Chapter 4 The Quantum Atom

 

The regions of the electromagnetic spectrum

Region

Approx wave

length, m

 

Comments

 

Type of transition in atoms and uses

 

 

1000

AM band 190—560 m short-wave band 14- 75 m FM band 2.8—3.4 m

 

 

radio waves

 

television bands 5.6-4.2 m (chs. 2, 3, 4) 4.0-3.4 m (chs. 5, 6) 1.7-1.4 m (chs. 7-13)

Transitions involving nuclei. Used for signal transmission

 

 

1

includes radar; used to probe rotational motion of molecules and in microwave ovens

 

 

microwave

 

 

Transitions involving electron spins. Used for cooking

 

10-4

 

 

 

infrared light

 

can be felt as heat; used to probe vibrational motions of molecules

Transitions associated with vibrations and rotations of molecules, stretching of atoms connected by chemical bonds. Used for cooking

 

7 x 10-7

 

 

 

visible light

 

consists of the colors red, orange, yellow, green, blue, indigo, and violet

Transitions associated with valence electrons in atoms and molecules. Used for illumination

 

4 x 10-7

 

 

ultraviolet light

10-8

 

causes sunburn

Transitions associated with valence electrons in atoms and molecules. Used as a germicide

 

X-rays

 

penetrate human tissue and other matter

Transitions associated with electrons making huge shifts in orbitals of larger atoms

Used for medical pictures

 

10-11

 

 

gamma rays

 

emitted by energetic nuclei; very penetrating radiation;

Transitions resulting from the decay of nuclei

Used to kill cancer cells

cosmic rays

10-14

very high-energy, penetrating radiation of cosmic origin

 

 

4.1  Electromagnetic Radiation

4.2 Continuous And Bright-Line Spectra

1.   What is the reason why atoms emit radiation?

2.   Comment on the relative size of the visible spectrum compared to the total electromagnetic spectrum.

3.   Concerning prisms,

a)   Explain what Isaac Newton did with a prism.

b)   What did he learn from the experiment?

4.   Concerning continuous spectra,

a)   What does a continuous spectrum look like?

b)   Why is sunlight capable of producing a continuous spectrum?

5.   Concerning elements

a)   What type of spectrum is created when individual elements are energized?

b)   How does the spectrum of each element compare?

6.   The scientists in each of the following areas use spectroscopy.  Discuss what they would use the spectroscopic information for in each case:

      a) Astronomy         b) Medical                    c) Detective work

7.   When copper salts are heated in a flame, green light is emitted. How would you experimentally determine whether the light is of one wavelength or a mixture of two or more wavelengths?

4.3  The Quantum Theory

4.4 Electromagnetic Radiation In One Respect Acts Like A Particle

4.5 Electromagnetic Radiation Has A Wave Nature, Too

8.   a) What is the Quantum Theory?

      b) Which of the following is quantized? (i) notes on a piano, (ii) sounds from a violin, iii) walking up the rungs of a ladder.

9.   Very specifically account for the production of bright-line spectra by elements in terms of the quantum theory. (In other words, why do elements produce unique bright-line spectra?)

10. Concerning the Photoelectric Effect,

a)   What attributes of photons is verified by the Photoelectric Effect experiment?

b)   What phenomena is noted in this procedure that revealed this attribute?

c)   What other nature do photons exhibit?

11. What relationship exists between wavelength and frequency in terms of size?

12. How do radio waves compare to ultraviolet rays in

      a) wavelength?        b) frequency?

13. A red light has a frequency of 4.6 x 1014 sec-1. Calculate its wavelength in

      a) meters                b) Angstroms.

4.6  Electromagnetic Radiation Has Distinct Energy Values

14. The blue light of the sky is due to the scattering of sunlight by air molecules. Blue light has a frequency of about 7.5 x 1014 s-1.

a.   Calculate the wavelength associated with this radiation.

b.   Calculate the energy in joules of a single photon of this frequency.

15. Our eyes are sensitive to light in the approximate frequency range of 4.0 x 1014 s-1 to 7.5 x 1014 s-1.

a.   Calculate the wavelengths in nanometers that correspond to these two frequencies. 1 nm = 10-9 m

b.   Find the frequency of a photon of wavelength equal to 2100 A°.

16. UV radiation is capable of destroying a variety of bacteria by rupturing chemical bonds in certain critical molecules of the bacteria. The wavelength of such a germicidal light is about 100 nm. Calculate the energy of the critical chemical bonds that are broken upon UV radiation of these bacteria.

