1. on the Diagram Below, Label the Following Characteristics of a Light Wave

Chem 124Dr. Neff

Partial Key to Chapter 7-8 Workbook – this is NOT a key to the entire workbook, nor is it meant to be totally representative of what’s on the quiz – this is a PARTIAL KEY, that’s it. Please see me if you have questions about any of the other problems

Quantum Theory & Periodic Properties

Solutions will be shown in color or inbold. Please attempt these problems before consulting the key!

1. On the diagram below, label the following characteristics of a light wave:

Wavelength, 

Amplitude

Node

A higher frequency wave would have shorter wavelength, as shown. (this wave also has lower amplitude.)

2. Consider the following types of electromagnetic radiation:

i) microwave

ii) ultraviolet

iii) radio waves

iv) infrared

v) x-ray

a) arrange them in order of increasing wavelength x-ray < UV< infrared< micro< radio

a)arrange them in order of increasing frequency reverse of a)

b)arrange them in order of decreasing energy same as a)

3. Cobalt-60 is a radioactive isotope used to treat cancers of the brain and other tissues. A gamma ray emitted by an atom of this isotope has a wavelength of 9.32 x 10-13 m.

a. What is this wavelength in nm?

b. What is the frequency of this light in Hz?

c. What is the energy of one photon of this light in J?

d. What is the energy of one mole of these photons in J/mol?

e. What is the energy of one photonof this light in electron volts eV (1 eV = 1.602 x 10-19 J)?

f. Does radiation with = 242 nm have greater or lesser energy than the radiation emitted by the gamma ray above? What about radiation with = 2200 Å (1 Å = 1 x 10-10 m)? (You shouldn’t need to do calculations to answer these questions)

This light, with  = 242 nm, has longer wavelength and thus less energy than the gamma ray above.

4. One watt (W) is equal to 1 J/s. Assuming that 5.0% of the energy output of a 75 W light bulb is

visible light and that the average wavelength of the visible light is 550 nm, how many photons are emitted by the light bulb per second?

5. At its closest approach, Mars is 56 million km from earth. How long would it take to send a radio message from a space probe of Mars to earth when the planets are at this closest distance? (Don’t try to associate this question with the previous one, it will only confuse you!)

6. Microwave ovens work by irradiating food with microwave radiation, which is absorbed and converted into heat. Assume radiation with = 15.0 cm is used and that all the energy is converted to heat. How many photons are necessary to raise the temperature of a 350. mL quantity of water from 20.0˚C to 95.0˚C?

8. The photoelectric work function of a metal is the minimum energy needed to eject an electron by irradiating the metal with light. For calcium, this work function equals 4.34 x 10-19 J. What is the minimum frequency of light required to observe the photoelectric effect in calcium?

9. Light of wavelength 345 nm shines on a piece of calcium metal. What is the speed of the ejected electron? (Light energy greater than that of the work function of calcium or any metal ends up as kinetic energy of the ejected electron.) We did this in class

10. a) Which of these transitions correspond to absorption and which to emission of radiation (or energy in general)? Illustrate each transition on the provided energy level diagram.

i) n = 2 to n = 4 absorption

ii) n = 3 to n = 1 emission

iii) n = 5 to n = 2 emission

iv) n = 3 to n = 4 absorption

b) Of the transitions listed above, which corresponds to emission of radiation with the longest wavelength? Explain. You should not need to use your calculator to answer this!

Emission transition from 5 to 2 has less energy than other emission, so longer wavelength

c) Of the transitions listed above, which corresponds to absorption of radiation with the highest frequency? Explain. You should not need to use your calculator to answer this!

Absorption transition from 2 to 4 has highest energy so highest frequency

See me for help with 11 & 12

13. An electron in a hydrogen atom undergoes a transition from the ni= 6 level to some lower energy level. In doing so, energy is released in the form of light.

a) Calculate the frequency in s-1 (to 3 significant figures) of a photon of light associated with the highest frequency transition (i.e., largest difference in frequency) possible from the ni = 6 to a lower level. (HINT: Try drawing a picture first.)

