Questions & explanations
1. Which of the following correctly distinguishes an 'orbit' (Bohr model) from an 'orbital' (quantum mechanical model)?
- A. An orbit is a well-defined circular path, while an orbital is a three-dimensional region where the probability of finding an electron is high.
- B. An orbit can have any radius, while an orbital has a fixed size.
- C. An orbit has a fixed energy, while an orbital does not.
- D. An orbit can hold only one electron, while an orbital can hold two electrons.
Answer: A. An orbit is a well-defined circular path, while an orbital is a three-dimensional region where the probability of finding an electron is high.
In Bohr's model, electrons move in fixed circular paths (orbits). In quantum mechanics, an orbital is a region of space around the nucleus where the probability of finding an electron is high (typically 90%). Option B is false because Bohr orbits have fixed, quantized radii. Option C is false because orbitals also have fixed energies (eigenvalues). Option D is not a fundamental distinction; the Bohr model was not defined for multiple electrons in an orbit.
2. Heisenberg's uncertainty principle states that it is impossible to simultaneously determine the exact values of which pair of properties for a subatomic particle?
- Position and momentum
- Energy and time
- Angular momentum and magnetic moment
- Kinetic energy and potential energy
Answer: Position and momentum
Heisenberg's uncertainty principle mathematically states Δx·Δp ≥ h/(4π), meaning the more precisely one measures position (x), the less precisely momentum (p) can be known, and vice versa. The other pairs are not the fundamental pair defined by the principle in its standard form, though energy-time also has an uncertainty relation, but the question specifically refers to the most commonly cited form.
3. Which of the following is a correct postulate of Bohr's model of the hydrogen atom?
- Electrons revolve in elliptical orbits around the nucleus.
- Angular momentum of the electron is quantized and is an integral multiple of h/(2π).
- Energy is emitted continuously by the electron while revolving.
- The nucleus consists of protons and neutrons.
Answer: Angular momentum of the electron is quantized and is an integral multiple of h/(2π).
Bohr's model postulates that electrons revolve only in certain allowed circular orbits where the angular momentum is quantized as n·h/(2π), where n is a positive integer. Elliptical orbits were introduced by Sommerfeld, continuous emission contradicts Bohr's quantum jumps, and the composition of the nucleus is not part of Bohr's postulates.
4. How many unpaired electrons are present in the ground state of an iron atom (Z = 26)?
- 2
- 4
- 6
- 0
Answer: 4
Iron's ground-state configuration is [Ar] 3d⁶ 4s². In the 3d subshell, according to Hund's rule, the five orbitals are first occupied singly, giving five unpaired electrons for 3d⁵. The sixth electron pairs in one orbital, leaving four orbitals with one electron each. Thus, there are 4 unpaired electrons.
5. Which of the following is a known limitation of Bohr's model of the atom?
- It accurately explains the fine structure of spectral lines.
- It accounts for the Stark effect in hydrogen.
- It violates the Heisenberg uncertainty principle.
- It predicts discrete energy levels for electrons.
Answer: It violates the Heisenberg uncertainty principle.
Bohr's model treats the electron as having a definite circular orbit with known position and momentum at the same time, which violates the Heisenberg uncertainty principle. It cannot explain fine structure or the Stark effect, and predicting discrete energy levels is actually a success, not a limitation.
6. Which statement correctly describes the effect of increasing the principal quantum number n on an atomic orbital?
- The energy becomes more negative and the orbital size decreases
- The energy becomes less negative (increases) and the orbital size increases
- The energy becomes more negative and the orbital size increases
- The energy remains constant and only the shape changes
Answer: The energy becomes less negative (increases) and the orbital size increases
As n increases, the electron is farther from the nucleus on average (size increases) and its energy is higher (less negative, closer to zero). More negative energy corresponds to lower n (more tightly bound). Thus the correct description is that energy increases (less negative) and size increases.
7. Pauli's exclusion principle states that:
- No two electrons in an atom can have the same set of all four quantum numbers.
- Electrons fill orbitals in order of increasing energy.
- Each orbital can hold a maximum of two electrons with opposite spins.
- Electrons occupy degenerate orbitals singly before pairing.
Answer: No two electrons in an atom can have the same set of all four quantum numbers.
Pauli's exclusion principle precisely states that no two electrons can have identical values for all four quantum numbers (n, l, m_l, m_s). Option C is a consequence of the principle, not the statement itself. Options B and D refer to the Aufbau principle and Hund's rule, respectively.
8. Hund's rule of maximum multiplicity states that:
- In a set of degenerate orbitals, electrons fill them in a way that gives the maximum number of parallel spins.
- Electrons are filled in orbitals in order of increasing energy.
- No two electrons can have the same spin in a degenerate set.
- The total spin of an atom is always zero.
Answer: In a set of degenerate orbitals, electrons fill them in a way that gives the maximum number of parallel spins.
Hund's rule states that electrons occupy degenerate orbitals singly with parallel spins to maximize the total spin (multiplicity). Option B is the Aufbau principle, option C is incomplete (the rule maximizes parallel spins, not just prohibits same spin), and option D is false.
9. Which orbital is represented by the quantum numbers n = 4, l = 1, m = 0?
- 4s
- 4pₓ
- 4p_z
- 4d_{z²}
Answer: 4p_z
n = 4 indicates the fourth shell, l = 1 indicates a p subshell, m = 0 corresponds to the p orbital oriented along the z-axis (p_z). Option A (4s) would require l=0, option B (4pₓ) corresponds to m = +1 or -1 depending on convention, and option D (4d_{z²}) would require l=2.
10. According to the Aufbau principle and the (n+l) rule, which orbital is filled immediately after the 4s orbital?
- 3d
- 4p
- 5s
- 4d
Answer: 3d
The (n+l) rule states that orbitals with lower n+l are filled first. For 4s, n+l=4; for 3d, n+l=5; for 4p, n+l=5. Among orbitals with the same n+l, the one with lower n is filled first, so 3d (n=3) fills before 4p (n=4). Hence, after 4s, the next orbital filled is 3d.
11. The anomalous electronic configuration of copper (Z = 29) is best explained by:
- The (n + l) rule
- The extra stability of half-filled subshell
- The extra stability of fully-filled subshell
- Pauli's exclusion principle
Answer: The extra stability of fully-filled subshell
Copper adopts [Ar] 3d¹⁰ 4s¹ instead of [Ar] 3d⁹ 4s² because a completely filled 3d¹⁰ subshell provides extra stability due to symmetrical charge distribution and exchange energy. The (n+l) rule would predict [Ar] 3d⁹ 4s², which is not observed.
12. The de Broglie wavelength λ associated with a particle of mass m moving with velocity v is given by:
- λ = h/(mv)
- λ = mv/h
- λ = hv/m
- λ = m/(hv)
Answer: λ = h/(mv)
De Broglie's relation states that a particle with momentum p = mv has a wavelength λ = h/p = h/(mv). The other options are incorrect: mv/h has dimensions of 1/λ, hv/m has dimensions of momentum×area, and m/(hv) has dimensions of 1/(momentum).