17. X-rays are known to causes cancer by rupturing bonds in DNA molecules in human cells. Given that the average chemical bond energy in DNA molecules is about 300,000 J/mole, estimate the number of chemical bonds that can be ruptured by a 1-nm X-ray photon.

18. A photographic plate produces an image when the incoming light hits an AgBr unit and dissociates it. It takes 1 x 10-19 J to do this to such a unit. Calculate the frequency and wavelength of such a photon to produce the photographic image.

19. Calculate the energy for the following electromagnetic radiation

a.   violet light    n = 7.3 x 1014 s-1

b.   red light         l = 6.5 x 10-7 m

c.   blue light       l = 4340 A

20. Some experimental lights use salts of lithium because excited lithium atoms emit a photon that is in the red (l = 7.0 x 103 A°) region of the spectrum. Calculate the energy emitted from an excited state lithium atom as it returns to its ground state.

21. Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles the following reaction occurs:

AgCl     Ag + Cl

      The silver metal that is formed causes the lenses to darken. The energy change for this reaction is 3.10 x 102 kJ/mol. Assuming all this energy must be supplied by light what is the maximum wavelength of light that can cause this reaction?

22. Spectral analysis shows that the familiar yellow light of sodium lamps is made up of photons of two wavelengths, 589.0 nm and 589.6 nm. What is the difference in energy between photons possessing these wavelengths?

23. The functioning part of a photoelectric cell (an electric eye) used on elevator door closure mechanisms is coated on one side with cesium metal or a compound of cesium. A voltage is applied across the cell and when light strikes the cesium, an electron is removed, thus completing the circuit. In order to remove an electron from a cesium atom, 3.89 electron volts (eV) are required. There is 1.6 x 10-19 Joule per electron volt. Calculate the wavelength of light that would be necessary to remove the electron from a neutral cesium atom and activate the photoelectric cell. Would photons of visible light have enough energy?

24. If the energy needed to remove  (or ionize) an electron from one of the energy levels of sodium is 8.2 x 10-19 J per electron, calculate the energy required to ionize a mole of atoms.     

25. Sunlight reaches the earth’s surface at Madison, Wisconsin, with an average power of about 1.0 kJ/s/m2. If the sunlight consists of photons with an average wavelength of 510 nm, how many photons strike a 1-cm2 area per second?

26. In the process of photosynthesis in green plants it has been calculated that 8 photons of wavelength 6850 A° are theoretically needed to produce 1 molecule of O2. However, the experimentally-determined energy stored in plants associated with the production of one mole of O2 is 4.686 x 105 J. Calculate the energy conversion efficiency by plants through photosynthesis (i.e. the actual energy/theoretical energy).

27. An electron is excited from the n = 1 ground state to the n = 3 state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true.

a.   It takes more energy to ionize the electron from n = 3 than from the ground state.          

b.   The electron is further from the nucleus on average in the n = 3 state than in the n = 1 state.

c.   The wavelength of light emitted if the electron drops from n = 3 to n = 2 will be shorter than the wavelength of light emitted if the electron falls to n = 1 from n = 3

d.   The wavelength of light emitted when the electron returns to the ground state from n = 3 will be the same as the wavelength of light absorbed to go from n  = 1 to n = 3.

e.   For n = 3 the electron is in the first excited state.

28. Note the following energy-level diagram for an electron in the hydrogen atom:

 

      Suppose energy is directed at a hydrogen atom in the ground state such that it is absorbed and promoted to the six energy level (n = 6). It then cascades down to the second energy level and gives off a photon, and then to the ground state and gives off another photon.

a.   Calculate the energy absorbed.

b.   Calculate the energy of both emitted photons.

c.   Calculate the wavelength of both photons.

d.   A photon from which energy state to the ground state has a wavelength of 91.18 nm?

29. Calculate all the wavelengths emitted by hydrogen atoms excited to the fifth (n = 5) energy level.

30. X-rays are produced when the electron stream in an x-ray tube knocks an electron out of a low-lying shell of an atom in the target, and the electron in a higher shell falls all the way into the vacant lower shell. The x-ray is the photon of energy equivalent to the energy transition made by the electron. The most intense x-rays produced by an x-ray tube with a copper target have wavelengths of 1.542 A° and 1.392 A°. Calculate the energy associated with these x-rays.

31. A compact disc player uses light with a frequency of 3.85 x 1014 s-1.

a.   What is this light’s wavelength?

b.   In what portion of the electromagnetic spectrum does this wavelength fall?

c.   What is the energy of 1.00 mole of photons at this frequency?

