L5-Atomic orbitals & Quantum numbers

What is the Schrödinger Wave Equation primarily used for?

To describe both the particle and wave nature of the electron.

For which atom can the Schrödinger equation be solved exactly?

The hydrogen atom and one-electron ions.

What do the first three quantum numbers define?

Different atomic orbitals that electrons can occupy.

What does the principal quantum number (n) determine in a hydrogen atom?

The energy of an orbital and the distance of the electron from the nucleus.

What is the angular momentum quantum number (l) associated with?

The shape of the volume of space (orbital) occupied by the electron.

How many types of orbitals correspond to l = 0, 1, 2, and 3?

l = 0 (s orbital), l = 1 (p orbitals), l = 2 (d orbitals), l = 3 (f orbitals).

What does the magnetic quantum number (ml) indicate?

The orientation of the orbital in space. -ml is the magnetic quantum number for a given value of l

What are the possible values for the spin quantum number (ms)?

Only two values: +1/2 and -1/2.

What is the significance of nodes in atomic orbitals?

Regions where the electron density is zero.

What are radial nodes?

Spherical regions where the probability density is zero.(can be radial or angular), all orbitals apart from the 1s feature nodes(radial nodes are spherical)

What are angular nodes?

Planar regions where the electron probability density is zero, associated with the shape of the orbital (can be radial or angular)

How is the number of radial nodes calculated?

Number of radial nodes = n - 1 - l.

What is the relationship between wavefunctions and electron density?

The square of the wavefunction (Ψ) indicates the probability density of finding an electron.

What does the radial probability distribution show?

The likelihood of finding an electron at various distances from the nucleus.

What is the role of quantum numbers in describing electrons?

They uniquely characterize the state of an electron in an atomic orbital.

What does the term 'electron configuration' refer to?

The distribution of electrons among various orbitals in an atom.

What is a key feature of standing waves in atomic orbitals?

They exhibit nodes where the electron density is zero.

What is the significance of the boundary surface diagrams for orbitals?

They illustrate the regions enclosing about 90% of the total electron density.

What does a higher principal quantum number (n) indicate about an orbital?

It indicates that the orbital is larger and further from the nucleus.

What is the maximum number of electrons that can occupy an orbital?

Two electrons, each with opposite spins.

What does the wavefunction (Ψ) define about an electron?

Where the electron can be found and its energy.

What does the wavefunction determine

-Energy of the electron

-Where to find the electron(probability of finding an electron in a certain region)

What does the fourth quantum number define

The behaviour of a specific electron in an atomic orbital

Why was the ms (spin quantum number) introduced

-Electrons have an intrinsic magnetic moment causing the electron to behave as if it was spinning, creating a magnetic field

-Introduced to describe the orientation of the electron in space

Radial Probability

Shows shift for orbitals further away from nucleus (with higher n)