SPS 101 Principles Quiz on Orbital Energy

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Questions and Answers

What does the principal quantum number (n) represent in Bohr's model?

The energy of the atom

The allowed energy levels of an electron (correct)

The mass of the electron

The charge of the nucleus

What is the Rydberg constant (R_H) value used in Bohr's energy equation?

3.00 × 10^8 J

6.63 × 10^-34 J

1.60 × 10^-19 J

2.18 × 10^-18 J (correct)

What happens to an electron when an atom emits electromagnetic radiation?

The electron is destroyed

The electron's mass increases

The electron moves to a higher energy level

The electron moves to a lower energy level (correct)

According to de Broglie, what is the relationship between wavelength and kinetic energy of an electron?

Higher kinetic energy results in a shorter wavelength Signup and view all the answers

Which physicists contributed to the quantum theory of the atom?

Louis de Broglie, Werner Heisenberg, and Erwin Schrödinger Signup and view all the answers

What characterizes the spectral lines produced when an electron transitions between energy states?

They correspond to specific frequency changes Signup and view all the answers

What occurs when an atom is in its ground state according to Bohr's model?

It remains stable without emitting or absorbing radiation Signup and view all the answers

How does the speed of an electron affect its wavelength according to de Broglie's hypothesis?

Faster electrons have a shorter wavelength Signup and view all the answers

Which principle states that a maximum of two electrons may occupy the same orbital with opposite spins?

Pauli Exclusion Principle Signup and view all the answers

Which of the following electron configurations represents neon?

1s2 2s2 2p6 Signup and view all the answers

According to Hund's Rule, how should electrons be arranged in degenerate orbitals?

One electron should be placed in each orbital before pairing. Signup and view all the answers

What happens when two electrons occupy separate orbitals of equal energy?

They have a lower repulsive interaction. Signup and view all the answers

Which element is represented by the electron configuration 1s2 2s2 2px2 2py1 2pz1?

Oxygen Signup and view all the answers

Which of the following orbital diagrams demonstrates the filling of orbitals according to Hund's Rule for oxygen?

Electrons are distributed among 2px, 2py with one paired in 2pz. Signup and view all the answers

What is the main objective of Hund's Rule in electron configuration?

To minimize electron repulsion among electrons. Signup and view all the answers

Which of the following orbital configurations represents an incorrect arrangement for an atom according to the exclusion principle?

2px3 Signup and view all the answers

What does the wave function 𝜓 represent in relation to electrons in an atom?

The wave properties of the electron Signup and view all the answers

How is the probability of finding an electron in an atomic orbital determined?

By the density of the electron cloud Signup and view all the answers

What can be deduced from the wave function regarding an atomic orbital?

Its shape and orientation in space Signup and view all the answers

Which quantum number describes the energy level of an electron?

Principal quantum number (n) Signup and view all the answers

What does a high electron density in an electron cloud diagram indicate?

High probability of finding the electron Signup and view all the answers

What does a dotted circle in an electron cloud diagram represent?

The volume with a 90% probability of finding the electron Signup and view all the answers

What does the angular momentum quantum number (l) indicate?

The shape of the atomic orbital Signup and view all the answers

Which of these is NOT a quantum number used to describe electron properties?

Energy quantum number (e) Signup and view all the answers

What is the order of increasing energy sublevels within a principal level?

ns < np < nd < nf < ng Signup and view all the answers

What are the possible values of the magnetic quantum number (ml) if l = 3?

-3, -2, -1, 0, 1, 2, 3 Signup and view all the answers

How many orbitals are present in a d subshell (l = 2)?

5 Signup and view all the answers

In terms of orientation, how many different p orbitals exist?

3 Signup and view all the answers

What does the spin quantum number (ms) represent?

The magnetic behavior of electrons Signup and view all the answers

If an electron spins clockwise, what is its spin quantum number?

+1/2 Signup and view all the answers

For an s subshell, how many orbitals are there?

1 Signup and view all the answers

What is the total number of orbitals in a principal level with l = 2?

5 Signup and view all the answers

What does the de Broglie relation express?