32. The light reaching us from distant stars is extremely dim. Consequently, astronomers must use instruments capable of detecting a small number of photons. An infrared photon detector registers a signal at 1250 nanometer (nm) from Alpha Centauri with a total energy of 1.20 x 10-16 J. How many photons were detected?

33. The human eye can detect as little as 2.35 x 10-18 J of green light of wavelength 510 nm. Calculate the minimum number of photons that can be detected by the human eye.

34. Light energy of 6.00 x 10-19 J is absorbed by a metal in a photoelectric effect experiment, and the kinetic energy of the ejected electron is 2.00 x 10-19 J. Calculate the (a) frequency of the light and the (b) ionization [binding] energy in joules per electron.

35. Ruby lasers use crystals of Al2O3 that contain small amounts of Cr3+ ions. When visible light shines on the crystals, the Cr3+ ions strongly absorb light between 400 and 500 nm. Excited Cr3+ ions lose a portion of their energy as heat. They then emit red light of wavelength 694.3 nm as they return to their ground state.

a.   Calculate the energy of the 500 nm radiation used to excite one mole of Cr3+ ions.

b.   Calculate the energy of the emitted light per mole.

c.   Calculate the fraction of the excitation energy emitted as red photons and the fraction lost as heat.

d.   Draw an electronic energy level diagram that summarizes these processes.

36. Gaseous helium atoms absorb x-rays of wavelength 53.7 nm. After absorbing an x-ray of this wavelength, a helium atom may emit light of wavelength 501.6 nm.

a.   What is the net energy change for a helium atom that has gone through this absorption-emission sequence?

b.   Draw an energy level diagram that shows the sequence.

37. Volcanic eruptions change the earth's energy balance by adding large amounts of smoke particles to the troposphere and stratosphere. Spectacular red sunsets demonstrate that these particles deflect shorter-wavelength light from going to the earth's surface.

a.   What effect does this have on the earth’s average temperature?

b.   Draw a graph of intensity of light versus wavelength to support your answer.

38. The temperature drops more on clear nights than on cloudy nights. What feature of clouds accounts for this?

39. Give three examples of things that are “quantized” in the macroscopic world.

40.       It takes 216.4 kJ/mole to remove electrons from a potassium surface. If UV light at 250 nm strikes such a surface, what is the velocity of an ejected electron. (KE = ½ mv2 and mass of an electron = 9.1 x 10-31 kg)

41. In a typical photoelectric effect experiment, light of energy 5.00 x 10-19 J is absorbed by a metal, and the ejected electrons have a maximum kinetic energy of 2.70 x 10-19 J.

a.   What is the ionization [binding] energy of electrons in the metal?

b.   What is the wavelength of the light?

42. The photoelectric effect for magnesium has a threshold frequency of 8.95 x 1014 s-1. Can this metal be used in photoelectric devices that sense visible light?

43. In the figure the light bulb glows only when light is directed at the cesium surface but not when light is directed at the Cu surface. Explain.

44. Cancerous tumors selectively absorb a dye after it has been injected into a person. The dye selectively absorbs highly tuned laser photons.

a)   The laser photon has l = 1.06 x 104 nm. Calculate the energy of this photon.

b)   Why would a doctor have the laser aimed at a section of the body holding a tumor?

 

Answer to numerical questions

13a) 6.5 x 10-7 m          13b) 6.5 x 103        14a) 4 x 10-7 m             14b) 5.0 x 10-19 J        

15a) 7.5 x 102 nm, 4.0 x 102 nm                       15b) 1.4 x 1015 s-1                    16) 2.0 x 10-18 J

17) 400 bonds              18) 2.0 x 10-6 m           19a) 4.8 x 10-19 J          19b) 3.1 x 10-19 J/photon

19c) 4.58 x 10-19 J/photon                                20) 2.8 x 10-19 J/photon            21) 3.86 x 10-11 m

22) 3.47 x 10-22 J         23) 3.2 x 10-7m            24) 4.9 x 105 J/mol e-                                      

25) 2.6 x 1025 photons/s                                   26) 33.5%                                          28a) 2.1185 x 10-18 J   

28b) 4.8427 x 10-19J, 1.6342 x 10-18 J, 1.6342 x 10-18 J           28c) 4.10 x 10-7 m, 1.22 x 10-7 m        

28d) 2.1801 x 10-18 J               29) 4.05 x 10-6 m. 1.28 x 10-6 m, 4.34 x 10-7 m, 9.50 x 10-8 m 

30) 1.29 x 10-15 J, 1.43 x 10-15 J                       31a) 7.8 x 10-7 m                      31c) 1.54 x 105 J/n

