Quantum Mechanics and Electron Behavior
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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.

<p>lower</p> Signup and view all the answers

How many orbitals are in n=1?

<p>1</p> Signup and view all the answers

How many orbitals are in n=2?

<p>4</p> Signup and view all the answers

How many orbitals are in n=3?

<p>9</p> Signup and view all the answers

How many orbitals are in n=4?

<p>16</p> Signup and view all the answers

How to find the number of orbitals in n=x?

<p>Multiply the number of n by itself.</p> Signup and view all the answers

The Bohr model correctly predicts the energy level of a single hydrogen atom, which has a single electron.

<p>True</p> Signup and view all the answers

The Bohr model correctly predicts the energy levels of atoms with more than one electron.

<p>False</p> Signup and view all the answers

Solving the Schrodinger wave equation for a single electron hydrogen atom predicts the same values for energy level as the Bohr model.

<p>True</p> Signup and view all the answers

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.

<p>False</p> Signup and view all the answers

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.

<p>True</p> Signup and view all the answers

Squaring a wave function from the Schrodinger equation will tell you exactly where you find an electron.

<p>False</p> Signup and view all the answers

Squaring a wave function from the Schrodinger equation will tell you where you will likely find an electron.

<p>True</p> Signup and view all the answers

What is the principal quantum number?

<p>n</p> Signup and view all the answers

What is the orbital quantum number?

<p>l</p> Signup and view all the answers

What is the magnetic quantum number?

<p>ml</p> Signup and view all the answers

What does the plot showing the probability of finding the electron near a particular point in space represent?

<p>probability density</p> Signup and view all the answers

Why does the probability of finding a 1s electron at any given point depend only on its distance from the nucleus?

<p>The 1s orbital is spherically symmetrical.</p> Signup and view all the answers

The probability density is ___ at r = 0 (at the nucleus) and ___ steadily with increasing distance.

<p>greatest, decreases</p> Signup and view all the answers

At very large values of r, the electron probability density is tiny but not exactly zero.

<p>True</p> Signup and view all the answers

At very large values of r, the electron probability density is zero.

<p>False</p> Signup and view all the answers

What is the probability of finding a 1s electron at a distance r from the nucleus called?

<p>radial probability</p> Signup and view all the answers

How do you calculate the radial probability?

<p>Adding together the probabilities of an electron being at all points on a series of x spherical shells of radius r1, r2, r3,..., rx − 1, rx.</p> Signup and view all the answers

The surface area of each spherical shell is equal to 4πr2, which increases rapidly with ___ r.

<p>increasing</p> Signup and view all the answers

Describe the relationship between a small r, surface area of a shell, and probability.

<p>When r is very small, the surface area of a spherical shell is so small that the total probability of finding an electron close to the nucleus is very low; at the nucleus, the electron probability vanishes because the surface area of the shell is zero.</p> Signup and view all the answers

List 3 things that happen to s orbitals as n increases.

<ol> <li>They become larger, extending farther from the nucleus. 2. They contain more nodes. 3. For a given atom, the s orbitals also become higher in energy as n increases because of the increased distance from the nucleus.</li> </ol> Signup and view all the answers

The value of ms, electron spin quantum number, designates the direction of quantum spin.

<p>True</p> Signup and view all the answers

The value of ms is independent of n, l, and ml.

<p>True</p> Signup and view all the answers

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.

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