GATE Life Sciences Atomic Structure and Periodicity Syllabus

What is the physical meaning of the wavefunction $\psi$ and of $\psi^{2}$ in the quantum mechanical model?

$\psi$ itself has no direct physical meaning, but $\psi^{2}$ gives the probability density of finding the electron at a given point in space.

Define an orbital in the quantum mechanical model.

An orbital is a three-dimensional region around the nucleus where the probability of finding an electron is maximum (typically ~90–95%).

Write the ground-state electronic configuration of a neutral chlorine atom ($Z = 17$).

$\ce{Cl}$: $1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{5}$.

State the Aufbau principle for filling atomic orbitals.

Electrons occupy the available orbitals in order of increasing energy, filling the lowest-energy orbital first before moving to higher-energy ones.

State the $(n + l)$ rule used to determine the order of orbital filling.

Orbitals fill in order of increasing $(n + l)$ value. If two orbitals have the same $(n + l)$, the one with the lower $n$ is filled first.

Write the electronic configuration of the $\ce{Fe^{2+}}$ ion ($Z$ of Fe $= 26$).

$\ce{Fe^{2+}}$: $1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{6}\,3d^{6}$ (the two $4s$ electrons are removed first).

When forming a cation from a transition metal, from which subshell are electrons removed first?

Electrons are removed first from the subshell with the highest principal quantum number $n$, i.e. the $ns$ electrons are removed before the $(n-1)d$ electrons.

State Hund's rule of maximum multiplicity.

Electrons fill degenerate (equal-energy) orbitals singly with parallel spins first, and pairing begins only after each orbital in the subshell has one electron.

Why is the half-filled $p^{3}$ configuration relatively stable according to Hund's rule?

Because all three electrons occupy separate orbitals with parallel spins, giving maximum exchange energy and minimum electron-electron repulsion, resulting in extra stability.

State Pauli's exclusion principle.

No two electrons in an atom can have the same set of all four quantum numbers ($n$, $l$, $m_l$, $m_s$); thus an orbital can hold at most two electrons with opposite spins.

What is the maximum number of electrons that can be accommodated in a shell with principal quantum number $n$, as a consequence of Pauli's principle?

$2n^{2}$ electrons.

How many electrons can a single orbital hold, and what must be true of their spins?

A single orbital holds a maximum of 2 electrons, and they must have opposite (antiparallel) spins, $m_s = +\tfrac{1}{2}$ and $-\tfrac{1}{2}$.

Write the anomalous ground-state configuration of chromium ($Z = 24$) and explain why.

$\ce{Cr}$: $[\text{Ar}]\,3d^{5}\,4s^{1}$ instead of $3d^{4}\,4s^{2}$, because the half-filled $3d^{5}$ and $4s^{1}$ arrangement gives extra exchange-energy stability.

Write the anomalous ground-state configuration of copper ($Z = 29$) and explain why.

$\ce{Cu}$: $[\text{Ar}]\,3d^{10}\,4s^{1}$ instead of $3d^{9}\,4s^{2}$, because a completely filled $3d^{10}$ subshell confers extra stability.

Define ionization energy (ionization enthalpy).

The minimum energy required to remove the most loosely bound electron from an isolated neutral gaseous atom in its ground state: $\ce{X(g) -> X^{+}(g) + e^{-}}$.

How does first ionization energy generally vary across a period (left to right) and down a group?

It generally increases across a period (due to increasing nuclear charge and decreasing size) and decreases down a group (due to increasing atomic size and shielding).

Why is the second ionization energy always greater than the first ionization energy of an element?

Removing an electron from a positively charged cation is harder because the remaining electrons experience a greater effective nuclear charge and are held more tightly.

Why is the first ionization energy of nitrogen higher than that of oxygen?

Nitrogen has a stable half-filled $2p^{3}$ configuration which resists electron removal, whereas oxygen ($2p^{4}$) has one paired electron whose repulsion makes it easier to remove.

Why is the first ionization energy of beryllium higher than that of boron?

Beryllium has a stable fully-filled $2s^{2}$ configuration, while boron's electron is removed from the higher-energy, less penetrating $2p$ orbital, requiring less energy.

Define electron affinity (electron gain enthalpy).

The energy change when an electron is added to an isolated neutral gaseous atom to form a negative ion: $\ce{X(g) + e^{-} -> X^{-}(g)}$. A more negative value indicates greater attraction for the electron.

How does electron affinity generally vary across a period and down a group?

Electron affinity generally becomes more negative (electron gain more favorable) across a period left to right, and becomes less negative down a group.

Why is the electron affinity of chlorine more negative (higher) than that of fluorine?

Fluorine's small size causes strong electron-electron repulsion in its compact $2p$ subshell, so the incoming electron is less readily accommodated than in the larger chlorine atom.

Why do noble gases have electron affinity values that are positive (or nearly zero)?

They have stable, completely filled valence shells ($ns^{2}np^{6}$); adding an electron requires energy and is unfavorable.

Define electronegativity.

Electronegativity is the relative tendency of an atom in a chemical bond to attract the shared pair of bonding electrons toward itself.

Name the most electronegative element and give its value on the Pauling scale.

Fluorine is the most electronegative element, with a Pauling electronegativity of $4.0$.

How does electronegativity vary across a period and down a group?

It increases across a period (left to right) due to increasing nuclear charge and decreasing size, and decreases down a group due to increasing atomic size and shielding.

State two key differences between electronegativity and electron affinity.

Electron affinity is a measurable energy change for an isolated gaseous atom gaining an electron, whereas electronegativity is a relative, dimensionless property of an atom within a bond. Electron affinity has energy units; electronegativity does not.

Define atomic radius (atomic size).

Atomic radius is the distance from the nucleus to the outermost shell of electrons; it is commonly measured as covalent radius, metallic radius, or van der Waals radius.

How does atomic size vary across a period and down a group?

Atomic size decreases across a period left to right (increasing effective nuclear charge pulls electrons inward) and increases down a group (addition of new shells increases the radius).

Compare the size of a cation and an anion with their respective neutral parent atoms.

A cation is smaller than its parent atom (fewer electrons, higher effective nuclear charge per electron), while an anion is larger than its parent atom (more electrons, increased electron-electron repulsion).

For an isoelectronic series, how does ionic radius depend on nuclear charge? Illustrate with $\ce{N^{3-}}$, $\ce{O^{2-}}$, $\ce{F^{-}}$, $\ce{Na^{+}}$, $\ce{Mg^{2+}}$.

In an isoelectronic series, ionic radius decreases as nuclear charge (atomic number) increases. Thus size order is $\ce{N^{3-}} > \ce{O^{2-}} > \ce{F^{-}} > \ce{Na^{+}} > \ce{Mg^{2+}}$.