32) 750 photons           33) 6 photons               34a) 9.06 x 1014 s-1                  34b) 4.00 x 10-19 J

35a) 2.4 x 105 J/n photon                                 35b) 1.72 x 105 J/n photon       35c) 72%        

36a) 3.3 x 10-18 J          40) 9.8 x 105 m/s          41a) 2.3 x 10-19 J                      41b) 4.0 x 10-7 m

42) 3.35 x 10-7 m         44a) 1.88 x 10-20 J

 

Albert Einstein (1879‑1955) was born in Germany. Nothing in his early development suggested genius; even at the age of 9 he did not speak clearly, and his parents feared that he might be handicapped. When asked what profession Einstein should follow, his school principal replied, “It doesn't matter; he'll never make a success of anything.” When he was 10, Einstein entered the Luitpold Gymnasium (high school), which was typical of German schools of that time in being harshly disciplinarian. There he developed a deep suspicion of authority and a skepticism that encouraged him to question and doubt—valuable qualities in a scientist.

                In 1905, while a patent clerk in Switzerland, Einstein published a paper explaining the photoelectric effect via the quantum theory. For this revolutionary thinking he received a Nobel Prize in 1921. Highly regarded by this time, he worked in Germany until 1933, when Hitler's persecution of the Jews forced him to come to the United States. He worked at the Institute for Advanced Studies at Princeton University until his death in 1955. He requested a salary of $3,000 because of his low interest in money — Princeton countered with an offer of $15,000. He once used a paycheck for a bookmark, then lost the book.

                Einstein was undoubtedly the greatest physicist of our age being more of a theoretician than an experimenter. Even if someone else had derived the theory of relativity, his other work would have ensured his ranking as the second greatest physicist of his time. Our concepts of space, time, mass, and motion were radically changed by ideas he first proposed when he was 26 years old. From then until the end of his life, he attempted unsuccessfully to find a single unifying theory that would explain all physical events.

In addition to science, Einstein enjoyed playing the violin and was intensely interested in world peace. His famous 1939 letter to President Franklin Roosevelt warned of the possible preparation of nuclear weapons by Nazi Germany. This letter was instrumental in initiating the project which led to the development of nuclear weapons in the United States

           

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Chapter 5 The Nucleus

 

5.1  Nuclear Forces

5.2  Binding Energy

5.3  Matter-Energy Interconversion

5.4  Comparison of Chemical Reactions and Nuclear Reactions

1.     What are pions and how do they contribute to the stability of a nucleus?

2.     What type of processes is the mass-energy inter conversion significant?

3.     What information about isotopes is revealed by comparing their binding energies?

4.     From the binding energy curve list 3 unstable isotopes.

5.     The Be atom (mass 7.0169 amu) decays to a Li atom (Mass 7.0160 amu) by electron capture. How much energy is produced per atom by this reaction? (There are 1.66 x 10-27 kg per 1 amu. The speed of light is 3.00 x 108 m/s)

6.     The mass of a deuterium (H) is 2.01355 amu; that of an a-particle, 4.00150 amu. How much energy per mole of He produced is released by the reaction

H  +  H  ———>  He

        (There are 1.66 x 10-27 kg per 1 amu. The speed of light is 3.00 x 108 m/s)

7.     For the chemical reaction involving the combustion of gasoline, 6.0 x 106 Joules/mole of energy are evolved.

a.     Calculate the mass of matter per mole lost to the environment as heat.

b.     The transmutation of radium

Ra  ———>  He  +  Rn

        causes the liberation of 4.7 x 1011 Joules/mole. Calculate the mass of matter per mole lost to the environment as heat.

c.          How many times greater is the loss of mass for the nuclear transmutation compared to the chemical combustion reaction?      

d.          Hydrogen is a fuel that releases a large amount of chemical energy or 242 kJ/mol of hydrogen. Calculate the change in mass that occurs when 1.00 kg of H2  burns.

8.     How is the energy, generated in a nuclear reactor, used to make electricity?

9.     What creates a greater explosion: a ton of fissionable U-235 or a ton of T.N.T.?

5.5  Basic Factors That Determine The Stability Of Nuclei

10.   Indicate whether each of the following nuclides lie within the belt of stability. If they do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability.

a. In             b. Ag           c. N              d. Rn

5.6 Nuclear Equations

11.   Identify the particle resulting from these natural decay processes:

        a. U  ———>  ?  +  He                                b. Bi  ———> ?  +  e

        c. Np  ———>  ?  +  e                               d. Ra  ———>  Rn  +  ?

        e. U  ———>  Np  +  ?                             f. Pa  ———>  U  +  ?

