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Questions and Answers
What is the correct magnetic quantum number (ml) for a 2p-orbital?
What is the correct magnetic quantum number (ml) for a 2p-orbital?
An s-orbital has a dumbbell shape.
An s-orbital has a dumbbell shape.
False
How many total orbitals are associated with l = 2?
How many total orbitals are associated with l = 2?
five
The shape of p-orbitals is often described as __________.
The shape of p-orbitals is often described as __________.
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Match the orbital types with their characteristics:
Match the orbital types with their characteristics:
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What is the angular momentum quantum number for an s-orbital?
What is the angular momentum quantum number for an s-orbital?
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The 2s orbital has a higher energy level than the 3s orbital.
The 2s orbital has a higher energy level than the 3s orbital.
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What shape do p-orbitals take?
What shape do p-orbitals take?
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The total number of orbitals for a d-subshell is ______.
The total number of orbitals for a d-subshell is ______.
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Match the following quantum numbers with their corresponding meanings:
Match the following quantum numbers with their corresponding meanings:
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Which of the following statements about electron probability densities is true?
Which of the following statements about electron probability densities is true?
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Degenerate orbitals have different energies.
Degenerate orbitals have different energies.
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What is the magnetic quantum number (ml) for a 3p orbital?
What is the magnetic quantum number (ml) for a 3p orbital?
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What is the shape of the 1s-orbital?
What is the shape of the 1s-orbital?
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The 2s-orbital has both positive and negative values throughout its volume.
The 2s-orbital has both positive and negative values throughout its volume.
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What quantum number represents the shape and type of orbital?
What quantum number represents the shape and type of orbital?
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The probability of finding an electron in a specific volume is proportional to __________.
The probability of finding an electron in a specific volume is proportional to __________.
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What is the primary characteristic of p-orbitals?
What is the primary characteristic of p-orbitals?
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At what probability level does the boundary surface for the 1s-orbital typically enclose the electron?
At what probability level does the boundary surface for the 1s-orbital typically enclose the electron?
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Match the quantum number with its significance:
Match the quantum number with its significance:
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The electron density cloud of the 2s-orbital approaches __________ as it moves away from the nucleus.
The electron density cloud of the 2s-orbital approaches __________ as it moves away from the nucleus.
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Study Notes
Atomic Orbitals
- Atomic orbitals are mathematical functions that describe the wave-like behavior of electrons in atoms.
- Probability of finding an electron is high within the orbital's boundary surface.
- Degenerate orbitals have the same energy level.
- Orthogonal functions are independent of each other; they do not interfere.
p-orbital shapes
- p-orbitals have a dumbbell shape, with a node at the nucleus.
- p-orbitals are oriented along the x, y, or z axes.
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p-orbital designation:
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2pz: n = 2, l = 1, ml = 0 -
3pz: n = 3, l = 1, ml = 0 -
4pz: n = 4, l = 1, ml = 0
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d-orbitals
- d-orbitals have more complex shapes than s and p orbitals.
- d-orbitals have five different shapes, designated as dxy, dxz, dyz, dz^2, and dx^2-y^2.
Quantum Numbers
- Principal quantum number (n) describes the energy level of an electron.
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Angular momentum quantum number (l) describes the shape of an electron's orbital.
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l = 0: s-orbital (spherical) -
l = 1: p-orbital (dumbbell) -
l = 2: d-orbital (complex) -
l = 3: f-orbital (complex)
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Magnetic quantum number (ml) defines the orientation of the orbital in space.
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ml = -l, -l+1, -l+2, ….., +l
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Number of orbitals for a given l value:
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l = 0: 1 s-orbital -
l = 1: 3 p-orbitals -
l = 2: 5 d-orbitals -
l = 3: 7 f-orbitals
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Energy Levels
- Schrodinger equation is used to calculate the energies of atomic orbitals.
- Energy level of the hydrogen atom is determined by the principal quantum number (n) only.
Orbital Size and "Atomic Radius"
- Probability of finding an electron at a specific distance from the nucleus is defined by the atomic orbital.
- 99% probability boundary surface encloses the area where the electron is most likely to be found.
- Atomic radius is a measure of the size of an atom.
- Average distance of an electron from the nucleus can be calculated.
s-orbital shapes
- s-orbitals are spherical in shape.
- 2s-orbital has a radial node, where the probability of finding the electron is zero.
p-orbital properties
- p-orbitals have a dumbbell shape.
- p-orbitals are oriented along the x, y, or z axes.
- Probability of finding the electron is zero in the nodal plane.
- 2p-orbitals (2px, 2py, 2pz) have a dumbbell shape with two lobes.
Visualizing Atomic Orbitals
- Boundary surface represents a 99% probability contour, where the electron is most likely to be found.
- Boundary surface provides a visual representation of the shape and orientation of the atomic orbital.
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