You don’t need to do any calculations to figure out what nfinal is, just draw a picture like the one below. From this picture and from knowing the relationship between E and frequency, you should be able to determine that the highest frequency transition is that from n= 6 to n=1, as that has the largest difference in energy so largest difference in frequency.

b) Calculate the wavelength (in nm) of this photon of light.

See me for help with 14

15. Two objects are moving at the same speed. Which (if any) of the following statements about them are true?  = h/mu deBroglie Wavelength

The wavelength of the heavier object is longer. False
If one object has twice as much mass as the other, its wavelength is one-half the wavelength of the other. True
Doubling the mass of one of the objects will have the same effect on its wavelength as does doubling its speed. True

16.The speed of the electron in the ground state of the hydrogen atom is 2.2 x 106 m/s. What is the wavelength of the electron?

We did this one in class.

See me about 17

18. At what speed must a human weighing 150. lb. be traveling in order to have a wavelength in the visible region, say at 650 nm? Does it seem likely that a human would attain such a speed?

19. What is the momentum of a photon with a wavelength of 532 nm? (Remember to include the correct units with your answer!)

20. Heisenberg's uncertainty principle can be expressed mathematically as , where ∆u and ∆x represent the uncertainty in the speed and the position and h is Planck's constant.

(a) If an electron's speed is measured as 3.0x106 m/s with an accuracy of 1.0%, what is the minimum uncertainty in the position of the electron?

an accuracy of 1.0% means our u is 1.0% of the speed, or

u = 0.01(3.0x106 m/s) = 3.0x104 m/s

Then

(b) Repeat the calculation in part (a), but for a 12 g bullet whose speed is 200 m/s measured with 1.0% accuracy.

u = 0.01(200 m/s) = 2 m/s

Then

This shows us that we can know where the bullet is with greater accuracy than we can know where the electron is.

The uncertainty in the position of the electron is ~10 times greater than the size of the atom (~10-10 m), electrons are much smaller than atoms (~10-15 m?), so this uncertainty is huge compared to the size of the electron itself.

In stark contrast, the uncertainty in position of the bullet is miniscule in comparison to the size of the bullet.

This is logical – the larger an object is, the easier it is to locate it.

21. Fill in the following table: Did this in class

Quantum Number / Orbital or Electron Property / Allowed Values
ml / Orientation of orbital in 3-D space / Can range from –l to + l, including 0
n / energy level and size / n = 1 to 
l / orbital shape / l ranges from 0 to
n-1
ms / Electron spin / +1/2 or –1/2

22. a) If the principal quantum number n of an atomic orbital is 4, what are the possible values

of l?

If n = 4, l= 3, 2, 1, 0

b) If the angular momentum quantum number lis 3, what are the possible values of ml?

If l= 3, ml = 3, 2, 1, 0, -1, -2, -3

23. Explain why each of the following sets of quantum numbers would not be permissible for an electron in an atom:

a) n = 1, l = 0, ml= 0, ms = +1

ms = 1/2 or –1/2 only

b) n = 1, l = 3, ml = +3, ms = +1/2

When n = 1, lcan only =0

c) n = 3, l= 2, ml = +3, ms = -1/2

l= 2, soml = 2, 1, 0, -1, -2 only

d) n = 0, l = 1, ml = 0, ms = +1/2

n can never be 0

24.
Identify the pictured orbital as s, p or d (write your answer next to the picture) and then answer the following questions:

a. What is the l value for this type of orbital?this is a d orbital, L = 2

b. Can this type of orbital be found in the n = 2 energy level? If not, explain why.

a d orbital cannot be found in the n = 2 level, when n = 2, l can only be either 1 or 0, for l to equal 2, must be in n = 3 or higher

c. List one complete and valid set of allowed quantum numbers for an electron occupying this type of orbital in the n = 4 level.

n = 4, l = 2 (we’re talking about d orbitals), ml= 1, ms = 1/2 (these last two, just pick an allowed value.)

d. How many nodal planes are found within this type of orbital?