 12.  Write balanced nuclear equations for the following transformations:

a.     Hf-181 undergoes beta decay;

b.     radium-226 decays to a radon isotope;

c.     lead-205 undergoes positron emission;

d.     tungsten-179 undergoes orbital electron capture.

13.   Write balanced nuclear equations for the following transformations of historical significance:

a.     Decay of naturally occurring polonium-212, the first radioactive element discovered (in 1898) by Polish scientist Marie Currie and her husband Pierre to a lead isotope.

b.     Technetium-98, an artificial radioactive element prepared in 1937, decaying to ruthenium-98.

c.     Uranium-235 undergoing fission in the first nuclear reactor (1942) after being hit by a neutron to produce bromine-87, lanthanum-146, and three neutrons.

d.     The fusion reaction during the detonation of a hydrogen bomb by fusing hydrogen-3 with hydrogen-2 to produce helium-4 and a neutron.

e.     The first element prepared by artificial means (1919) by bombarding nitrogen-14 atoms with alpha particles to produce hydrogen-1 and the artificial isotope.

5.7 The Uranium Disintegration Series

5.8 Half Life

14.   Why must samples of uranium-238 contain lead-206 also?

15.     How many of the following are lost in the uranium disintegration series?

a) protons             b) neutrons

16.   The half-life of Co-60 is 5.27 years. Co-60 has displaced the X-ray tube as a radiation source for the treatment of cancer.

a.  A sample is used at a hospital for 21.08 year. How many half-lives did it experience?

b.  How many milligrams remain if the initial supply was 100 mg?

17.   If radioactive wastes must be stored for seven half-lives before disposal (a) how long must P-32 be held (which has a half-life of 14.3 days and is a beta emitter).  (b) What fraction of the P-32 originally set aside remains after this time?

18.  A radioactive substance decays as follows

Time (day)

Mass (g)

0

500

1

389

2

303

3

236

4

184

5

143

6

112

       Calculate the (a) first‑order decay constant, k, and the (b) half‑life of the reaction.

19.  The radioactive decay of Tl‑206 to Pb‑206 has a half‑life of 4.20 min. Starting with 5.00 x 1022 atoms of Tl‑206, calculate the number of such atoms left after 8 days.

20.  A freshly isolated sample of 90Y was found to have an activity of 9.8 x 105 disintegrations per minute at 1:00 PM on December 3, 1982. At 2:15 PM on December 17, 1982, its activity was re-determined and found to be 2.6 x 104 disintegrations per minute. Calculate the half-life of 90Y.

21.  Consider the following decay series:

A ——> B ——> C ——> D

       where A, B, and C are radioactive with half lives of 4.50 s, 15.0 days, and 1.00 s, respectively, and D is nonradioactive. Starting with 1.00 mole of A, and none of B, C, or D, calculate the number of moles of A, B. C, and D left after 30 days.

22.  Radioactive potassium‑40 isotope decays to argon- 40 with a half‑life of 1.2 x 109 yr. (a) Write a balanced equation for the reaction. (b) A sample of moon rock is found to contain 18 percent potassium‑40 and 82 percent argon by mass. Calculate the age of the rock in years.

23.  In April 1903 Professor Curie announced in Scientific American that “radium possessed the extraordinary property of continuously emitting heat without combustion, without chemical change of any kind, and without change in its molecular structure. Radium maintained its own temperature 1.5°C above the surrounding atmosphere. The salt also maintained its potency “indefinitely”. Would you at the present time accept this as a correct statement?  Explain.

5.10 Radioactive Dating Is An Application Of Decay

24.  Organic material discovered in an excavation of Cave of Uchcumachay (Peru) has an activity of 3.48 disintegrations per minute per gram of carbon (counts/min/g carbon) for the oldest level containing evidence of human occupancy. Determine the age of the material.

25.     A long-cherished dream of alchemists was to produce gold from cheaper and more abundant elements. This dream was finally realized when Hg was converted into gold upon neutron bombardment. Write a balanced equation for this process.

