Chemistry with problem solving worksheet 8 PDF

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JOHNS HOPKINS UNIVERSITY Department of Chemistry Chemistry with Problem Solving- II Worksheet 8 – Quantum Theory and Atomic Structure Some constants: Mass of an electron me = 9.1 x 10-31 kg Planck’s constant k = 6.626 x 10-34 J.s Speed of light c = 3.0 x 108 m/s R = 8.314 J/mol.K = 0.08206 L.atm/mol.K 1 bar = 0.9869 atm

1. Proton therapy is a form of radiation therapy used to shrink tumors by aiming high-energy protons (H+ atoms) at cancerous cells and thereby damaging DNA and promoting cell death. The large relative mass of hydrogen ions in comparison to x-rays results in minimal scattering in the tissue, meaning less damage to healthy tissue surrounding a target tumor. If a proton accelerator produces a beam of protons (mw = 1.008 g/mol) with an average speed of 2.11x107 m/s, what is the wavelength of the protons? 2. By analyzing how the energy of a system is measured, Heisenberg and Bohr discovered that the uncertainty in the energy, ∆E, is related to the time ∆t, required to make the measurement by the relation: ∆E∆t > h/4π. The excited state of an atom responsible for the emission of a photon typically has an average life of 10-10 s. What energy uncertainty corresponds to this value? What is the corresponding uncertainty in the frequency associated with the photon? 3. The uncertainty principle is negligible for macroscopic objects. Electronic devices, however, are being manufactured on a smaller and smaller scale, and the properties of nanoparticles that range from a few to several hundred nanometers may be different from those of larger particles as a result of quantum mechanical phenomena. a. Calculate the minimum uncertainty in the speed of an electron confined in a nanoparticle of diameter 200 nm and compare that uncertainty in speed of an electron confined to a wire of length 1.00mm. b. Calculate the minimum uncertainty in the speed of a Li+ ion confined in a nanoparticle that has a diameter of 200 nm and is composed of a lithium compound through which the lithium ions can move at elevated temperatures (ionic conductor). c. Which could be measured more accurately in a nanoparticle the speed of an electron or the speed of a Li+ ion?

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JOHNS HOPKINS UNIVERSITY Department of Chemistry Chemistry with Problem Solving- II Worksheet 8 – Quantum Theory and Atomic Structure 4. The radiation emitted in the transition from n = 3 to n = 2 in a neutral hydrogen atom has a wavelength of 656.1 nm. What would be the wavelength of radiation emitted from doubly ionized lithium atom if a transition occurred from n = 3 to n = 2? In what region of the spectrum does this radiation lie?

hν =

⎞ Z 2e 4me ⎛ 1 1⎟ ⎜ – 8ε20h2 ⎜⎝nf2 ni2 ⎟⎠

e 4me 8ε 20h3 ν =

= 3.29 ×1015 s –1

⎞ Z 2e 4me ⎛⎜ 1 1⎟ – 8ε02h3 ⎜⎝ nf2 ni2 ⎟⎠

⎛ ⎞ 1 1⎟ ν = (3.29 x 1015 s −1)Z 2 ⎜ 2 – ⎜n ni2 ⎟⎠ ⎝ f

Absorption: ni < n

f

Emission: n > n i

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f

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The Periodic Table of the Elements 1

2

H

He

Hydrogen

Helium

1.00794

4.003

4

5

6

7

8

9

10

Be

B

C

N

O

F

Ne

Oxygen

Fluorine

Neon

Lithium

Beryllium

Boron

Carbon

Nitrogen

6.941

9.012182

10.811

12.0107

14.00674

15.9994 18.9984032 20.1797

11

12

13

14

15

16

17

18

Na

Mg

Al

Si

P

S

Cl

Ar

Sodium

Magnesium

Aluminum

Silicon

Phosphorus

22.989770

24.3050

26.981538

28.0855 30.973761

Sulfur

Chlorine

Argon

32.066

35.4527

39.948

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

Manganese

Cobalt

Nickel

Potassium

Calcium

Scandium

Titanium

Vanadium

Chromium

39.0983

40.078

44.955910

47.867

50.9415

51.9961 54.938049

Iron

Copper

Zinc

Gallium

Germanium

Arsenic

Selenium

Bromine

Krypton

63.546

65.39

69.723

72.61

74.92160

78.96

79.904

37

38

39

40

41

42

43

44

45

83.80

46

47

48

49

50

51

52

53

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

54

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

Rubidium

Strontium

Yttrium

Zirconium

Niobium

Molybdenum

Technetium

85.4678

87.62

88.90585

91.224

92.90638

95.94

(98)

Ruthenium

Rhodium

Palladium

Silver

Cadmium

Indium

Tin

Antimony

Tellurium

Iodine

Xenon

101.07

102.90550

106.42

107.8682

112.411

114.818

118.710

121.760

127.60

126.90447

131.29

55.845

58.933200 58.6934

55

56

57

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

Cs

Ba

La

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

Platinum

Gold

Cesium

Barium

Lanthanum

Hafnium

Tantalum

Tungsten

Rhenium

Osmium

Iridium

132.90545

137.327

138.9055

178.49

180.9479

183.84

186.207

190.23

192.217

87

88

89

104

105

106

107

108

109

Fr

Ra

Ac

Rf

Db

Sg

Bh

Hs

Mt

Francium

Radium

Actinium

Rutherfordium

Dubnium

Seaborgium

Bohrium

Hassium

Meitnerium

(223)

(226)

(227)

(261)

(262)

(263)

(262)

(265)

(266)

195.078 196.96655

Mercury

Thallium

Lead

Bismuth

Polonium

Astatine

Radon

200.59

204.3833

207.2

208.98038

(209)

(210)

(222)

113

114

110

111

112

(269)

(272)

(277)

58

59

60

61

62

63

64

65

66

67

68

69

70

71

Ce

Pr

Nd

Pm

Sm

Eu

Gd

Tb

Dy

Ho

Er

Tm

Yb

Lu

Promethium

Samarium

Europium

Gadolinium

Terbium

Dysprosium

Holmium

Erbium

Thulium

Ytterbium

Lutetium

(145)

150.36

151.964

157.25

158.92534

162.50

164.93032

167.26

168.93421

173.04

174.967

103

Cerium

Praseodymium Neodymium

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140.116 140.90765

144.24

90

91

92

93

94

95

96

97

98

99

100

101

102

Th

Pa

U

Np

Pu

Am

Cm

Bk

Cf

Es

Fm

Md

No

Lr

Thorium

Protactinium

Uranium

Neptunium

Plutonium

Americium

Curium

Berkelium

Californium

Einsteinium

Fermium

Mendelevium

Nobelium

Lawrencium

(237)

(244)

(243)

(247)

(247)

(251)

(252)

(257)

(258)

(259)

(262)

232.0381 231.03588 238.0289 1995 IUPAC masses and Approved Names from http://www.chem.qmw.ac.uk/iupac/AtWt/ masses for 107-111 from C&EN, March 13, 1995, p. 35 112 from http://www.gsi.de/z112e.html

JOHNS HOPKINS UNIVERSITY Department of Chemistry Chemistry with Problem Solving- II Worksheet 8 – Quantum Theory and Atomic Structure

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