Atomic Theory Lecture 2
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Questions and Answers

What determines the energy of an orbital in a hydrogen atom?

  • n, l, and ml values
  • n and l values
  • l and ml values
  • Only the value of n (correct)

Which statement correctly describes a subshell?

  • Only specific orbitals with aligned electron spins
  • All orbitals within the same shell
  • All orbitals with the same value of n and l (correct)
  • All orbitals with the same value of n and m

How many orbitals are contained in a subshell where l = 2?

  • 1
  • 4
  • 6 (correct)
  • 5

According to the Pauli Exclusion Principle, how must two electrons in the same orbital differ?

<p>By their ms values (D)</p> Signup and view all the answers

What are the quantum numbers that fully describe an electron in an orbital?

<p>n, l, ml, and ms (A)</p> Signup and view all the answers

What describes the relationship between the wavelength and momentum of a moving body?

<p>Wavelength is inversely proportional to momentum. (B)</p> Signup and view all the answers

Which constant is used in the equation for energy quantisation?

<p>Planck's constant (D)</p> Signup and view all the answers

According to the photoelectric effect, what determines the number of electrons ejected?

<p>The intensity of the light. (D)</p> Signup and view all the answers

Which principle addresses the limitation in defining the position and momentum of electrons?

<p>Uncertainty Principle (D)</p> Signup and view all the answers

What is the correct expression for calculating momentum?

<p>Momentum = mass x velocity (D)</p> Signup and view all the answers

What kind of mechanics describes the motion of large bodies?

<p>Classical Mechanics (C)</p> Signup and view all the answers

Who developed the wave equation related to electron behavior?

<p>Erwin Schrödinger (B)</p> Signup and view all the answers

What did classical theory predict about the energy of ejected electrons?

<p>Energy would increase uniformly with light intensity. (B)</p> Signup and view all the answers

What does the principal quantum number (n) represent?

<p>The shell in which electrons reside (A)</p> Signup and view all the answers

Which statement regarding quantum numbers is true?

<p>Every electron in an atom has a unique set of quantum numbers. (D)</p> Signup and view all the answers

What does the magnetic quantum number (ml) denote?

<p>The orientation of the orbital in space (C)</p> Signup and view all the answers

Which of the following is not a valid orbital type indicated by the angular momentum quantum number (l)?

<p>q (B)</p> Signup and view all the answers

In which quantum number is the shape of an orbital defined?

<p>Angular momentum quantum number (l) (C)</p> Signup and view all the answers

What do the quantum numbers collectively provide information about?

<p>The probability distribution of electrons in an atom (C)</p> Signup and view all the answers

If an electron is in the 4d subshell, what are its possible values for the magnetic quantum number (ml)?

<p>-2, -1, 0, 1, 2 (A)</p> Signup and view all the answers

How many total orbitals are present in a shell where n = 3?

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

Describe the significance of the Pauli Exclusion Principle in terms of electron spin.

<p>It states that no two electrons in the same orbital can have the same set of quantum numbers, necessitating different spins.</p> Signup and view all the answers

What does the quantum number l indicate about an electron's orbital?

<p>The quantum number l indicates the subshell type and the orbital shape, with values ranging from 0 to n-1.</p> Signup and view all the answers

Explain how the spin quantum number (ms) contributes to orbital occupancy.

<p>The spin quantum number ms determines the orientation of the electron's spin, with values of +1/2 or -1/2.</p> Signup and view all the answers

In an f subshell where l = 3, how many orbitals are present?

<p>Seven orbitals</p> Signup and view all the answers

What do quantum numbers represent in the context of electron configurations?

<p>Quantum numbers represent spatial constraints that define the energy levels, shapes, and orientations of electron orbitals.</p> Signup and view all the answers

Why is it impossible to know the exact position of an electron?

<p>The exact position of an electron cannot be known due to the principles of quantum mechanics, specifically the Heisenberg Uncertainty Principle.</p> Signup and view all the answers

How is the principal quantum number (n) related to the periodic table?

<p>The principal quantum number (n) corresponds to the number of the period or row of the periodic table where a shell begins filling with electrons.</p> Signup and view all the answers

What is the significance of the angular momentum quantum number (l)?

<p>The angular momentum quantum number (l) defines the shape of the orbital and indicates the subshell where the electron is located.</p> Signup and view all the answers

What does the magnetic quantum number (ml) tell us about an electron's orbital?

<p>The magnetic quantum number (ml) indicates the orientation of an orbital within a given subshell.</p> Signup and view all the answers

What does the Born's Interpretation indicate about the wave function of an electron?

<p>Born's Interpretation indicates that the square of the wave function, $\Psi^2$, represents the probability density of finding an electron in a given space.</p> Signup and view all the answers

How does the concept of quantized energy levels affect electron orbitals?

<p>The concept of quantized energy levels means electrons can only occupy discrete energy states, affecting their distribution in orbitals.</p> Signup and view all the answers

What are the possible values of l for a principal quantum number of n = 3?

