Chapter 2: Structure of Atom Long Questions | chemistry Class 11 CBSE

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Chapter 2: Structure of Atom Long Questions | chemistry Class 11 CBSE | ByteNotes.in

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Question 1

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Compare and contrast Thomson's model, Rutherford's nuclear model, and Bohr's model of the atom, highlighting the experimental evidence that led to each model and the drawbacks that necessitated the next.

Thomson's 'plum pudding' model (1898) described the atom as a uniform positive sphere of radius ~10^-10 m with electrons embedded like plums, explaining overall electrical neutrality but assuming mass was evenly distributed.
Rutherford's alpha-particle scattering experiment (1909) disproved Thomson's model: most alpha particles passed undeflected (atom is mostly empty), a few deflected greatly (positive charge concentrated in tiny nucleus of radius ~10^-15 m), and electrons orbit in circular paths held by electrostatic attraction.
Rutherford's model failed because an orbiting (accelerating) electron should radiate energy continuously (per Maxwell's theory) and spiral into the nucleus within ~10^-8 s, predicting atomic collapse; it also gave no information about electron energies or distribution.
Bohr resolved stability by quantising angular momentum (mevr = nh/2π) and energy (En = −RH/n²), allowing only fixed orbits and restricting radiation to transitions between orbits; energy levels and spectral lines of hydrogen were successfully predicted.
Bohr's model failed for multi-electron atoms, fine spectral structure, Zeeman and Stark effects, and contradicted both wave-particle duality of matter and the Heisenberg uncertainty principle by assuming definite electron paths.
The quantum mechanical model (Schrödinger, 1926) overcame all these failures by treating the electron as a wave (de Broglie), accepting fundamental uncertainty in position/momentum (Heisenberg), and describing electrons through probabilistic wave functions (orbitals).

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Question 2

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Describe the quantum mechanical model of the atom. Discuss its five important features and explain how it differs fundamentally from Bohr's model.

The quantum mechanical model is based on Schrödinger's equation ĤΨ = EΨ, which accounts for the wave-particle duality of matter and the Heisenberg uncertainty principle; it gives quantised energy levels and wave functions (Ψ) for electrons.
Feature 1: Electron energy in atoms is quantised — electrons can only have specific energy values when bound to the nucleus; Feature 2: quantised energy levels arise directly from the wave-like properties of electrons as allowed solutions of Schrödinger's equation.
Feature 3: Both exact position and exact velocity of an electron cannot be simultaneously determined (Heisenberg); the electron's path in an atom is therefore unknowable, and we speak only of the probability of finding the electron at various points.
Feature 4: An atomic orbital is defined as the wave function Ψ for an electron, characterised by quantum numbers n, l, ml; each orbital holds at most two electrons; in multi-electron atoms, electrons fill orbitals in order of increasing energy.
Feature 5: |Ψ|² (probability density) at any point gives the probability per unit volume of finding the electron; regions of high |Ψ|² indicate where the electron is most probably found.
Unlike Bohr's model (which assumed definite circular orbits and ignored wave character), the quantum mechanical model treats electrons as quantum waves with no defined trajectory, uses probabilistic descriptions, applies to all atoms, and correctly predicts all observed spectral phenomena including those Bohr could not explain.

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Question 3

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Describe the shapes of s, p, and d atomic orbitals as represented by boundary surface diagrams. How do the number of nodes relate to the quantum numbers?

Boundary surface diagrams enclose the region where the probability of finding the electron is about 90%; the shape of this enclosed region represents the orbital shape. s-orbitals (l=0) are spherical and spherically symmetric for all values of n; size increases as 1s < 2s < 3s.
p-orbitals (l=1) consist of two lobes (dumbbell-shaped) on either side of a nodal plane through the nucleus; there are three p-orbitals (px, py, pz) with mutually perpendicular axes, identical in size, shape, and energy but differing in orientation.
d-orbitals (l=2) have five orientations (dxy, dyz, dxz, dx²−y², dz²); the first four have four lobes between the axes, while dz² has two lobes along z and a ring in the xy-plane; all five 3d orbitals are equivalent in energy.
Nodes are regions of zero probability density. Angular nodes (planes through the nucleus) = l; radial nodes (spherical surfaces) = n − l − 1; total nodes = n − 1.
For example, 2p (n=2, l=1): 1 angular node, 0 radial nodes (total=1); 3d (n=3, l=2): 2 angular nodes, 0 radial nodes (total=2); 3s (n=3, l=0): 0 angular nodes, 2 radial nodes (total=2).
As the principal quantum number increases, both the size of the orbital and the number of nodes increase; increasing l within a shell adds more angular nodes and changes orbital shape from spherical (l=0) to increasingly complex geometries.

