1. The maximum number of orbitals in the shell with principal quantum number n = 4 is:
- 4
- 32
- 8
- 16
Show answer and explanation
Answer: (D) 16
A shell with principal quantum number n has n² orbitals: 4² = 16.
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Answer: (D) 16
A shell with principal quantum number n has n² orbitals: 4² = 16.
Answer: (B) 12
The ground-state configuration of Cu (Z = 29) is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s¹. Electrons with azimuthal quantum number l = 1 are p-electrons. Cu contains electrons in 2p (6 electrons) and 3p (6 electrons), giving a total of 6 + 6 = 12 electrons.
Answer: (D) h² / (32π² m L²)
With Δx ≈ L, the minimum uncertainty in momentum is Δp ≈ h / (4πL). Since the momentum cannot be less than its uncertainty, p_min ≈ h / (4πL). The minimum kinetic energy is K_min = p_min² / (2m) = h² / (32π² m L²).
Answer: (A) 27 : 5
ΔE₁ = 13.6 · (1/1² - 1/2²) = 13.6 · (3/4) eV. ΔE₂ = 13.6 · (1/2² - 1/3²) = 13.6 · (5/36) eV. Ratio ΔE₁ / ΔE₂ = (3/4) / (5/36) = (3/4) · (36/5) = 27/5.
Answer: (B) [Ar] 3d⁷
Neutral cobalt has the configuration [Ar] 3d⁷ 4s². During ionization, electrons are first removed from the outermost 4s orbital before the 3d orbital, giving Co²⁺ the configuration [Ar] 3d⁷.
Answer: (A) n = 6, 6d
The number of angular nodes is l = 2, which corresponds to a d subshell. The number of radial nodes is n - l - 1 = 3. Substituting l = 2 gives n - 2 - 1 = 3, which yields n = 6. Thus, the orbital is 6d.
Answer: (B) 2h / π
The total energy is E = -KE = -0.85 eV. For hydrogen, Eₙ = -13.6 / n² eV. Setting -13.6 / n² = -0.85 gives n² = 16, so n = 4. The orbital angular momentum is L = nh / (2π) = 4h / (2π) = 2h / π.
Answer: (B) 4d < 5p < 6p < 5f
Calculate (n + l) values: for 4d, n + l = 4 + 2 = 6; for 5p, n + l = 5 + 1 = 6; for 6p, n + l = 6 + 1 = 7; for 5f, n + l = 5 + 3 = 8. Between 4d and 5p (both have n + l = 6), 4d has smaller n so lower energy (4d < 5p). Next is 6p (n + l = 7), followed by 5f (n + l = 8). Hence, the order is 4d < 5p < 6p < 5f.
Answer: (B) 600 nm
Power P = n × (hc/λ), where n is the number of photons emitted per second. Substituting the given values: 33 = 1.0 × 10²⁰ × (6.6 × 10⁻³⁴ × 3.0 × 10⁸) / λ. This gives 33 = (1.98 × 10⁻⁵) / λ, so λ = 1.98 × 10⁻⁵ / 33 = 6.0 × 10⁻⁷ m = 600 nm.
Answer: (C) v ∝ Z / n
The orbital velocity of an electron in Bohr's model is given by v = (2.18 × 10⁶) × (Z / n) m/s. Thus, velocity is directly proportional to Z and inversely proportional to n.
Answer: (D) 4
Total energy E_n = Potential Energy / 2 = -1.70 eV / 2 = -0.85 eV. Using E_n = -13.6 / n² eV, we get -0.85 = -13.6 / n², which gives n² = 13.6 / 0.85 = 16, so n = 4.
Answer: (D) Starts at a positive finite value, crosses the r-axis once, and approaches zero from negative values as r increases
For an s orbital, R(0) is finite and non-zero. Since a 2s orbital has (n - l - 1) = 2 - 0 - 1 = 1 radial node, R(r) must cross the horizontal r-axis exactly once, transitioning from positive to negative values before asymptotically reaching zero.
Answer: (D) 1 : 1
Radius of Bohr orbit is given by r ∝ n² / Z. For H (n = 1, Z = 1), r₁ = 1²/1 = 1. For Be³⁺ (n = 2, Z = 4), r₂ = 2²/4 = 1. Therefore, the ratio r(H, 1) : r(Be³⁺, 2) is 1 : 1.
Answer: (B) The electron's mass is extremely small
For macroscopic objects the uncertainties are vanishingly small. For an electron, small mass makes Δv very large, ruling out precise orbits.
NCERT Class 11
Answer: (B) E / 9
The de Broglie wavelength is related to kinetic energy by λ = h / √(2mE), so E = h² / (2mλ²). When the wavelength becomes 3λ, the kinetic energy becomes E' = h² / [2m(3λ)²] = E / 9.