<p>For n = 3, the possible values of l are 0, 1, and 2, corresponding to s, p, and d orbitals respectively.</p> Signup and view all the answers

How does the wavelength of an electron compare to that of a golf ball based on their respective momenta?

<p>The wavelength of an electron is much larger than that of a golf ball due to its significantly smaller mass and momentum.</p> Signup and view all the answers

What is the energy quantization formula developed by Einstein related to the photoelectric effect?

<p>The energy quantization formula is given by $E = nh$, where $n$ is an integer and $h$ is Planck's constant.</p> Signup and view all the answers

What is the significance of Schrödinger's wave equation in quantum mechanics?

<p>Schrödinger's wave equation is significant because it describes how electrons behave as waves and provides wave functions that offer probabilities of an electron's position.</p> Signup and view all the answers

In the context of the Uncertainty Principle, what cannot be simultaneously defined for electrons?

<p>Position and momentum (or energy) of electrons cannot be simultaneously defined according to the Uncertainty Principle.</p> Signup and view all the answers

Describe how light intensity affects the number of electrons ejected in the photoelectric effect.

<p>The number of ejected electrons depends on light intensity, as higher intensity results in more photons that can impart energy to electrons.</p> Signup and view all the answers

What mechanics theory applies to large bodies, as compared to particles like electrons?

<p>Classical mechanics is used to describe the motion of large bodies, while quantum mechanics applies to particles like electrons.</p> Signup and view all the answers

What does the symbol 'h' represent in the equations for energy quantization and the photoelectric effect?

<p>'h' represents Planck's constant, valued at $6.626 x 10^{-34} J imes s$.</p> Signup and view all the answers

What problem does Heisenberg's Uncertainty Principle address regarding electrons in atoms?

<p>Heisenberg's Uncertainty Principle addresses the problem of the inability to precisely know both the energy and the position of electrons in atoms.</p> Signup and view all the answers

Flashcards

Electron Orbital Energy

In hydrogen-like atoms, electron orbital energy depends only on the principal quantum number (n).

Quantum Numbers and Orbitals

Orbitals are precisely defined by three quantum numbers (n, l, and ml). Each shell (n) contains subshells.

Subshell and Orbitals

A subshell (defined by 'l') contains a specific number of orbitals (2l+1).

Electron Spin

Electron spin (ms) is a fundamental property that can have two values +1/2 and -1/2 (spin up/down).

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Pauli Exclusion Principle

No two electrons in an atom can have the same set of four quantum numbers (n,l,ml, ms).

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Electron's Wavelength

The wavelength of a moving electron is inversely proportional to its momentum. Wavelength is dependent on the electron's mass and velocity.

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Quantum Mechanics

Describes the movements of very small particles like electrons, which classical mechanics cannot adequately explain.

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Energy Quantization

Energy comes in discrete packets (quanta).

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Photoelectric Effect

Emission of electrons when light shines on a material. Light's intensity doesn't change the ejected electron energy.

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Wave Function

Mathematical expressions describing electron behavior in an atom.

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Uncertainty Principle

It's impossible to precisely know both the position and momentum of a particle at the same time.

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Schrödinger's Wave Equation

Mathematical equation describing electron behaviour in an atom.

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Momentum

Mass times velocity of an object.

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Electron's Position

The exact position of an electron cannot be precisely known, only the probability of finding it in a region of space.

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Wave Function (Ψ)

The wave function doesn't directly show an electron's location; it describes the probability distribution of the electron.

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Probability Density (Ψ²)

The square of the wave function represents the probability of finding an electron in a specific region of space.

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Quantum Numbers

Numbers that describe the properties of atomic orbitals, such as energy level, shape, and orientation.

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Principal Quantum Number (n)

Indicates the energy level or shell of an electron, and roughly corresponds to the row in the periodic table.

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Angular Momentum Quantum Number (l)

Specifies the shape of the electron's orbital (s, p, d, f).

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Magnetic Quantum Number (ml)

Indicates the orientation of the orbital in space.

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Electron Energy Levels

The energy properties of electrons in atoms are restricted to certain discrete levels; they're not continuous.

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What determines the energy of a one-electron atom's orbital?

The energy of an orbital in a hydrogen atom or any one-electron atom is solely determined by the principal quantum number (n).

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What is a shell in atomic structure?

A shell encompasses all orbitals with the same principal quantum number (n).

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What is a subshell in atomic structure?

A subshell consists of all orbitals with the same values of n and the angular momentum quantum number (l). It represents a group of orbitals with similar shapes.

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How many subshells are in each shell?

Each shell with principal quantum number (n) contains n subshells, meaning the number of subshells is equal to the shell's energy level designation.

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How many orbitals are in a subshell?

Each subshell with angular momentum quantum number (l) contains 2l + 1 orbitals. This means the number of orbitals in a subshell depends on its shape.

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Electron's Position Uncertainty

We can't know both the exact position and momentum of an electron at the same time. This limitation is described by the Heisenberg Uncertainty Principle.

