DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
3.091 Introduction to Solid State Chemistry
Professor Harry L. Tuller
Professor David I. Paul
Spring Term 2003
Homework #2 solutions
1) Sodium salts give off a characteristic yellow-orange light when added to the flame
of a Bunsen burner. The yellow-orange color is due to two narrow bands of
radiation with wavelengths of 588.9953 and 589.5923 mm. Calculate the
frequencies of these emission lines.
Solution: Here there is a mistake in the question; the wavelengths are actually nm not
mm. However, you will be given credit in both the cases in this case.
The relation between wavelength and frequency is
(Wavelength) * (frequency) = (velocity of light)
Therefore frequency for wavelength of 588.9953nm is 5.093 * 1016 cycles/sec
Similarly Frequency for wavelength of 588.5923 nm is 5.096 * 1016 cycles/sec
Velocity of light used: 3 * 108 m/sec
2) Cl2 molecules can dissociate to form chlorine atoms by absorbing
electromagnetic radiation. It takes 243.5 kJ of energy to break the bonds
in a mole of Cl2 molecules. What is the wavelength of the radiation
that has just enough energy to decompose a chlorine molecule to chlorine
atoms? In what portion of the spectrum is this wavelength found?
Solution: we know that E = h * frequency
Which is same as E = h * (velocity of light) / (wavelength)
243.5 kJ is required to break one mole of Cl2 molecules.
Therefore to break one Cl2 molecule we need 243.5 kJ / 6.023 * 1023
Wavelength is therefore: 491.6846 nm
Therefore this falls in visible region.
3) Suppose that 2.091 * 10-18 J is absorbed by the electron of the
hydrogen atom in the n=1 energy state. Describe the final energy state of
the atom.
Solution: We have the energy equation is:
1
1
- 2)
2
ni n f
Given an energy of 2.091 * 10-18 J.
And ni is 1; there fore substituting in the equation we have nf is 4.8
Therefore final state of electron is 4th level.
E = -kz 2 (
†
4) Estimate the first ionization energy for Br.
Solution: We can estimate this from the graph 3.6
However for this question everyone will be given points.
The equation below, is only for hydrogen like ions.
1
1
E = -kz 2 ( 2 - 2 )
ni n f
†
5) Explain why the first ionization energy of hydrogen is so much larger than the
first ionization energy of sodium
Solution: This is because of the shielding effect in Sodium and also because, the
distance between the nucleus and the last electron in Sodium is so much larger than
that in the case of Hydrogen.
6) What element do you think should give rise to the photoelectron spectrum shown
in Figure below? Explain your reasoning.
Solution: The element is Mg. Because the first peak corresponds to 1s2, second peak
corresponds to 2s2, third peak corresponds to 2p6, and 4th peak corresponds to 3s2.
7) Which of the following elements should have largest first Ionization energy?
a) B
b) C
c) N
d) Mg
e) Al
Solution: The largest ionization energy would be that for nitrogen.
8) Which of the following is a legitimate set of n, l, ml, and ms quantum numbers?
a) 0, 0, 0, 1/2
c) 3,3,2, +1/2
e) 5, 3, 3, -1
b) 8, 4, -3, -1/2
d) 2, 1, -2, -1/2
Solution: The legitimate set of quantum numbers is B.