The relationship between a particle's mass, velocity, and wavelength. Signup and view all the answers

What is the formula for calculating the wavelength (λ) according to de Broglie's relation?

$λ = \frac{h}{mν}$ Signup and view all the answers

What does the Heisenberg uncertainty principle state?

Position and momentum cannot both be known accurately at the same time. Signup and view all the answers

What do Δx and Δp represent in the context of the uncertainty principle?

The uncertainties in position and momentum, respectively. Signup and view all the answers

Who developed the equation to describe the behavior and energy of electrons in atoms?

Erwin Schrödinger Signup and view all the answers

What challenge does the Heisenberg uncertainty principle address?

The overlapping properties of waves and particles. Signup and view all the answers

In the de Broglie relation, what is the value of Planck's constant (h)?

$6.626 \times 10^{-34} J.s$ Signup and view all the answers

What is the result of knowing a particle's position more precisely according to the uncertainty principle?

The momentum measurement must become less precise. Signup and view all the answers

Study Notes

Energy Levels and Sublevels

Sublevels increase in energy as follows: ns < np < nd < nf < ng.
For principal quantum number n = 1: only the 1s sublevel exists; n = 2 includes 2s and 2p; n = 3 includes 3s, 3p, and 3d; n = 4 includes 4s, 4p, 4d, and 4f.

Magnetic Quantum Number (ml)

Determines the orientation of atomic orbitals relative to the nucleus.
Allowed values of ml vary from –l to +l.
The number of ml values corresponds to the number of orbitals in a subshell, calculated using (2l + 1).
Example for l = 1 (p subshell): three p orbitals with ml values of -1, 0, and +1.

Spin Quantum Number (ms)

Describes the spin and magnetic behavior of electrons, indicating rotation along their own axis.
Electrons can have two spin states: spin up (½) and spin down (-½).
Only two electrons may occupy the same orbital, requiring opposite spins.

Electron Configuration

Follows the exclusion principle for assigning electrons to orbitals.
Example configurations:
- Hydrogen (H): 1s¹
- Helium (He): 1s²
- Neon (Ne): 1s² 2s² 2p⁶.

Hund’s Rule

States that degenerate orbitals are first filled with one electron each before pairing occurs.
Fewer repulsive interactions occur when electrons are distributed in separate orbitals.

Bohr's Model of the Hydrogen Atom

Allowed energy states of the H electron are expressed as: [ E_n = -R_H \left( \frac{1}{n^2} \right) ]
Rydberg constant ( R_H = 2.18 \times 10^{-18} ) J.
Transitions between energy levels involve absorption or emission of electromagnetic radiation, corresponding to spectral lines.

Quantum Theory of the Atom

Developed through contributions from Louis de Broglie, Werner Heisenberg, and Erwin Schrödinger.
Explains electron behavior in atoms and their role in chemical and physical properties.

de Broglie Relation

Proposes that particles, like electrons, exhibit wave properties, connecting wave properties to kinetic energy.
Wavelength (( \lambda )) associated with mass (m) and velocity (v): [ \lambda = \frac{h}{mv} ] where ( h = 6.626 \times 10^{-34} ) J.s.

Heisenberg Uncertainty Principle

States that one cannot precisely know both the position and momentum of a particle simultaneously.
Expressed mathematically as: [ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} ]

Schrödinger Equation

Developed in 1926 to describe electron behavior and energy in atoms: [ H\psi = E\psi ]
The wave function (( \psi )) represents a region of space with a high probability of finding an electron.
The electron cloud diagram shows areas of varying electron density, indicating probabilities of electron location.

Quantum Numbers

Four quantum numbers describe electrons:
- Principal quantum number (n) indicates energy level.
- Angular momentum quantum number (l) relates to subshell type.
- Magnetic quantum number (ml) defines orbital orientation.
- Spin quantum number (ms) specifies electron spin direction.

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Description

Test your understanding of the increasing energy levels of sublevels within a principal energy level in atomic structure. This quiz covers the organization of orbitals from ns to ng as well as the arrangement of n values and their corresponding l sublevels. Perfect for reinforcing concepts in quantum chemistry.