequency and larger photon energy?

wave b

Calculate these values. Frequency 1.5e+12 s-1 photon energy 9.9e-22 J

Which wave has the faster velocity? neither What type of electromagnetic radiation is illustrated? infrared 2. An FM radio station broadcasts at 97.2 MHz. Calculate the wavelength of the corresponding radio waves. 3.08 m 3. A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon having a wavelength of 22 nm? 9.0e-18 J What is the energy of a mole of UV photons having a wavelength of 22 nm?

5.4e+06 J

4. Carbon absorbs energy at a wavelength of 150. nm. The total amount of energy emitted by a carbon sample is 1.91 105 J. Calculate the number of carbon atoms present in the sample, assuming that each atom emits one photon. 1.44e+23 atoms

5. The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is 279.7 kJ/mol (that is, it takes 279.7 kJ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal? 427.7 nm 6. Calculate the de Broglie wavelength for each of the following. (a) a proton with a velocity 85% of the speed of light

1.6e-06 nm

(b) a tennis ball (55 g) served at 27 m/s (~62 mi/h)

4.5e-25 nm

7. Neutron diffraction is used in determining the structures of molecules. (a) Calculate the de Broglie wavelength of a neutron moving at 9.00% of the speed of light. 1.47e-14 m (b) Calculate the velocity of a neutron with a wavelength of 90. pm

4400 m/s

8. Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? (a) n = 5

n=1

95 nm ultraviolet

(b) n = 5

n=2

434 nm

(c) n = 4

n=3

1880 nm infrared (1.88 µm or 0.00188 mm)

visible (blue end of visible spectrum)

9. Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by the following. n=2

365 nm

n=4

1460 nm

10. An excited hydrogen atom with an electron in the n = 5 state emits light having a frequency of 6.90 1014 s-1. Determine the principal quantum level for the final state in this electronic transition. n=2 11. Which of the following subshell designations is (are) incorrect? 1p

3f

2d

12. Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, indicate what is wrong in each set. (a) n = 3, = 2, m = 2

allowed - a 3d orbital

(b) n = 4, = 3, m = 4 not allowed if (c) n = 0, = 0, m = 0

not allowed

(d) n = 2, = -1, m = 1 momentum, anyway).

not allowed

=3, m can only be -3, -2, -1, 0, 1, 2, or 3 n can’t = 0 if n = 2,

can only = 0 or 1 (and can never have a negative angular

13. How many orbitals in an atom can have the following designation? 3dz2 1

5p 3

4d 5

n = 5 25

n=4

16

14. How many electrons in an atom can have the following designations? 1p 0 6dx2 - y2 2

5px 2

7py 2

2s 2

5f 14f

15. Give the maximum number of electrons in an atom that can have these quantum numbers. (a) n = 0, = 0, m = 0 0 (b) n = 4

32

(c) n = 1, = 0, m = 0 2 (d) n = 3

18

(e) n = 2, = 2

0

16. The elements Cu, O, La, Y, Ba, Tl, and Bi are all found in high-temperature ceramic superconductors. Write the expected electron configuration for these atoms. Kind of odd question – none of these atoms are is in the zero oxidation state in the superconducting compounds, but clearly they’re expecting that as an answer so I’ll go with it: Cu [Ar]4s1 3d10

in superconducting samples it’s actually a mix of Cu+2 and Cu+3)

O [He] 2s2 2p4

in superconducting samples it’s actually a mix of O-2 and O-1

La [Xe] 6s2 5d1

in superconducting samples it’s actually La+3

[Xe]

Y [Kr] 5s2 4d1

in superconducting samples it’s actually Y+3

[Kr]

Ba [Xe] 6s2

in superconducting samples it’s actually Ba+2

[Xe]

Tl [Xe] 6s2 4f14 5d10 6p1 in superconducting samples it’s actually Tl+3 Bi

[Xe] 6s2 4f14 5d10 6p3

[Ar] 3d8

[He]2s2 2p6

[Xe] 4f14 5d10

in superconducting samples it’s actually Bi+3

[Xe] 4f14 5d10

17. A certain oxygen atom has the electron configuration 1s22s22px22py2. How many unpaired electrons are present?

0 Is this an excited state of oxygen ? Yes

In going from this state to the ground state would energy be released or absorbed?

