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108
Chapter 7
14.
The principal quantum number n indicates the energy of the orbital. As n
increases, the electron is found on average further from the nucleus. The
secondary (or angular momentum) quantum number l indicates the shape
of the orbital. The magnetic quantum number ml indicates the orientation
of the orbital in the space around the nucleus.
15.
The values allowed for the three quantum numbers depend upon each other.
The principal quantum n can have any integer value from 1, 2, 3, 4...to
infinity. The secondary (or angular momentum) quantum number l can
have values from 0, 1, 2, 3, to a maximum of n –1. The magnetic quantum
number ml can have integer values from –l through 0 to +l. The number of
different values ml can have equals 2l +1. This equals the number of orbitals within a set. For example, s orbitals come in sets of one only, p orbitals
always come in sets of three, d orbitals always come in sets of five, and so on.
The secondary quantum number l
can be related to the number of
planar nodes (nodal surfaces) in the
wavefunction.
Natural science does not simply
describe and explain nature, it is a
part of the interplay between
nature and ourselves.
Study Questions and Problems
1.
Werner Heisenberg
(1901-1976)
a. Calculate the wavelength of electromagnetic radiation that has a frequency of 5.56 MHz.
b. Calculate the frequency of electromagnetic radiation that has a wavelength equal to 667 nm.
2.
Draw the first few stationary waves possible for a violin string fixed at ends
1 meter apart.
a. What is the wavelength of the lowest frequency vibration?
b. How many nodes (not including the ends) are there in the n =5 vibration?
c. How many wavelengths fit within the boundaries in the n =4 vibration?
d. At what points are the nodes in the n =4 vibration?
e. What is the relationship between the frequency of the n =2 vibration
and the n =4 vibration?
3.
Electromagnetic radiation at the blue end of the visible spectrum has a
wavelength of 400 nm.
a. Calculate the frequency of the radiation.
b. Calculate the energy of one photon of this radiation.
c. Calculate the energy of one mole of photons of this radiation.
4.
Examine the emission spectrum of hydrogen (Figure 7.12 page 267 in text).
a. How many lines appear in the visible region (Balmer series)?
b. Why so few?
The Lyman series occurs in the UV region.
c. How many lines would you expect in the Lyman series?