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Question 4

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Explain the electronic configuration of atoms using the aufbau principle, Pauli's exclusion principle, and Hund's rule. Write the configurations of N (Z=7), Fe (Z=26), and Cu (Z=29).

Aufbau principle: electrons fill orbitals in order of increasing energy — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p… — determined by the (n+l) rule; electrons occupy the lowest available energy orbital.
Pauli's exclusion principle: no two electrons in an atom can have the same set of four quantum numbers; each orbital can accommodate at most two electrons with opposite spins (+½ and −½).
Hund's rule: electrons occupy each degenerate orbital singly with parallel spins before any pairing begins; pairing in p, d, or f orbitals starts with the 4th, 6th, and 8th electrons respectively.
Nitrogen (Z=7): 1s²2s²2p³ — three 2p electrons each occupy separate 2p orbitals with parallel spins, giving a half-filled p subshell with extra stability.
Iron (Z=26): [Ar]3d⁶4s² — five 3d electrons are singly filled, and the 6th pairs with one; 4s has 2 electrons; total = 18 (Ar) + 8 = 26.
Copper (Z=29): [Ar]3d¹⁰4s¹ (exception — not 3d⁹4s²) because a fully-filled 3d¹⁰ subshell is more stable; one electron shifts from 4s to 3d to achieve this extra stability from symmetrical distribution and maximum exchange energy.

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Question 5

Long Form

Analyse the photoelectric effect experimentally and theoretically. How did Einstein's explanation using Planck's quantum theory resolve the failures of classical physics?

Experimental observations of the photoelectric effect: (i) electron ejection is instantaneous when light strikes the metal surface — no time lag; (ii) number of ejected electrons is proportional to light intensity; (iii) kinetic energy of ejected electrons increases with frequency but not intensity; (iv) below a threshold frequency ν₀, no electrons are ejected regardless of intensity.
Classical physics predicted that any frequency of light, given sufficient intensity, should eventually eject electrons (since energy depends on intensity). It could not explain the existence of a threshold frequency or the instantaneous ejection.
Einstein (1905) used Planck's quantum theory: light consists of photons, each carrying energy E = hν. A single photon interacts with a single electron; if hν ≥ hν₀ (work function W₀), the electron is ejected instantaneously.
The kinetic energy of the ejected electron is: KE = hν − hν₀ = hν − W₀. Greater frequency means more energy per photon and thus higher KE of ejected electrons, explaining why KE depends on frequency not intensity.
Higher intensity means more photons (not more energetic), so more electrons are ejected (explaining intensity–number relationship), but KE per electron stays the same.
Einstein's photon model thus fully explains all observed features: instantaneous ejection (one photon–one electron collision), threshold frequency (minimum photon energy needed), KE–frequency relationship, and intensity–number relationship. He received the Nobel Prize in Physics in 1921 for this explanation.

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Question 6

Long Form

Describe how Bohr's model of hydrogen explains the line spectrum of hydrogen. Derive an expression for the wavenumber of spectral lines and identify the Balmer series.

Bohr postulated that electrons move in quantised orbits with energy En = −RH/n² (RH = 2.18 × 10^-18 J). When an electron transitions from a higher orbit (ni) to a lower orbit (nf), it emits a photon; energy absorbed corresponds to the reverse.
The energy difference between orbits: ΔE = RH(1/ni² − 1/nf²) for emission (ni > nf). The frequency of emitted radiation: ν = ΔE/h = (RH/h)(1/nf² − 1/ni²).
In terms of wavenumber: ν̄ = ν/c = (RH/hc)(1/nf² − 1/ni²) = 1.09677 × 10⁷(1/n₁² − 1/n₂²) m⁻¹, where RH/hc = 109,677 cm⁻¹ is the Rydberg constant.
Lyman series: nf=1, ni=2,3…, UV region; Balmer series: nf=2, ni=3,4…, visible region; Paschen: nf=3, infrared; Brackett: nf=4, infrared; Pfund: nf=5, infrared.
The Balmer series is the only hydrogen series in the visible region; Balmer empirically showed ν̄ = 109,677(1/2² − 1/n²) cm⁻¹ (n ≥ 3); Bohr's theory derived this formula theoretically from first principles.
The intensity of spectral lines depends on the number of photons of that wavelength emitted, which depends on the population of atoms undergoing that transition; Bohr's model matched the empirical Rydberg formula perfectly, validating its concept of quantised energy levels.

