Atomic 1 0 4 X 4

Northrup's Chem 111 SectionTTU General Chemistry

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Chem 1110 - Chapter 7: Quantum Theory of the Atom
Practice Quiz 1

Atomic mass unit (amu): 1.661 x 10-24g Atomic weight: Average mass of all isotopes of a given element; listed on the periodic table Example: Hydrogen atomic weight = 1.008 amu Carbon atomic weight = 12.001 amu Carbon atoms are 12 times as massive as hydrogen atoms Practice: Ca atomic mass = 40.08 amu Ne atomic mass = 20.18 amu. Let your back not slip Let it slide right down on your hip.

Physical constants: h=6.626 x 10^-34 Joule-sec; c=3.00 x 10⁸ m/s; mass of electron = 9.1 x 10^-31 kg

1. What is the frequency of light having a wavelength of 440 nm (the light used in the colorimetry lab experiment)?

a) 1.32 x 10² s^-1
b) 6.82 x 10⁵ s^-1
c) 6.82 x 10^-4 s^-1
d) 6.82 x 10¹⁴ s^-1

2. What is the energy in Joules of a photon of light having a frequency of a typical radio wave? (frequency = 1 x 10⁹ Hz or 1 gigahertz)

a) 6.6 x 10^-25J
b) 6.6 x 10^-43J
c) 1.5 x 10⁴²J
d) 1.5 x 10^-34J

3. Which of the following provisions of the Bohr atomic model of hydrogen turned out to be false?

a) The line spectrum of hydrogen is produced when photons are emitted having energies which are differences between quantum energy levels.
b) The energy of the electron is quantized.
c) An electron moves in a circular orbit around the nucleus.
d) The energy of the electron is inversely proportional to the square of the quantum number n.

4. The characteristic wavelength of a 1 kilogram object moving at 1 meter/second will be:

a) about the size of the object itself.
b) about the same as the that of the electron in an atom.
c) large compared to the atomic scale.
d) immeasurably small compared to any dimensions we care about.

5. What is the wavelength in meters of microwave radiation, having a typical frequency of 3 x 10⁹ Hz?

a) 9 x 10^-17 m
b) 9 x 10¹⁷ m
c) 10 m
d) 0.1 m

6. What is the energy in Joules of a mole of photons of microwave light having a frequency typical of microwave? (frequency = 3.0 x 10⁹ Hz). (A Joule is enough energy to raise the temperature of 1 gram of water about a quarter of a degree Celsius.)

a) 1.2 x 10²³ J
b) 1.98 x 10^-24 J
c) 1.2 J
d) 1.98 x 10^-34 J

7. Rank the following types of radiation from highest energy to lowest:

ultraviolet / visible / xray / microwave / infrared

4. The characteristic wavelength of a 1 kilogram object moving at 1 meter/second will be:

a) about the size of the object itself.
b) about the same as the that of the electron in an atom.
c) large compared to the atomic scale.
d) immeasurably small compared to any dimensions we care about.

5. What is the wavelength in meters of microwave radiation, having a typical frequency of 3 x 10⁹ Hz?

a) 9 x 10^-17 m
b) 9 x 10¹⁷ m
c) 10 m
d) 0.1 m

6. What is the energy in Joules of a mole of photons of microwave light having a frequency typical of microwave? (frequency = 3.0 x 10⁹ Hz). (A Joule is enough energy to raise the temperature of 1 gram of water about a quarter of a degree Celsius.)

a) 1.2 x 10²³ J
b) 1.98 x 10^-24 J
c) 1.2 J
d) 1.98 x 10^-34 J

7. Rank the following types of radiation from highest energy to lowest:

ultraviolet / visible / xray / microwave / infrared

a) xray, ultraviolet, microwave, infrared, visible
b) ultraviolet, xray, visible, infrared, microwave
c) infrared, microwave, ultraviolet, visible, xray
d) xray, ultraviolet, infrared, visible, microwave
e) xray, ultraviolet, visible, infrared, microwave

8. An excited Hydrogen atom in the n=3 energy level decays to the n=2 energy level and emits a photon of light. If the energies of these two levels are separated by 3.029 x 10^-19 J, what will be the wavelength of the light emitted in nanometers?

a) 656 nm
b) 484 nm
c) 1073 nm
d) 1.07 x 10^-19 nm
e) 3.3 x 10^-10 nm

9. According to the deBroglie equation, the characteristic wavelength of an electron moving around an atomic nucleus will be:

a) about the size of the nucleus.
b) about the same size as the atom.
c) large compared to the atomic scale.
d) immeasurably small compared to any dimensions we care about.