 

26.     Identify the unknown particles, ?,  in the picture below:

 

 

 

 

 

 

 

 

 

 

 

 

 


Answers to numerical questions

5) 1.34 x 10-13 J/atom   6) 2.3 x 1012 J                          7a) 6.7 x 10-11 kg         7b) 5.2 x 10-6 kg

7c) 7.8 x 104                7d) loss of 1.34 x 10-6 g            16a) 4                          16b) 6.25 mg  

17a) 100 days              17b) 0.78%                              18a) 0.25 day-1 18b) 2.77 days

19) ?                            20) 64.4 hr                               21) For A: close to zero

For B: 0.25 n                For C: close to zero                  For D: 0.75 mole          22b) 3.0 x 109 yr

 

TIME MACHINE Nuclear Energy

1898        Radioactivity is discovered.

1898        Marie and Pierre Curie discover and name the elements polonium and radium.

1934        Enrico Fermi, in Rome, begins his first experiments bombarding uranium with neutrons.

1939        Lise Meitner publishes the first report on the fission of uranium.

1942        On December 2 the first self-sustaining chain reaction and consequent controlled release of nuclear energy are achieved.

1945        Uranium is used as a fissionable material in atomic bomb dropped on Hiroshima, Japan

1954        United States launches the first nuclear submarine, U.S.S. Nautilus.

1957        First full-scale nuclear electric-power plant begins commercial operation in Shippingport, Pennsylvania.

1963        First breeder reactor to provide commercial electricity is completed near Detroit, Michigan.

1966        Lise Meitner is the first woman to receive the Fermi Award

                issued by the Atomic Energy Commission.

1967        Sculptor Henry Moore is commissioned to create Birth of the Atomic Age in Chicago to commemorate the twenty-fifth anniversary of the first nuclear reactor.

Chapter 6 Electrons

“It is a truth very certain that when it is not in our power to determine what is true we ought to follow what is most probable”                     

Rene Descartes (1596-1650) from Discourse on Method

 

 

Energy Level, n

 

 

 

                          1, 2, 3...

Energy Level, n, is the principal quantum number and, in general, is the energy of the shell as well as the volume of space in which the electron moves.

                          1, 2, 3, ...

Sublevel    

 

       

                             s

                             p

                             d

                             f

Angular momentum number l,  designates the shape of the region, or subshell, that the electron occupies

                              0

                              1

                              2

                              3

Orbital           

 

   

                            s__

                     p__ __ __

               d__ __ __ __ __

         f__ __ __ __ __ __ __

Magnetic number, ml, designates in a general way the orientation of the charge cloud in space.

                              0

                         -1, 0, +1

                    -2, -1, 0, +1, +2 

               -3, -2, -1, 0, +1, +2,+3

Electron in orbital

 

Spin number, ms, specifies the direction of spin of the electron about its own axis and can be either clockwise or counterclockwise:

                                + ½ ,- ½_

 

1.         Why did the 1913 model of the atom give way to the Quantum Mechanical Model?

2.     What property does matter exhibit at the atomic level?

3.    Concerning the Heisenberg Uncertainty Principle

a)   Define it.

b)   Why can’t powerful X-rays be used to delineate the interior of atoms?

4.    What information is derived from the Schroedinger Wave Equation?

 

5.    Copy and complete the following chart.  (Note how it is completed for the 1st energy level):

Principle Energy Level, n

Sublevel

Number of

orbitals per sublevel

Number of electrons per sublevel

Number of orbitals per energy level, n

Number of electrons per energy level, n

1

s

1

2

1

2

2

——

——

——

——

——

——

 

——

 

——

3

——

——

——

——

——

——

——

——

——

 

 

——

 

 

——

4

——

——

——

——

——

——

——

——

——

——

——

——

16

32

 

 

 

 

6.    Write the corresponding electron configuration for each of the following pictorial representations. Name the element, assuming that the configuration describes a neutral atom:

 

7.     Which of the following are incorrect designations for an atomic orbital?      

4f,    2d,     2s,    5p,    1p,    3f,    3d

8.    Use the electron-filling map to write the complete electron configuration for these elements:

       a) Sr             b) The element with the atomic number 52                 c) Ta

9.    Use the periodic table only to write the complete electron configuration for these elements:             a) Se                b) Y                  c) Pb

10.  Based on electron configuration why are there 14 elements in a row of the rare-earth series?

11.  If the generalized outer electron configuration for an element in group IIIa is ns2np1, write the generalized outer electron configuration for elements in groups

       a) Ia          b) IIa                c) IVa              d) Va               e) VIa               f) VIIa       g) VIIIa

12.  What is the maximum number of electrons that may be designated

       a) 2s         b) 2p                c) 3s                 d) 3d                e) 4f

13.  Write the abbreviated electron configuration for the transition elements of the 5th period.

14.  According to Hund’s rule

a.     which of the following electron configurations are in the ground states are correct?

b.    what is true about the spin orientation of all unpaired electrons in an atom in the ground state that has more than one orbital with unpaired electrons?

c.     what is true about the spin orientation of both electrons in an orbital?

