Questions and Answers
How do you calculate momentum?
mass (m) x velocity (v)
How do you calculate wavelength?
h (6.62607004*10^-34) / momentum (p)
The higher the n shell (or the farther away from the nucleus), the ___ energy.
higher
The lower the n shell (or the closer to the nucleus), the ___ energy.
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How many orbitals are in n=1?
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How many orbitals are in n=2?
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How many orbitals are in n=3?
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How many orbitals are in n=4?
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How to find the number of orbitals in n=x?
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The Bohr model correctly predicts the energy level of a single hydrogen atom, which has a single electron.
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The Bohr model correctly predicts the energy levels of atoms with more than one electron.
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Solving the Schrodinger wave equation for a single electron hydrogen atom predicts the same values for energy level as the Bohr model.
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The Schrodinger wave equation is successful at predicting energy levels for multi-electron systems because it focuses only on the particle nature of electrons, treating the wave-like traits of electrons as negligible.
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The Schrodinger wave equation is successful at predicting energy levels for multi-electron systems because, unlike Bohr, it addresses the wave-like nature of electrons.
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Squaring a wave function from the Schrodinger equation will tell you exactly where you find an electron.
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Squaring a wave function from the Schrodinger equation will tell you where you will likely find an electron.
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What is the principal quantum number?
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What is the orbital quantum number?
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What is the magnetic quantum number?
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What does the plot showing the probability of finding the electron near a particular point in space represent?
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Why does the probability of finding a 1s electron at any given point depend only on its distance from the nucleus?
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The probability density is ___ at r = 0 (at the nucleus) and ___ steadily with increasing distance.
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At very large values of r, the electron probability density is tiny but not exactly zero.
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At very large values of r, the electron probability density is zero.
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What is the probability of finding a 1s electron at a distance r from the nucleus called?
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How do you calculate the radial probability?
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The surface area of each spherical shell is equal to 4πr2, which increases rapidly with ___ r.
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Describe the relationship between a small r, surface area of a shell, and probability.
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List 3 things that happen to s orbitals as n increases.
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The value of ms, electron spin quantum number, designates the direction of quantum spin.
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The value of ms is independent of n, l, and ml.
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Study Notes
Momentum and Wavelength
- Momentum is calculated as the product of mass (m) and velocity (v).
- Wavelength can be determined using the formula ( \frac{h}{p} ), where ( h ) is Planck's constant (approximately ( 6.626 \times 10^{-34} ) J·s) and ( p ) is momentum.
Energy Levels and Electron Shells
- Higher n shells indicate higher energy levels, as they are farther from the nucleus.
- Lower n shells correspond to lower energy levels due to their proximity to the nucleus.
Orbitals in Electron Shells
- The number of orbitals increases with each shell:
- n=1 has 1 orbital (1s)
- n=2 has 4 orbitals (1s and 2p)
- n=3 has 9 orbitals (1s, 3p, 3d)
- n=4 has 16 orbitals (1s, 4p, 4d, 4f).
- The total number of orbitals in any shell n is calculated as ( n^2 ).
Bohr Model and Quantum Mechanics
- The Bohr model accurately predicts the energy levels of a single electron hydrogen atom.
- It fails to predict energy levels for multi-electron atoms.
- Solving Schrödinger's wave equation for a hydrogen atom yields energy values consistent with the Bohr model.
- Schrödinger's equation successfully addresses the wave-like nature of electrons, unlike the Bohr model.
Wave Functions and Probability
- Squaring a wave function gives the probability density, indicating where you are likely to find an electron, not an exact position.
- The principal quantum number (n) determines the electron shell and distance from the nucleus.
- The orbital quantum number (l) describes orbital shape and identifies subshells.
- The magnetic quantum number (ml) denotes the orientation of orbitals within a subshell.
Probability Density and Radial Probability
- Probability density indicates the likelihood of finding an electron at a specific distance from the nucleus.
- In a 1s orbital, probability density is greatest at the nucleus (r=0) and decreases with increasing distance due to the spherical symmetry.
- Radial probability is calculated by summing the probabilities over spherical shells at various radii.
- Surface area of spherical shells grows with the square of the radius, affecting the probability of finding electrons at different distances.
Characteristics of s Orbitals
- As the principal quantum number (n) increases, s orbitals become larger, contain more nodes, and have higher energy levels due to increased distance from the nucleus.
Electron Spin Quantum Number
- The electron spin quantum number (ms) determines the direction of quantum spin and is independent of other quantum numbers (n, l, ml).
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Description
This quiz covers key concepts in quantum mechanics, including momentum, wavelength, and electron shells. Learn how the Bohr model describes energy levels and the arrangement of orbitals in atomic structures. Test your understanding of these fundamental principles in physics.
