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Core Chemistry 1 > Structure & Bonding > Flashcards

Structure & Bonding Flashcards

1
Q

What does the de Broglie postulate state?

A

All matter possesses characteristics of both waves and particles.

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2
Q

What can electrons and neutrons exhibit due to their wave properties?

A

Diffraction.

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3
Q

What are particles of light called?

A

Photons.

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4
Q

Using the de Broglie relation, how is momentum defined for a particle?

A

Momentum (p) is mass (m) x velocity (v).

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5
Q

Using the de Broglie relation, how is momentum defined for a wave?

A

Momentum (p) is Planck’s constant (h) divided by wavelength (λ).

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6
Q

Fill in the blank: For a tennis ball and an electron both at 100 mph, only the _______ has any consequences regarding wavelength.

A

electron.

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7
Q

What does the Schrödinger equation describe?

A

The behavior of a wave.

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8
Q

What is the kinetic energy of a wave related to in the Schrödinger equation?

A

How curved it is (the second differential).

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9
Q

What must the total energy of a wave consist of according to the Schrödinger equation?

A

Kinetic energy plus potential energy.

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10
Q

What is the mathematical expression that describes the behavior of an electron as a wave?

A

Wavefunction (ψ).

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11
Q

What conditions must a wavefunction satisfy?

A
  • 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.
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12
Q

What is the wavefunction for an electron in a 1D box of length a?

A

ψ = sin(nπx/a)

Where n is an integer (1, 2, 3, …).

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13
Q

What is the formula for the energy (E) of an electron in a 1D box?

A

E = (n²h²)/(8ma²)

Where h is Planck’s constant, m is the mass of the electron, and a is the length of the box.

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14
Q

What does the value of ψ represent in the context of an electron wave?

A

The amplitude of the electron wave

The physical meaning of ψ itself is not significant.

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15
Q

What is the Born interpretation of the wavefunction?

A

ψ² is the probability of finding the electron at that point

ψ² will always be positive.

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16
Q

What is the form of the wavefunction in two dimensions?

A

ψ = sin(nπx/l) sin(mπy/l)

Where l is the length of the square box edges.

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17
Q

How is the energy of the 2D wavefunctions expressed?

A

E = (h²/8m)(n²/l² + m²/l²)

n and m are quantum numbers for the respective dimensions.

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18
Q

What does it mean for two wavefunctions to be degenerate?

A

They have the same energy

Example: n=1, m=2 has the same energy and shape as n=2, m=1.

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19
Q

What is required to draw a wavefunction in n dimensions?

A

A graph with n + 1 dimensions

The extra dimension is for the ψ value.

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20
Q

What type of coordinates are used for atoms in three dimensions?

A

Spherical Polar coordinates

These include radius, colatitude, and azimuth (r, θ, φ).

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21
Q

True or False: The wavefunctions in three dimensions can be represented using Cartesian coordinates.

A

False

Atoms are spherical, necessitating spherical coordinates.

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22
Q

What are the three quantum numbers needed to describe an electron in three dimensions?

A
  1. Principal quantum number (n)
  2. Orbital angular momentum quantum number (l)
  3. 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.

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23
Q

In what coordinate system do we describe the position of electrons in atoms?

A

Spherical Polar coordinates

This system includes radius (r), colatitude (θ), and azimuth (φ).

24
Q

What is the significance of the radial wavefunction ψr?

A

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.

25
Q

What is the radial distribution function for an electron?

A

4πr2ψr2

This function accounts for the surface area of a sphere when calculating the probability of finding an electron at a certain radius.

26
Q

What is a node in the context of wavefunctions?

A

A point, line, or surface where the wavefunction passes through zero.

For ns wavefunctions, there are n-1 radial nodes.

27
Q

What is the maximum radius for finding the electron in a 1s wavefunction?

A

0.529Å (1 atomic unit, a0)

This is the most likely radius at which to find the electron with this wavefunction.

28
Q

How do the radial wavefunctions differ for ns and np states?

A

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.

29
Q

What is the maximum of the 2p radial distribution function?

A

4a0

The maximum occurs at a distance of 4 times the atomic unit (a0 = 0.529Å).