15.  Which columns on the periodic table correspond to the following electron formulas?

      

16.  Valence electrons are those in the outermost shell of an atom. They are the electron(s) represented by the highest filled quantum level for that atom. The Part of the atom excluding the valence electrons is the kernel. How many electrons are in the valence shell and in the kernel for the following?

a) Al                     b) Ca               c) P                  d) Cu               e) Br

 

17.  Orbitals with nearly the same energy are called near-degenerate orbitals.

a.   List two examples of this condition from the fourth period on the periodic table.

b.   What accounts for the fact that this condition is noted for many elements beyond atomic number 40 [such as 41-47, 57, 58, 64, 78, 79, 89, 91-93. 96]?

18.  If greater stability is associated with a fully-filled sublevel why can’t the principle of near-degenerate orbitals be used to explain why fluorine's electron configuration is not 1s22s12p6?

19.  Name the two orbitals to fill after 7p.

20.  A few metals have electrons in their p orbitals. Which metal(s) have more than one p electron?

21.  Write the electron configuration for the following

       a) Cl-                    b) K+              c) Al3+ d) Br-               e) Ba2+

22.  Write the electron configuration of

a)   argon.

b)   Name two positive and two negative ions that have this configuration.

23.       Write the abbreviated electron configuration for the following:

a) Ag                    b) Ag+             c) Ti2+

24.  Experiments were done on manganese (Z = 25) to determine its electron configuration. The atom was tested for paramagnetism and shown to have five unpaired electrons. The divalent [+2] ion also showed the same level of paramagnetism. Write the electron configuration for the

a.   Mn atom

b.   Mn2+ ion

c.   What would the level of paramagnetism be for the gallium atom and for the gallium ion?

25.  What electrical charge, if any, must be assigned to each of the following atoms to make it isoelectronic with S2-:

       a) P                       b) Ca               c) Cl                 d) Ar               e) K?

26.  From each of the following sets, identify the species that is not isoelectronic with the other three:

       a) O-, F-, Mg2+, Ne;                      b) Br, Se -, As2-, Rb+;               c) Xe+, I-, Te-, Cs2+

27.  Arrange the following species into groups of isoelectronic species:

            F-            Sc3+             Be2+                 Rb+            O2-             Na+

            Ti4+          Ar                B3+                   He             Se2-             Y3+

28.  Identify the group containing the element composed of atoms whose last electron (a) enters and fills an s orbital. (b) enters but does not fill an s orbital, (c) is the first to enter a p sublevel, (d) is the next to the last in a given p sublevel, (e) enters and fills a given p sublevel, (f) is the first to enter a d sublevel, (g) half fills a d sublevel.

29.  Give the total number of half-filled orbitals in atoms which have the following electron configurations:

       a) (Ar)4s23d3        b) (Ar)4sl3d5                c) (Ar)4s23d7

30.  Use the periodic table only to write the abbreviated electron configuration for the following elements:

       a) S                       b) I                               c) Th

31.  Referring only to the periodic table, determine the element of lowest atomic number whose ground state contains:

       a) an f electron,                             b) three s electrons,                  c) a complete d sublevel, 

       d) ten p electrons,                          e) four complete s sublevels.

32.  Write the permissible set of four quantum numbers for each of the following electrons (n, l, ml, ms):

       a)  1s2                   b)  2p5              c) 3d6               d) 4s1               e) 4f3                f) 6p6    

          g) arsenic’s outer shell electron

 

 

 

 

33.  Which of the following are sets of quantum numbers that are impossible. Explain what is wrong.

 

n

l

ml

ms

a

5

3

-2

-1

b

5

3

-3

½

c

3

3

-3

½

d

3

0

0

  

e

3

-1

-1

½

f

3

1

-1

 

g

3

1

2

½

h

3

2

2

½

34.  How many sets of quantum number values are there for a 4p electron?

35.  How many electrons in an atom can have the following sets of quantum numbers?

a) n = 3                b)n = 2, l = 0      c)n = 2, l = 2             d) n = 2, l = 0, ml = 0, ms = +1/2  

36.  Which of the following as isolated atoms in the ground state are paramagnetic? diamagnetic?

       a) Cu                    b) Cr                c) Li                             d) Kr

37.  Which of the following species are paramagnetic? diamagnetic?

       a) KF                    b) ZnCl2           c) Ti

d)  Explain why halides [compounds containing halogens] of cobalt(II) are colored, whereas halides of zinc(II) are colorless.