10. Fill in the blank: The l quantum number tells which sublevel the electron is in and most directly specifies the _______ of the atomic orbital.

a) orientation
b) size
c) energy
d) shape

11. A police officer is measuring traffic speed with radar operating at 1.0 x 10⁹ Hz. What is the wavelength of this electromagnetic energy?

a) 0.30 nm
b) 3.30 m
c) 0.30 m
d) 3 x 10¹⁷ m
e) 0.30 Å

12. What is the wavelength in Ångstroms of radiation that has a frequency of 4.00 x 10¹⁴ s^-1?

a) 4.06 x 10² Å
b) 6.28 x 10^-1 Å
c) 7.50 x 10³ Å
d) 1.33 x 10² Å
e) 7.96 x 10^-20 Å

13. When sodium compounds are heated in a bunsen burner flame, they emit light at a wavelength of 5890 Å. If 1.0 x 10^-4 mole of sodium atoms each emit a photon of this wavelength, how many kilojoules of energy are emitted?

a) 1.21 kJ
b) 2.03 x 10^-2 kJ
c) 2.03 x 10^-3 kJ
d) 8.08 x 10^-3 kJ
e) 6.20 x 10^-2 kJ

14. An alpha particle of mass 4.0026 amu has a velocity of 10.0% of the speed of light. What is its de Broglie wavelength (in m)?

a) 3.50 x 10^-21 m
b) 3.30 x 10^-18 m
c) 3.70 x 10^-16 m
d) 3.32 x 10^-15 m
e) 1.22 x 10^-15 m

KEY

1)d 2)a 3)c 4)d 5)d 6)c 7)e 8)a 9)b 10)d 11)c 12)c 13)b 14)d To send electronic mail to Dr. Northrup >snorthrup@tntech.edu, or call 931-372-3421, or come to Foster Hall 407

Resolution in terms of electron density is a measure of the resolvability in the electron density map of a molecule. In X-ray crystallography, resolution is the highest resolvable peak in the diffraction pattern, while resolution in cryo-electron microscopy is a frequency space comparison of two halves of the data, which strives to correlate with the X-ray definition.^[1]

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Qualitative measures[edit]

In structural biology, resolution can be broken down into 4 groups: (1) sub-atomic, individual elements^{[clarification needed]} are distinguishable and quantum effects can be studied, (2) atomic, individual atoms are visible and an accurate three-dimensional model can be constructed, (3) helical, secondary structure, such as alpha helices and beta sheets; RNA helices (in ribosomes), (4) domain, no secondary structure is resolvable.^{[clarification needed]}

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X-ray crystallography[edit]

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As the crystal's repeating unit, its unit cell, becomes larger and more complex, the atomic-level picture provided by X-ray crystallography becomes less well-resolved (more 'fuzzy') for a given number of observed reflections. Two limiting cases of X-ray crystallography are often discerned, 'small-molecule' and 'macromolecular' crystallography. Small-molecule crystallography typically involves crystals with fewer than 100 atoms in their asymmetric unit; such crystal structures are usually so well resolved that its atoms can be discerned as isolated 'blobs' of electron density. By contrast, macromolecular crystallography often involves tens of thousands of atoms in the unit cell. Such crystal structures are generally less well-resolved (more 'smeared out'); the atoms and chemical bonds appear as tubes of electron density, rather than as isolated atoms. In general, small molecules are also easier to crystallize than macromolecules; however, X-ray crystallography has proven possible even for viruses with hundreds of thousands of atoms.^[2]

A rough guide to the resolution of protein structures^[3][4]

Resolution (Å)	Meaning
>4.0	Individual atomic coordinates meaningless. Secondary structure elements can be determined.
3.0 - 4.0	Fold possibly correct, but errors are very likely. Many sidechains placed with wrong rotamer.
2.5 - 3.0	Fold likely correct except that some surface loops might be mismodelled. Several long, thin sidechains (lys, glu, gln, etc.) and small sidechains (ser, val, thr, etc.) likely to have wrong rotamers.
2.0 - 2.5	As 2.5 - 3.0, but number of sidechains in wrong rotamer is considerably less. Many small errors can normally be detected. Fold normally correct and number of errors in surface loops is small. Water molecules and small ligands become visible.
1.5 - 2.0	Few residues have wrong rotamer. Many small errors can normally be detected. Folds are rarely incorrect, even in surface loops.
0.5 - 1.5	In general, structures have almost no errors at this resolution. Individual atoms in a structure can be resolved. Rotamer libraries and geometry studies are made from these structures.