30
Q

What is the maximum of the 3d radial distribution function?

A

9a0

This value represents the most probable distance for finding an electron in a 3d orbital.

31
Q

True or False: The wavefunction ψr can be negative.

A

True

Only ψr2 has a physical meaning and must be non-negative.

32
Q

Fill in the blank: The 2s wavefunction has a radius where the wavefunction changes sign, known as a _______.

A

node

This node occurs where ψr = 0.

33
Q

What characterizes the 3s wavefunction?

A

It has two radial nodes.

The maximum in the radial distribution function occurs at about 13a0.

34
Q

What is the relationship between the shape quantum number l and the radial nodes in ns wavefunctions?

A

ns wavefunctions have n-1 radial nodes, where l = 0.

The shape quantum number l determines the type of orbital.

35
Q

What is the maximum probability of finding the 1s electron in the ground state hydrogen atom?

A

1a0 from the nucleus

This corresponds to the maximum of the radial distribution function.

36
Q

What happens to the radial distribution function for wavefunctions with radial nodes?

A

The maximum occurs in the outermost part of the wavefunction.

This is observed for wavefunctions such as 2s, 3s, and others.

37
Q

What happens when an electric discharge is passed through hydrogen gas?

A

Excited H* atoms are produced

This occurs due to the energy provided by the electric discharge.

38
Q

What do excited H* atoms do as they transition to lower energy states?

A

They emit excess energy as light

This light corresponds to specific wavelengths.

39
Q

What is the equation that describes the experimental energy levels of hydrogen?

A

E = –R_H / n^2

R_H is the Rydberg constant.

40
Q

Fill in the blank: The wavelengths of light emitted by excited hydrogen atoms can be fitted to an _______.

A

equation

41
Q

True or False: The energy levels of hydrogen can be calculated using the formula E = –R_H / n^2.

A

True

42
Q

What is the ground state electron configuration for hydrogen?

A

1s1

The quantum numbers for hydrogen in the ground state are n = 1, l = 0, ml = 0.

43
Q

How is the energy of the ground state for hydrogen related to the principal quantum number?

A

Energy is proportional to -1/n²

This means that 2s has the same energy as 2px, 2py, and 2pz.

44
Q

What approximation is used for many-electron atoms when solving the Schrödinger equation?

A

Orbital approximation

This involves using hydrogen-like solutions for other atoms.

45
Q

What principle states that no two electrons in an atom can have the same set of quantum numbers?

A

Pauli exclusion principle

This leads to the Pauli exclusion rule.

46
Q

What are the quantum numbers for the two electrons in helium?

A

n = 1, l = 0, ml = 0, ms = +½ and -½

This configuration is described as 1s².

47
Q

In lithium, where do the first two electrons occupy?

A

1s²

The third electron goes into 2s.

48
Q

Why is 2s lower in energy than 2p in lithium?

A

2s has a greater effective nuclear charge

The shielding effect of 1s electrons causes this difference.

49
Q

What is the ground state electron configuration for beryllium?

A

1s² 2s²

Beryllium has a total of four electrons.

50
Q

What is the ground state electron configuration for boron?

A

1s² 2s² 2p¹

Boron has a total of five electrons.

51
Q

What rule states that electrons will occupy different orbitals with parallel spins before pairing up?

A

Hund’s rule of maximum spin multiplicity

This applies to the filling of p orbitals.

52
Q

What principle describes the method of ‘building up’ the electron configuration?

A

Aufbau principle

This principle guides the order of filling orbitals.

53
Q

What is the effective nuclear charge for helium?

A

Approximately 1.9+

This is lower than the actual nuclear charge of 2+.

54
Q

What is the ionization energy related to?

A

The energy difference between atomic orbitals

This energy difference can determine chemical behavior.

55
Q

What happens to the energy difference between 2s and 2p levels from beryllium to neon?

A

It increases

This trend will be discussed further in later lectures.

56
Q

Fill in the blank: The ground state electron configuration of carbon is ______.

A

1s² 2s² 2p²

57
Q

True or False: The energy of orbitals for hydrogen is dependent on the principal quantum number.

A

True

The energy is proportional to -1/n².

Core Chemistry 1 (1 decks)

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