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What does Born's Interpretation tell us about an electron's probability?

Born's Interpretation states that the wave function squared (Ψ²) is proportional to the probability of finding an electron in a specific region of space.

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What are Quantum Numbers?

Quantum Numbers are a set of numbers that describe the properties of atomic orbitals, defining the energy level, shape, and orientation of electrons.

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What is the relationship between n, l, and valid orbitals?

The 'l' value (angular momentum quantum number) can range from 0 to (n-1). For a given 'n' value, we can have a 'l' number less than or equal to (n-1). This relationship defines the number of subshells possible for a given shell.

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What is the significance of quantized energy levels?

Electrons in atoms can only occupy specific discrete energy levels, known as quantized energy levels. They cannot exist in between these levels.

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De Broglie Wavelength

The wavelength of a moving object, inversely proportional to its momentum. Smaller objects like electrons have longer wavelengths.

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Classical vs. Quantum Mechanics

Classical mechanics describes the motion of large objects, while quantum mechanics describes the behavior of very small particles like electrons.

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Energy Quanta

Energy comes in discrete packets called quanta, not as a continuous flow.

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Study Notes

Atomic Theory Lecture 2

  • Electron vs. Golf Ball: The wavelength of a moving object is inversely proportional to its momentum. Momentum is mass times velocity. Electrons have a much larger wavelength compared to a golf ball, due to their much smaller mass. Electrons' motion is better described by quantum mechanics, while large bodies are better described by classical mechanics.

Energy Quantization

  • Energy E equals h times frequency: The relationship between the temperature of a black body and the intensity of energy it emits as radiation is stepwise. Each step is a quantum.

Photoelectric Effect

  • Classical theory: Classical theory predicted that increasing light intensity would increase the energy of ejected electrons, but this was not observed.
  • Minimum energy required: An electron is only ejected if the incoming light has a minimum energy.
  • Number of ejected electrons: The number of ejected electrons is proportional to the light intensity.

Quantum or Wave Mechanics

  • Schrödinger's Wave Equation: Schrödinger applied the idea of electrons behaving as waves to the problem of electrons in atoms, creating the wave equation.
  • Wave Functions: Solutions to the wave equation are mathematical expressions called wave functions. These specify the probability of finding an electron in a particular space.

Uncertainty Principle

  • Defining energy/position of electrons: The problem of precisely defining the energy and position of electrons in atoms was solved by Heisenberg.
  • Position and momentum: You cannot simultaneously and precisely define both the position and momentum of an electron.
  • Defined properties: Chemists can define the energy of an electron precisely, but accept limitations in defining its exact position.

Born's Interpretation

  • Probability of finding an electron: Born's interpretation states that the square of the wave function(probability) is proportional to the probability of finding an electron in a certain portion of space, determined by quantum numbers.

Wave Motion

  • Nodes and Wavelength: Wave motion demonstrates different levels, with each level corresponding to a fraction of a complete wavelength (e.g., 1/2 λ, 1λ, 3/2 λ). Nodes are points where there is no movement or disturbance in the wave.

Quantum Numbers

  • Wave functions and electron energy: Not all wave functions are valid solutions to the Schrödinger equation.
  • Quantized electrons: Experiments prove that electrons and their energy levels are quantized.
  • Spatial Constraints (orbitals): Quantum numbers represent spatial constraints (or limit areas) where wave functions are valid. This means there's a high probability of finding electrons within those areas.

Shells and Subshells

  • Principal Quantum Number: Each shell is associated with a principal quantum number (n), which represents the period (or row) in the periodic table where that shell begins electron filling.
  • Sublevels grouped in shells: Subshells are grouped in shells.
  • Quantum Numbers define areas: Quantum numbers define the shell(limit area) and subshells(orbitals within the shell) where orbitals (and there is a high probability of finding electrons)

Quantum Numbers (continued)

  • Principal Quantum Number (n): n = 1, 2, 3, ... represents the shell
  • Angular Momentum Quantum Number (l): l = 0, 1, 2, ..., (n – 1) defines subshells (s, p, d, f, ...).
  • Magnetic Quantum Number (ml): ml = -l, -(l-1), ..., 0, ..., (l-1), l defines orbitals within a subshell.

Shells and Subshells (details)

  • Energy levels depend on n: Energy level of an electron's orbital in a hydrogen or single-electron atom depends only on the principal quantum number (n).

  • Subshells contain orbitals: Each shell contains a number of subshells (e.g., one in n = 1, two in n = 2, etc.). Each subshell contains a specific number of orbitals (2l + 1).

Electron Spin

  • Fourth Quantum Number: Electron spin (ms) is a property of the electron and can be +1/2 for spin "up" and -1/2 for spin "down".

Quantum Numbers, Orbitals, and Electrons

  • Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers. This means that electrons in an orbital must have different spin values.
  • Description of orbitals/electrons: Empty orbitals are entirely described by the three quantum numbers (n, l, ml) while electrons in an orbital are described by all four quantum numbers (n, l, ml, ms).

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