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Question 7

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Discuss the four quantum numbers of an electron in detail, including their allowed values, physical significance, and how they collectively define an electron's state in an atom.

Principal quantum number (n): positive integer (1, 2, 3…); determines the size and largely the energy of the orbital; identifies the shell (K, L, M, N…); number of orbitals per shell = n²; maximum electrons = 2n²; energy increases with n.
Azimuthal quantum number (l): values 0 to (n−1); determines the shape of the orbital and identifies the subshell (l=0: s, l=1: p, l=2: d, l=3: f); number of orbitals per subshell = (2l+1); also influences energy in multi-electron atoms (energy order: s < p < d < f).
Magnetic quantum number (ml): values −l to +l (total 2l+1 values); specifies the spatial orientation of the orbital relative to a coordinate axis; for example, l=1 gives ml = −1, 0, +1 (three p-orbitals in perpendicular orientations).
Spin quantum number (ms): values +½ or −½, representing the two spin states of the electron (spin up ↑ or spin down ↓); describes the intrinsic angular momentum of the electron; proposed by Uhlenbeck and Goudsmit in 1925.
Together, all four quantum numbers completely specify the state of an electron: n gives size/energy, l gives shape, ml gives orientation, ms gives spin; by Pauli's principle, no two electrons in an atom can share the same set of all four quantum numbers.
The four quantum numbers arise naturally as solutions to the Schrödinger equation for hydrogen; three (n, l, ml) characterise the orbital wave function, while ms describes the additional property of spin, needed to explain doublet spectral lines in multi-electron atoms.

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Question 8

Long Form

Explain why completely filled and half-filled subshells show extra stability. Illustrate with reference to Cr and Cu electronic configurations.

Completely filled and half-filled subshells show extra stability due to two main reasons: (1) symmetrical distribution of electrons, and (2) maximum exchange energy.
Symmetrical distribution: a half-filled or completely-filled subshell has equal electron density in all orbitals of that subshell; this symmetry reduces inter-electron repulsion and increases effective nuclear attraction, lowering the overall energy and raising stability.
Exchange energy: when two electrons with the same spin are present in degenerate orbitals, they can exchange positions, releasing exchange energy. The more exchanges possible, the greater the exchange energy and the greater the stability. Exchange energy is maximum in half-filled (one electron per orbital) and fully-filled subshells.
Chromium (Z=24) expected configuration: [Ar]3d⁴4s². Actual: [Ar]3d⁵4s¹. One electron moves from 4s to 3d to achieve a half-filled 3d⁵ configuration (10 possible exchanges), which is more stable than 3d⁴ (6 exchanges) + 4s², despite the slight energy cost.
Copper (Z=29) expected: [Ar]3d⁹4s². Actual: [Ar]3d¹⁰4s¹. One electron shifts from 4s to 3d to achieve a fully-filled 3d¹⁰ configuration, gaining maximum exchange energy and symmetrical electron distribution.
This concept extends to p³, p⁶, d⁵, d¹⁰, f⁷, f¹⁴ configurations, all of which exhibit extra stability. It is important to note that exceptions do exist and the stability argument applies broadly but not universally.

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Question 9

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Discuss the wave nature of electromagnetic radiation. Explain how the electromagnetic spectrum is organised and describe the relationship between frequency, wavelength, and speed of light.

