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SHANAL Practice Exams with Step-by-Step
Solutions | PDF Download
1. Which of the following best describes the wave-particle
duality of an electron?
Answer: Electrons exhibit both wave-like and particle-like
properties depending on the experiment.
Rationale: Wave-particle duality is a central concept of quantum
mechanics. In the double-slit experiment, electrons produce an
interference pattern (wave behavior), but they also strike the
detector as discrete particles (particle behavior).
2. What is the maximum number of electrons that can occupy
the n=3 shell?
Answer: 18 electrons.
Rationale: The maximum number of electrons in a shell is given by
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2n². For n=3, 2(3)² = 18. This includes the 3s (2), 3p (6), and 3d
(10) subshells.
3. Which set of quantum numbers is allowed? (n, l, m_l, m_s)
Answer: (3, 2, 0, +½)
Rationale: For n=3, l can be 0,1,2. For l=2, m_l ranges from –2
to +2, so 0 is allowed. m_s is ±½. Other choices may violate the
Pauli exclusion principle or quantum number rules.
4. Calculate the wavelength of a photon emitted when an
electron in a hydrogen atom falls from n=4 to n=2. (R_H =
1.097 × 10⁷ m⁻¹)
Answer: 486 nm
Rationale: Use 1/λ = R_H (1/n₁² – 1/n₂²) = 1.097×10⁷ (1/4 –
1/16) = 1.097×10⁷ (0.25 – 0.0625) = 1.097×10⁷ × 0.1875 =
2.057×10⁶ m⁻¹. λ = 1/(2.057×10⁶) = 4.86×10⁻⁷ m = 486 nm
(blue-green light, Balmer series).
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5. Which of the following statements about the Heisenberg
uncertainty principle is true?
Answer: It is impossible to simultaneously know both the exact
position and exact momentum of an electron.
Rationale: Δx·Δp ≥ ħ/2. The more precisely position is known, the
less precisely momentum is known. This is a fundamental limit, not
a measurement error.
6. How many orbitals are in the 4d subshell?
Answer: 5 orbitals.
Rationale: The d subshell (l=2) has five orbitals corresponding to
m_l = –2, –1, 0, +1, +2.
7. What is the ground-state electron configuration of a neutral
phosphorus atom (atomic number 15)?
Answer: 1s² 2s² 2p⁶ 3s² 3p³
Rationale: Phosphorus has 15 electrons. The order of filling
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follows the Aufbau principle: 1s² (2), 2s² (4), 2p⁶ (10), 3s² (12),
3p³ (15).
8. Which element has the electron configuration [Ar] 4s² 3d¹⁰
4p⁴?
Answer: Selenium (Se, atomic number 34).
Rationale: [Ar] accounts for 18 electrons. Adding 2 (4s²) + 10
(3d¹⁰) + 4 (4p⁴) = 34 total electrons, which is selenium.
9. Which of the following transitions in a hydrogen atom
emits the highest energy photon?
Answer: n=5 → n=1
Rationale: Energy difference ΔE ∝ (1/n_f² – 1/n_i²). The largest
ΔE occurs when n_f = 1 (ground state) and n_i is large. n=5→1
has greater energy than n=4→1, n=3→2, etc.
10. What is the de Broglie wavelength of an electron moving
at 2.0 × 10⁶ m/s? (mass of electron = 9.11 × 10⁻³¹ kg, h =
SHANAL Practice Exams with Step-by-Step
Solutions | PDF Download
1. Which of the following best describes the wave-particle
duality of an electron?
Answer: Electrons exhibit both wave-like and particle-like
properties depending on the experiment.
Rationale: Wave-particle duality is a central concept of quantum
mechanics. In the double-slit experiment, electrons produce an
interference pattern (wave behavior), but they also strike the
detector as discrete particles (particle behavior).
2. What is the maximum number of electrons that can occupy
the n=3 shell?
Answer: 18 electrons.
Rationale: The maximum number of electrons in a shell is given by
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2n². For n=3, 2(3)² = 18. This includes the 3s (2), 3p (6), and 3d
(10) subshells.
3. Which set of quantum numbers is allowed? (n, l, m_l, m_s)
Answer: (3, 2, 0, +½)
Rationale: For n=3, l can be 0,1,2. For l=2, m_l ranges from –2
to +2, so 0 is allowed. m_s is ±½. Other choices may violate the
Pauli exclusion principle or quantum number rules.
4. Calculate the wavelength of a photon emitted when an
electron in a hydrogen atom falls from n=4 to n=2. (R_H =
1.097 × 10⁷ m⁻¹)
Answer: 486 nm
Rationale: Use 1/λ = R_H (1/n₁² – 1/n₂²) = 1.097×10⁷ (1/4 –
1/16) = 1.097×10⁷ (0.25 – 0.0625) = 1.097×10⁷ × 0.1875 =
2.057×10⁶ m⁻¹. λ = 1/(2.057×10⁶) = 4.86×10⁻⁷ m = 486 nm
(blue-green light, Balmer series).
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5. Which of the following statements about the Heisenberg
uncertainty principle is true?
Answer: It is impossible to simultaneously know both the exact
position and exact momentum of an electron.
Rationale: Δx·Δp ≥ ħ/2. The more precisely position is known, the
less precisely momentum is known. This is a fundamental limit, not
a measurement error.
6. How many orbitals are in the 4d subshell?
Answer: 5 orbitals.
Rationale: The d subshell (l=2) has five orbitals corresponding to
m_l = –2, –1, 0, +1, +2.
7. What is the ground-state electron configuration of a neutral
phosphorus atom (atomic number 15)?
Answer: 1s² 2s² 2p⁶ 3s² 3p³
Rationale: Phosphorus has 15 electrons. The order of filling
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follows the Aufbau principle: 1s² (2), 2s² (4), 2p⁶ (10), 3s² (12),
3p³ (15).
8. Which element has the electron configuration [Ar] 4s² 3d¹⁰
4p⁴?
Answer: Selenium (Se, atomic number 34).
Rationale: [Ar] accounts for 18 electrons. Adding 2 (4s²) + 10
(3d¹⁰) + 4 (4p⁴) = 34 total electrons, which is selenium.
9. Which of the following transitions in a hydrogen atom
emits the highest energy photon?
Answer: n=5 → n=1
Rationale: Energy difference ΔE ∝ (1/n_f² – 1/n_i²). The largest
ΔE occurs when n_f = 1 (ground state) and n_i is large. n=5→1
has greater energy than n=4→1, n=3→2, etc.
10. What is the de Broglie wavelength of an electron moving
at 2.0 × 10⁶ m/s? (mass of electron = 9.11 × 10⁻³¹ kg, h =
