Structure & Bonding Flashcards
What does the de Broglie postulate state?
All matter possesses characteristics of both waves and particles.
What can electrons and neutrons exhibit due to their wave properties?
Diffraction.
What are particles of light called?
Photons.
Using the de Broglie relation, how is momentum defined for a particle?
Momentum (p) is mass (m) x velocity (v).
Using the de Broglie relation, how is momentum defined for a wave?
Momentum (p) is Planck’s constant (h) divided by wavelength (λ).
Fill in the blank: For a tennis ball and an electron both at 100 mph, only the _______ has any consequences regarding wavelength.
electron.
What does the Schrödinger equation describe?
The behavior of a wave.
What is the kinetic energy of a wave related to in the Schrödinger equation?
How curved it is (the second differential).
What must the total energy of a wave consist of according to the Schrödinger equation?
Kinetic energy plus potential energy.
What is the mathematical expression that describes the behavior of an electron as a wave?
Wavefunction (ψ).
What conditions must a wavefunction satisfy?
- Must be zero at the boundaries of the region occupied by the electron
- Must be continuous
- Must have only one value at a particular place.
What is the wavefunction for an electron in a 1D box of length a?
ψ = sin(nπx/a)
Where n is an integer (1, 2, 3, …).
What is the formula for the energy (E) of an electron in a 1D box?
E = (n²h²)/(8ma²)
Where h is Planck’s constant, m is the mass of the electron, and a is the length of the box.
What does the value of ψ represent in the context of an electron wave?
The amplitude of the electron wave
The physical meaning of ψ itself is not significant.
What is the Born interpretation of the wavefunction?
ψ² is the probability of finding the electron at that point
ψ² will always be positive.
What is the form of the wavefunction in two dimensions?
ψ = sin(nπx/l) sin(mπy/l)
Where l is the length of the square box edges.
How is the energy of the 2D wavefunctions expressed?
E = (h²/8m)(n²/l² + m²/l²)
n and m are quantum numbers for the respective dimensions.
What does it mean for two wavefunctions to be degenerate?
They have the same energy
Example: n=1, m=2 has the same energy and shape as n=2, m=1.
What is required to draw a wavefunction in n dimensions?
A graph with n + 1 dimensions
The extra dimension is for the ψ value.
What type of coordinates are used for atoms in three dimensions?
Spherical Polar coordinates
These include radius, colatitude, and azimuth (r, θ, φ).
True or False: The wavefunctions in three dimensions can be represented using Cartesian coordinates.
False
Atoms are spherical, necessitating spherical coordinates.
What are the three quantum numbers needed to describe an electron in three dimensions?
- Principal quantum number (n)
- Orbital angular momentum quantum number (l)
- Magnetic quantum number (ml)
The principal quantum number n can be 1, 2, 3, etc. The shape quantum number l can be 0, 1, …, (n-1). The orientation quantum number ml can be -l, …, 0, …, +l.
In what coordinate system do we describe the position of electrons in atoms?
Spherical Polar coordinates
This system includes radius (r), colatitude (θ), and azimuth (φ).
What is the significance of the radial wavefunction ψr?
It represents the probability of finding an electron at a certain distance from the nucleus.
According to the Born interpretation, ψ2 gives the probability density.
What is the radial distribution function for an electron?
4πr2ψr2
This function accounts for the surface area of a sphere when calculating the probability of finding an electron at a certain radius.
What is a node in the context of wavefunctions?
A point, line, or surface where the wavefunction passes through zero.
For ns wavefunctions, there are n-1 radial nodes.
What is the maximum radius for finding the electron in a 1s wavefunction?
0.529Å (1 atomic unit, a0)
This is the most likely radius at which to find the electron with this wavefunction.
How do the radial wavefunctions differ for ns and np states?
ns wavefunctions have n-1 radial nodes; np wavefunctions have n-2 radial nodes and are zero at the nucleus.