38.  How many electrons can each of the following hold?

       a) 2nd quantum level,         b) 5th quantum level,               c) 1st through 4th quantum levels,

       d) How many elements are in the 1st through 4th periods of the periodic table?

39.  Name two elements that could have the generalized outer electronic configuration:               (noble gas) ns2 ( n - 1 ) d10np2

40.  Which of the following are observable? (a) Position of electron in H atom; (b) frequency of radiation emitted by H atoms; (c) path of electron in H atom; (d) wave motion of electrons; (e) diffraction patterns produced by electrons; (f) diffraction patterns produced by light; (g) energy required to remove electrons from H atoms; (h) a light wave; (i) a photon; (j) an atom; (k) a molecule; (l) a water wave.

41.  Identify the elements whose neutral atoms have the electron configurations:

       a) 1s22s2                                       b) 1s22s22p3                 c) 1s22s22p63s2

       d) 1s22s22p63s23p3                        e) 1s2

42.  Which sublevel is filled next after the following sublevels are filled?

       a) 4f                      b) 3d                c) 6s                 d) 4p                e) 5d

43.  Determine the number of unpaired electrons in the ground state of the following species:     

a) F-                    b) Sn2+             c) Bi3+

44.  Chemists often consult tables of atomic radii in order to compare sizes of atoms. Why is it not strictly correct to say that a hydrogen atom has a radius of 0.52 A?

45.  Draw a diagram of the entire USM campus and include a sketch of the school in it. Draw a circle around the regions that represents the 90% probability of finding a USM student

a.   during the school day

b.   at around 3:20 p.m.

46.  Concerning the following diagram

 

 

       atoms in a hot furnace are blown through the slit screen. What is proven about the quantum mechanical model from the results of this experiment. Both spots on the detecting screen are equal in size and intensity.

 

47.  Which sample in the following diagram is paramagnetic?

 

(c)

 

 

48.  A computer solves the Schrφdinger wave equation for a number of orbitals. In one such solution a hologram picture appears on the monitor that appears spherical with a contrast revealing a denser color near the center with a diminishing of color intensity away from the center without any clear boundary. What is the significance of this hologram?

49.  Which noble gas element was tested to give the following graphic?

 

*50.     From the information below identify element X.

1.   The wavelength of the radio waves sent by a FM station broadcasting at 97.1 MHz [megahertz] is 30 million (3.00 x 107) times greater than the wavelength corresponding to the energy difference between a particular excited state of the hydrogen atom and the ground state.

2.   Let V represent the principal quantum number for the valence shell of element X. If an electron in the hydrogen atom falls from shell V to the inner shell corresponding to the excited state mentioned above in part 1 the wavelength of light emitted is the same as the wavelength of an electron moving at a speed of 570. m/s.

3.   The number of unpaired electrons for element X is the same as the maximum number of electrons in an atom that can have the quantum number designations n = 2, ml = ‑1 and ms = ‑1/2

4.   Let A represent the principal quantum number for the electron in an excited He+ ion in which the single electron has the same energy as the electron in the ground state of a hydrogen atom. This value of A also represents the angular momentum quantum number for the subshell containing the unpaired electron(s) for element X.

                                *This question is from James H. Burness of Penn State University ,York Campus.

 

 

THE TIME MACHINE

1925        Adolf Hitler publishes the book Mein Kampf

1925        40,000 white-robed Klansmen from the Ku Klux Klan parade through Washington, D.C.

1925        Dutch physicists George Uhlenbeck and Samuel Goudsmit propose that electrons have an intrinsic property called spin.

1925        Austrian-born scientist Wolfgang Pauli states that no two electrons can have the same set of four quantum numbers.

1926        Scottish inventor John L. Bird devises a machine that transmits moving pictures to members of the Royal Institution in London and calls it television.

1926        Screen star Marilyn Monroe is born

1926        Harry Houdini dies of peritonitis.

1926        St. Louis Cardinals beat New York Yankees in seventh game of World Series.

1926        Erwin Schrodinger proposes a paper that incorporates both the wavelike and particle-like behavior of the electron.

1926        President Coolidge signs a $338 million tax cut.

1926        Trotsky admits defeat and bows to Stalin group as leaders of U.S.S.R. in Moscow.

1927        Werner Heisenberg published in the Zeitschrift fur physik his Uncertainty principle.

1927        Charles Lindbergh flies from New York to Paris alone.

1927        Babe Ruth of the New York Yankees hits 60 home runs.