18. Which of the following electron configurations correspond to an excited state? Identify the atoms and write the ground-state electron configuration where appropriate. (Type your answer using the format [Ar]4s23d104p2. If the configuration is a noble gas, enter the noble gas in brackets, for example [Ne] for F —. If the configuration given corresponds to a ground state electron configuration, enter "ground state" in the electron configuration box.) (a) 1s22s23p1

element B

electron configuration [He] 2s2 2p1

(b) 1s22s22p6

element Ne

electron configuration ground state

(c) 1s22s22p43s1

element F

electron configuration [He] 2s2 2p5

(d) [Ar]4s23d54p1

element Fe

electron configuration

[Ar] 4s2 3d6

How many unpaired electrons are present in each of these species? (a) 1s22s23p1

1

ground-state

(b) 1s22s22p6

0

ground-state

(c) 1s22s22p43s1

3

ground-state [He] 2s2 2p5

(d) [Ar]4s23d54p1 6

ground-state [Ar] 4s2 3d6

19. How many unpaired electrons are present in each of the following in the ground state? O

2

Cl

1

O+

3

Mo

6

W

4

F

1

O-

1

Ar

0

20. Arrange the following groups of atoms in order of increasing size.

(a) Na, Rb, Be

Be < Na < Rb

(b) Ne, Sr, Se

Ne < Se < Sr

(c) P, Fe, O

O < P < Fe

21. Arrange the following groups of atoms in order of increasing first ionization energy. (a) Na, Rb, Be

Rb < Na < Be

(b) Ne, Sr, Se

Sr < Se < Ne

(c) P, Fe, O

Fe < P < O

22. In each of the following sets, which atom or ion has the smallest radius? (a)

C

Si

Ge

(b)

P

As

(c)

P

Cl

Br

Chlorine

(d)

Au Fe

Ga

Gallium

Carbon Phosphorus

23. In each of the following sets, which atom or ion has the smallest ionization energy? (a)

Ca

Sr

Ba

Barium

(b) Sc Co

As

Scandium

(c)

N

F

Oxygen

(d)

Cs Ge

O

Ar

Cesium

24. Rank the elements Be, B, C, N, and O in order of increasing first ionization energy. B < Be < C < O < N Explain your reasoning. The first electron to be removed from Boron is a 2p whereas for Beryllium it is a 2s, hence the dip in I.E. at B. Oxygen is lower than expected due to the electron being ionized sharing an orbital with another electron. The increased electron-electron repulsion lowers this energy enough to reak the trend (the nitrogen electron that is ionized is, in contrast, unpaired) B and O are the exceptions to the general IE trend. The IE of O is lower because of the extra electron-electron repulsions present when two electrons are paired in the same orbital. This makes it slightly easier to remove this first electron from O as compared to N.

B is an exception beause of the decreased penetrating ability of the 2p electron in B as compared to the 2s electrons in Be. (this results in more screening, hence decreased attraction/lower energy – easier to remove) The smaller penetrating ability makes it slightly easier to remove an electron from B as compared to Be. 25. For each of the given pairs of elements, pick the atom with the following characteristics. K (larger – less electron electron repulsion)

(a) more favorable (exothermic) electron affinity

K

Mg

(b) higher ionization energy

K

Mg Mg (smaller)

(c) larger size

K

Mg

(a) more favorable (exothermic) electron affinity

Cl

F

Cl (larger – less electron electron repulsion)

(b) higher ionization energy

Cl

F

F (smaller)

(c) larger size

Cl

F

Cl (greater principle quantum number)