Recall that nodal planes are regions where there is no electron density. As you can see from the picture, any d orbital has 2 nodal planes, and in general, the l value gives you the number of nodal planes.

25. In what way are the electron configurations of H, Li, Na, K, Rb and Cs similar? In what way are the electron configurations of O, S, Se, Te and Po similar?

H, Li, Na, K, Rb and Cs all have their electron configurations ending in “ns1” – that is, they all have one valence electron. These atoms will all LOSE that one electron to be ISOELECTRONIC with previous noble gas.

Similarly, O, S, Se, Te and Po have “ns4” at the end of their configurations, they have 4 valence electrons. These atoms will all GAIN two more electrons to fill their “p” sublevel. In doing so , they too are ISOELECTRONIC with a noble gas, the one after them on PT.

26. Identify the following atoms or ions:

a)It has the ground-state configuration [Ar] 4s23d104p131Ga

b)It has the ground-state configuration [Kr]4d1048Cd+2 the “5s” electrons are missing, this MUST be an ion

c) It forms a –3 ion that is isoelectronic with Kr33As

27. Write out BOTH the full electron configuration and the abbreviated electron configuration for each of the following. Predict if the atom would be paramagnetic or diamagnetic.

31Gaabbreviated configuration above, so neither here

b. 42MoTHIS IS AN EXCEPTION TO RULES, see text for more exceptions! 1s22s22p63s23p64s23d104p65s14d5 or [Kr]5s14d5

c. 79AuTHIS IS AN EXCEPTION TO RULES, see text for more exceptions! What makes it an exception is highlighted in red 1s22s22p63s23p64s23d104p65s24d105p66s14f145d10 or [Xe] 6s14f145d10

For this one, write out just the abbreviated configuration.

d.98Cf[Rn]7s25f9

28. For each of the atoms listed in the problem above, give the number of inner (core) and outer (valence) electrons and then list a set of quantum numbers representing an electron of highest energy (one of the last electrons to fill).

a) Ga has 13 valence electrons if count the “d” electrons, but REALLY only has three valence electrons, the 4 p and 4 s electrons. QN for last electron to fill : n= 4, l = 1, ml = 0, ms=1/2

b) Mo has 6 valence electrons, last electron to fill in is a “4d” electron, so n= 4, l = 2, ml = 0, ms=1/2

d) Cf has a “5f” electron filling in last, so n= 5, l = 3, ml = 0, ms=1/2

29. Shown in the table below are various elements with a corresponding list of possible quantum numbers for the "last" electron (highest energy) entering the atom. Check() the appropriate column if the quantum "address" for the electron is correct. Circle the incorrect quantum number(s) if the quantum "address" is incorrect.

Element / n = / l = / ml = / ms = / Correct "address"
7N / 2 / 1 / 0 / 1/2 / 
14Si / 3 / 1 / 1 / -1/2 / 
45Rh / 5 / 2 / -2 / 1 / n=4
37Rb / 6 / 0 / 0 / 1/2 / n=5
64Gd / 4 / 3 / -3 / -1/2 / 

For 45Rh, the last electron does go into a d orbital, but it’s the 4 d orbital, not 5d. ALSO, ms cannot equal 1.

For 37Rb, the last electron does go into an s orbital, but it’s the 5s orbital NOT THE 6s

30. Draw the electron orbital box diagram for each of the following neutral atoms, and indicate whether they are paramagnetic or diamagnetic:

a) Ge paramagnetic

b) Ca diamagnetic

31. Arrange the following elements in order of increasing effective nuclear charge, decreasing atomic radii (size), increasing 1st Ionization Energy, increasing electron affinity, and decreasing metallic behavior:

C, F, Li, K, O

Zeff K < Li < C < O < F

Radii K > Li > C > O > F

IE & EA K < Li < C < O < F

Metallic Behavior K > Li > C > O > F

32. How does the size of a cation compare to the size of the corresponding atom? How does the size of an anion compare to the size of the corresponding atom? Explain both. A cation, having less electrons than corresponding atom, is smaller – fewer electrons held by same nuclear charge. An anion, having more electrons, is larger – more electrons held by same nuclear charge.