For np states, the wavefunction does not pass through zero at the nucleus.
What is the maximum of the 2p radial distribution function?
4a0
The maximum occurs at a distance of 4 times the atomic unit (a0 = 0.529Å).
What is the maximum of the 3d radial distribution function?
9a0
This value represents the most probable distance for finding an electron in a 3d orbital.
True or False: The wavefunction ψr can be negative.
True
Only ψr2 has a physical meaning and must be non-negative.
Fill in the blank: The 2s wavefunction has a radius where the wavefunction changes sign, known as a _______.
node
This node occurs where ψr = 0.
What characterizes the 3s wavefunction?
It has two radial nodes.
The maximum in the radial distribution function occurs at about 13a0.
What is the relationship between the shape quantum number l and the radial nodes in ns wavefunctions?
ns wavefunctions have n-1 radial nodes, where l = 0.
The shape quantum number l determines the type of orbital.
What is the maximum probability of finding the 1s electron in the ground state hydrogen atom?
1a0 from the nucleus
This corresponds to the maximum of the radial distribution function.
What happens to the radial distribution function for wavefunctions with radial nodes?
The maximum occurs in the outermost part of the wavefunction.
This is observed for wavefunctions such as 2s, 3s, and others.
What happens when an electric discharge is passed through hydrogen gas?
Excited H* atoms are produced
This occurs due to the energy provided by the electric discharge.
What do excited H* atoms do as they transition to lower energy states?
They emit excess energy as light
This light corresponds to specific wavelengths.
What is the equation that describes the experimental energy levels of hydrogen?
E = –R_H / n^2
R_H is the Rydberg constant.
Fill in the blank: The wavelengths of light emitted by excited hydrogen atoms can be fitted to an _______.
equation
True or False: The energy levels of hydrogen can be calculated using the formula E = –R_H / n^2.
True
What is the ground state electron configuration for hydrogen?
1s1
The quantum numbers for hydrogen in the ground state are n = 1, l = 0, ml = 0.
How is the energy of the ground state for hydrogen related to the principal quantum number?
Energy is proportional to -1/n²
This means that 2s has the same energy as 2px, 2py, and 2pz.
What approximation is used for many-electron atoms when solving the Schrödinger equation?
Orbital approximation
This involves using hydrogen-like solutions for other atoms.
What principle states that no two electrons in an atom can have the same set of quantum numbers?
Pauli exclusion principle
This leads to the Pauli exclusion rule.
What are the quantum numbers for the two electrons in helium?
n = 1, l = 0, ml = 0, ms = +½ and -½
This configuration is described as 1s².
In lithium, where do the first two electrons occupy?
1s²
The third electron goes into 2s.
Why is 2s lower in energy than 2p in lithium?
2s has a greater effective nuclear charge
The shielding effect of 1s electrons causes this difference.
What is the ground state electron configuration for beryllium?
1s² 2s²
Beryllium has a total of four electrons.
What is the ground state electron configuration for boron?
1s² 2s² 2p¹
Boron has a total of five electrons.
What rule states that electrons will occupy different orbitals with parallel spins before pairing up?
Hund’s rule of maximum spin multiplicity
This applies to the filling of p orbitals.
What principle describes the method of ‘building up’ the electron configuration?
Aufbau principle
This principle guides the order of filling orbitals.
What is the effective nuclear charge for helium?
Approximately 1.9+
This is lower than the actual nuclear charge of 2+.
What is the ionization energy related to?
The energy difference between atomic orbitals
This energy difference can determine chemical behavior.
What happens to the energy difference between 2s and 2p levels from beryllium to neon?
It increases
This trend will be discussed further in later lectures.
Fill in the blank: The ground state electron configuration of carbon is ______.
1s² 2s² 2p²
True or False: The energy of orbitals for hydrogen is dependent on the principal quantum number.
True
The energy is proportional to -1/n².