Cryo-electron microscopy[edit]

In cryo-electron microscopy, resolution is typically measured by the Fourier shell correlation (FSC),^[5] a three-dimensional extension of the Fourier ring correlation (FRC),^[6] which is also known as the spatial frequency correlation function.^[7] The FSC is a comparison of two different Fourier transforms over different shells on frequency space. To measure the FSC, the data needs to be separated into two groups. Typically, the even particles form the first group and odd particles the second based on their order. This is commonly referred to as the even-odd test. Most publications quote the FSC 0.5 cutoff, which refers to when the correlation coefficient of the Fourier shells is equal to 0.5.^[1][8]

Determining the resolution threshold remains a controversial topic and many other criteria using the FSC curve exist, including 3-σ criterion, 5-σ criterion, and the 0.143 cutoff. However, fixed-value thresholds (like 0.5, or 0.143) were argued to be based on incorrect statistical assumptions.^[9] The new half-bit criterion indicates at which resolution one has collected enough information to reliably interpret the 3-dimensional volume, and the (modified) 3-sigma criterion indicates where the FSC systematically emerges above the expected random correlations of the background noise.^[9]

In 2007, a resolution criterion independent of the FSC, Fourier Neighbor Correlation (FNC), was developed using the correlation between neighboring Fourier voxels to distinguish signal from noise. The FNC can be used to predict a less-biased FSC.^[10] See also a 2011 review on Cyro-EM resolution measurements.^[11]

Notes[edit]

1. ^ ^abFrank, 2006, p250-251
2. ^Hopper, P.; Harrison, S.C.; Sauer, R.T. (1984). 'Structure of tomato bushy stunt virus. V. Coat protein sequence determination and its structural implications'. Journal of Molecular Biology. Elsevier Ltd. 177 (4): 701–713. doi:10.1016/0022-2836(84)90045-7. PMID6481803.
3. ^Huang, Yu-Feng (2007). Study of Mining Protein Structural Properties and its Application(pdf) (Ph.D.). National Taiwan University. Retrieved Nov 4, 2014.
4. ^Blow, David (June 20, 2002). Outline of Crystallography for Biologists. New York: Oxford University Press. p. 196. ISBN978-0198510512. Retrieved Nov 4, 2014.
5. ^Harauz & van Heel, 1986
6. ^van Heel, 1982
7. ^Saxton & Baumeister, 1982
8. ^Böttcher et al., 1997
9. ^ ^abvan Heel & Schatz, 2005
10. ^Sousa & Grigoreiff, 2007
11. ^Liao, HY; Frank, J (14 July 2010). 'Definition and estimation of resolution in single-particle reconstructions'. Structure (London, England : 1993). 18 (7): 768–75. doi:10.1016/j.str.2010.05.008. PMC2923553. PMID20637413.

References[edit]

• Harauz, G.; M. van Heel (1986). 'Exact filters for general geometry three dimensional reconstruction'. Optik. 73: 146–156.
• van Heel, M.; Keegstra, W.; Schutter, W.; van Bruggen E.F.J. (1982). Arthropod hemocyanin studies by image analysis, in: Structure and Function of Invertebrate Respiratory Proteins, EMBO Workshop 1982, E.J. Wood. Life Chemistry Reports. Suppl. 1. pp. 69–73. ISBN9783718601554.
• Saxton, W.O.; W. Baumeister (1982). 'The correlation averaging of a regularly arranged bacterial cell envelope protein'. Journal of Microscopy. 127: 127–138. doi:10.1111/j.1365-2818.1982.tb00405.x.
• Böttcher, B.; Wynne, S.A.; Crowther, R.A. (1997). 'Determination of the fold of the core protein of hepatitis B virus by electron microscopy'. Nature. 386 (6620): 88–91. Bibcode:1997Natur.386...88B. doi:10.1038/386088a0. PMID9052786.
• van Heel, M.; Schatz, M. (2005). 'Fourier shell correlation threshold criteria'. Journal of Structural Biology. 151 (3): 250–262. doi:10.1016/j.jsb.2005.05.009. PMID16125414.
• Frank, Joachim (2006). Three-Dimnsional Electron Microscopy of Macromolecular Assemblies. New York: Oxford University Press. ISBN0-19-518218-9.
• Sousa, Duncan; Nikolaus Grigorieff (2007). 'Ab initio resolution measurement for single particle structures'. J Struct Biol. 157 (1): 201–210. doi:10.1016/j.jsb.2006.08.003. PMID17029845.

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External links[edit]

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• EMstats Trends and distributions of maps in EM Data Bank (EMDB), e.g. resolution trends