K (greater principle quantum number)

26. Order the atoms in each of the following sets from the least exothermic FIRST electron affinity to the most. (a) N, O, F

N < O < F

(b) Al, Si, P

Al < P < Si

27. Use data from the text, to determine the following values. (a) the ionization energy of F —

+328 kJ/mol (the negative of the Electron Affinity)

(b) the ionization energy of Br —

+325 kJ/mol

(c) the electron affinity of Br (d) the electron affinity of F

-325 kJ/mol -328 kJ/mol

28. Give the name and formula of each of the binary compounds formed from the following elements. (a) Li and S

formula Li2S name lithium sulfide Na2S name sodium sulfide

(b) Na and S

formula

(c) Rb and H

formula RbH

name rubidium hydride

29. A certain microwave oven delivers 750. watts (joule/s) of power to a coffee cup containing 50.5 g of water at 25.0°C. If the wavelength of microwaves in the oven is 9.75 cm, how long does it take, and how many photons must be absorbed, to make the water boil? The specific heat capacity of water is 4.18 J/°C · g and assume only the water absorbs the energy of the microwaves.

21.1 s 7.77e+27 photons 30. Consider the following approximate visible light spectrum.

Barium emits light in the visible region of the spectrum. If each photon of light emitted from barium has an energy of 3.90 10-19 J, what color of visible light is emitted? yellow

red

green

orange

blue

violet

31. Although no currently known elements contain electrons in g orbitals in the ground state, it is possible that these elements will be found or that electrons in excited states of known elements could be in g orbitals. For g orbitals, the value of is 4. What is the lowest value of n for which g orbitals could exist? 5 What are the possible values of m ? -4 -3 -2 -1 0 1 2 3 4 (if n=5, max l=4) How many electrons could a set of g orbitals hold? 18 32. Complete and balance the equations for the following reactions. (a) Cs(s) + H2O(l) Cs(s) +1 H2O(l)

1 CsOH aq) + ½ H2(g)

( or 2 2 2 1)

(b) Na(s) + Cl2(g) 1 Na(s) + 1/2 Cl2(g)

1 NaCl (s)

( or 2 1

2)

33. The successive ionization energies for an unknown element are given below. I1 = 717 kJ/mol I2 = 1891 kJ/mol I3 = 16437 kJ/mol I4 = 17948 kJ/mol To which family in the periodic table does the unknown element most likely belong? alkaline earth metals 34. An unknown element is a nonmetal and has a valence electron configuration of ns2np3. (a) How many valence electrons does this element have? 5

(b) What are some possible identities for this element? (Enter your answer in order of increasing atomic mass separated by a comma. Type your answer using the format B for boron.) N, P, As (yes, As, is a metalloid, but it is above the metalloid line, so I included it) (c) What is the formula of the compound this element would form with potassium? K3A (d) Would this element have a larger or smaller radius than barium?

Smaller

(e) Would this element have a greater or smaller ionization energy than fluorine?

smaller

35. Using data from this chapter***, calculate the change in energy expected for each of the following processes. *** if your answer is slightly different, I used values from a different textbook (e.g. 197 vs 196 is o.k.) (a) Li(g) + Br(g) (b) Si(g) + F(g) (c) Si+(g) + F(g) (d) Si(g) + 2 F(g)

Li+(g ) + Br -(g) 196 kJ Si+(g) + F -(g) Si2+(g) + F -(g) Si2+(g) + 2 F -(g)

452 kJ 1250 kJ 1700 kJ

36. Answer the following questions assuming that ms could have three values rather than two and the rules for n, and m are the normal ones. (a) How many electrons would an orbital be able to hold? 3 (b) How many elements would the first period in the periodic table contain? 3 How many elements would the second period in the periodic table contain? 12 (c) How many elements would be contained in the first transition metal series? 15 (d) How many electrons would the set of 4f orbitals be able to hold?

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