James Maxwell (1870) proposed that accelerating charged particles produce oscillating electric and magnetic fields, transmitted as electromagnetic waves; these fields are perpendicular to each other and to the direction of propagation.
Properties of electromagnetic waves: (i) do not require a medium — they travel through vacuum; (ii) travel at c = 3.0 × 10^8 m/s in vacuum regardless of frequency; (iii) obey c = νλ, where ν is frequency (Hz, s⁻¹) and λ is wavelength (m); (iv) wavenumber ν̄ = 1/λ (m⁻¹ or cm⁻¹) is also used.
The electromagnetic spectrum spans a vast range: radio waves (~10^6 Hz, λ~10² m) → microwaves (~10^10 Hz) → infrared (~10^13 Hz) → visible light (~10^15 Hz, 400–750 nm) → ultraviolet → X-rays → gamma rays (~10^24 Hz).
Visible light (detected by human eyes) is only a tiny portion (~10^15 Hz) of the full spectrum; different spectroscopic techniques detect different regions for analytical purposes.
Wave phenomena like diffraction (bending around obstacles) and interference (superposition of waves) confirm the wave character of electromagnetic radiation; these phenomena cannot be explained by a particle model.
However, wave theory alone could not explain black body radiation, the photoelectric effect, or atomic line spectra — phenomena that required Planck's quantisation hypothesis — ultimately establishing the dual wave-particle character of electromagnetic radiation.

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Question 10

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Discuss the significance of Heisenberg's uncertainty principle. Why does it rule out the concept of definite electron trajectories, and what are its practical implications for microscopic versus macroscopic objects?

Heisenberg's uncertainty principle (1927) states that the exact position (Δx) and exact momentum (Δp) of a particle cannot be simultaneously determined: Δx × Δp ≥ h/4π; the more precisely position is known, the more uncertain the momentum, and vice versa.
The principle is a fundamental consequence of the wave-particle duality of matter and radiation, not a limitation of measurement technology; it is a basic property of nature at the quantum level.
A trajectory is defined by knowing both position and velocity at each instant. Since these cannot both be precisely known for an electron simultaneously, no trajectory can be defined. Electrons cannot be assigned definite circular orbits as Bohr assumed.
For a milligram-sized object (10^-6 kg): ΔvΔx = h/4πm ≈ 10^-28 m²s⁻¹ — negligibly small and of no practical consequence; classical mechanics works perfectly for macroscopic objects.
For an electron (mass ~9.11 × 10^-31 kg): ΔvΔx ≈ 10^-4 m²s⁻¹ — extremely large; localising the electron to 10^-8 m creates velocity uncertainty of ~10^4 m/s, making Bohr's fixed-orbit picture physically meaningless.
The principle led to the replacement of deterministic (position + velocity) descriptions with probabilistic ones: we speak of the probability density |Ψ|² of finding an electron at a given point, forming the conceptual foundation of the quantum mechanical model.

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Chapter 2: Structure of Atom | Long Questions

Compare and contrast Thomson's model, Rutherford's nuclear model, and Bohr's model of the atom, highlighting the experimental evidence that led to each model and the drawbacks that necessitated the next.

Describe the quantum mechanical model of the atom. Discuss its five important features and explain how it differs fundamentally from Bohr's model.

Describe the shapes of s, p, and d atomic orbitals as represented by boundary surface diagrams. How do the number of nodes relate to the quantum numbers?

Explain the electronic configuration of atoms using the aufbau principle, Pauli's exclusion principle, and Hund's rule. Write the configurations of N (Z=7), Fe (Z=26), and Cu (Z=29).

Analyse the photoelectric effect experimentally and theoretically. How did Einstein's explanation using Planck's quantum theory resolve the failures of classical physics?

Describe how Bohr's model of hydrogen explains the line spectrum of hydrogen. Derive an expression for the wavenumber of spectral lines and identify the Balmer series.

Discuss the four quantum numbers of an electron in detail, including their allowed values, physical significance, and how they collectively define an electron's state in an atom.

Explain why completely filled and half-filled subshells show extra stability. Illustrate with reference to Cr and Cu electronic configurations.

Discuss the wave nature of electromagnetic radiation. Explain how the electromagnetic spectrum is organised and describe the relationship between frequency, wavelength, and speed of light.

Discuss the significance of Heisenberg's uncertainty principle. Why does it rule out the concept of definite electron trajectories, and what are its practical implications for microscopic versus macroscopic objects?

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