Electrons in molecules can be found in orbitals that extend over more than one atom. Consider one electron that is confined in a molecular orbital that extends over 8 adjacent carbon atoms. The electron can move freely between the 8 atoms. a) Using the one-dimensional particle-in-the-box model, calculate the energy required to promote an electron from the n = 2 to the n = 5 level. The length of the box is determined by the C-C bond distance, which is 139 pm. Note: The following information may or may not be useful. ?? = ?2ℎ2 8???2 Planck's constant = 6.626 x 10-34 J·s; Mass of Electron = 9.109 x 10-28 g; Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1 b) What frequency of light would cause this excitation? c) Now imagine a straight chain of 2000 carbon atoms. Assume that the orbital extends over the entire chain and repeat the calculation for the required energy to promote an electron from the n = 2 to n = 5 level.
Atomic Structure
The basic structure of an atom is defined as the component-level of atomic structure of an atom. Precisely speaking an atom consists of three major subatomic particles which are protons, neutrons, and electrons. Many theories have been stated for explaining the structure of an atom.
Shape of the D Orbital
Shapes of orbitals are an approximate representation of boundaries in space for finding electrons occupied in that respective orbital. D orbitals are known to have a clover leaf shape or dumbbell inside where electrons can be found.
2. Electrons in molecules can be found in orbitals that extend over more than one atom. Consider
one electron that is confined in a molecular orbital that extends over 8 adjacent carbon atoms.
The electron can move freely between the 8 atoms.
a) Using the one-dimensional particle-in-the-box model, calculate the energy required to
promote an electron from the n = 2 to the n = 5 level. The length of the box is determined by
the C-C bond distance, which is 139 pm.
Note: The following information may or may not be useful.
?? = ?2ℎ2
8???2
Planck's constant = 6.626 x 10-34 J·s; Mass of Electron = 9.109 x 10-28 g;
Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1
b) What
c) Now imagine a straight chain of 2000 carbon atoms. Assume that the orbital extends over
the entire chain and repeat the calculation for the required energy to promote an electron
from the n = 2 to n = 5 level.
d) Would you expect the energy levels to get closer or farther apart if you increased the chain
to one million carbon atoms (i.e approaching bulk properties)? Provide a brief explanation
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