The Bohr Model of Atomic Structure - AP Physics 2

1. A Bohr-model atom has allowed energy levels $n=1,2,3$ and forbidden energies between; an electron is in $n=1$. Why is the electron stable in this model?
   Answer: It does not radiate while in an allowed orbit This question tests understanding of the Bohr model of atomic structure. The Bohr model postulates that electrons in allowed orbits do not radiate electromagnetic energy, solving the classical physics problem where accelerating charges must radiate. In classical physics, an orbiting electron would continuously lose energy and spiral into the nucleus, but Bohr's model prevents this by stating that electrons in quantized orbits are stable and do not radiate. The electron only emits or absorbs photons when transitioning between allowed levels. Choice D represents the classical misconception that electrons must continuously lose energy while orbiting. Remember that Bohr's key innovation was proposing stable, non-radiating orbits at specific energy levels.
2. In the Bohr model, only discrete orbits $n=1,2,3,4$ are allowed (forbidden between). Which transition emits a photon with the greatest frequency?
   Answer: An electron moves from $n=4$ to $n=1$ This question tests understanding of the Bohr model of atomic structure. In the Bohr model, photon frequency is directly proportional to photon energy through the relationship E = hf, where h is Planck's constant. The greatest frequency photon is emitted during the transition that releases the most energy, which occurs when an electron falls through the largest energy gap. Since energy levels get closer together as n increases, the largest gap is between n=4 and n=1, making this transition produce the highest frequency photon. Choice B represents a smaller energy change, illustrating the misconception that all transitions produce similar photon frequencies. The strategy is to identify the transition with the largest change in n value for maximum frequency.
3. In a Bohr-model atom, only $n=1,2,3$ are allowed; energies between are forbidden. An electron is observed at $n=3$. Which is consistent with the model?
   Answer: It remains at $n=3$ without radiating until a transition occurs. This question tests the Bohr model of atomic structure. According to Bohr's postulates, electrons in allowed orbits (like n=3) are stable and do not radiate energy while remaining in that orbit. This stability in allowed states is a cornerstone of the model, preventing the classical prediction of continuous radiation and orbital decay. The electron will remain at n=3 indefinitely until it undergoes a quantum transition to another allowed level. Choice B represents the classical physics prediction that Bohr's model specifically contradicts, choice C suggests a forbidden intermediate energy (n=2.7), and choice D incorrectly claims continuous energy values are possible. Remember: electrons in allowed Bohr orbits are stable and non-radiating.
4. A Bohr atom allows only discrete energies $n=1,2,3$ (forbidden between). An electron is at $n=2$ and absorbs energy. Which outcome is allowed?
   Answer: The electron moves to $n=3$ in a single jump This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only exist in discrete energy levels with integer quantum numbers n. When an electron at n=2 absorbs energy, it must absorb exactly the right amount to reach another allowed level like n=3; it cannot stop at intermediate positions like n=2.4. The electron makes an instantaneous quantum jump to the new level without passing through forbidden intermediate states. Choice B incorrectly suggests the electron can remain at n=2.4, which violates the fundamental quantization principle. Remember that only discrete energy levels with integer n values are allowed in the Bohr model.
5. In the Bohr model of hydrogen, electrons occupy only the allowed energy levels $n=1,2,3,4$ (forbidden: any energy between these). If an electron moves from $n=3$ to $n=2$, which statement is correct about the process?
   Answer: A photon is emitted because the electron moves to a lower allowed energy level. This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only occupy specific, quantized energy levels (n=1, 2, 3, etc.), and any energies between these levels are forbidden. When an electron transitions from a higher energy level (n=3) to a lower energy level (n=2), it must release energy equal to the difference between these levels. This energy is released as a photon, making the transition an emission process. Choice C incorrectly assumes continuous energies are allowed between levels, which violates the fundamental quantization principle of the Bohr model. Remember: transitions to lower energy levels always emit photons, while transitions to higher levels require photon absorption.
6. Consider allowed Bohr energy levels shown for a hydrogen atom (forbidden: energies between lines). Which transition corresponds to photon emission?
   Answer: An electron transitions from $n=5$ to $n=2$. This question addresses the Bohr model of atomic structure. In the Bohr model, photon emission occurs when an electron transitions from a higher allowed energy level to a lower allowed energy level. The transition from n=5 to n=2 represents a downward jump between allowed states, releasing energy as a photon with energy equal to E₅ - E₂. This is the fundamental emission process in the Bohr model. Choice C incorrectly suggests the electron can occupy an energy between allowed levels, which violates the quantization principle that defines the Bohr model. The key rule is that emission requires downward transitions between discrete allowed levels.
7. In the Bohr model, only $n=1,2,3,4$ are allowed and energies between are forbidden; an electron starts at $n=4$. Which event produces the highest-energy photon?
   Answer: The electron moves from $n=4$ to $n=1$ only This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only occupy discrete energy levels, and photon energy equals the energy difference between levels. The highest-energy photon is produced by the largest energy drop, which occurs when the electron falls to the lowest possible level. From n=4, the largest drop is to n=1, producing a photon with energy proportional to the difference between these levels. Choice C incorrectly suggests the electron can move to n=2.7, violating the principle that only integer values of n are allowed in the Bohr model. To find the highest-energy photon, always look for the transition with the largest change in n value.
8. In the Bohr model, electrons can occupy only allowed energies $n=1,2,3,4$ (forbidden between); an electron is at $n=2$. Which transition corresponds to absorption of a photon?
   Answer: The electron moves from $n=2$ to $n=4$ only This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only exist in specific quantized orbits, and photon absorption occurs when an electron gains energy to jump to a higher level. From n=2, absorption means the electron must move to a higher energy level like n=3 or n=4, not drop to n=1 (which would be emission). The electron gains exactly the energy difference between the two levels by absorbing a photon of that specific energy. Choice D incorrectly suggests the electron can drift to any radius, violating the fundamental principle of discrete orbits. Remember that absorption always involves transitions to higher n values.
9. A hydrogen atom is modeled with allowed orbits $n=1$ through $n=5$ and forbidden energies between. Which transition emits the highest-energy photon?
   Answer: The electron moves from $n=5$ to $n=1$. This question tests the Bohr model of atomic structure. In the Bohr model, the energy of emitted photons equals the difference between initial and final energy levels during downward transitions. The highest-energy photon comes from the largest energy difference, which occurs when an electron falls from the highest allowed level to the lowest allowed level. The transition from n=5 to n=1 represents the maximum possible energy difference among the given options, producing the highest-energy photon. Choice D incorrectly suggests the electron can transition to an energy between allowed levels, which violates the quantization principle. Remember: the largest energy gap between allowed levels produces the highest-energy photon.
10. An electron in a Bohr atom can occupy only $n=1,2,3,4$ (forbidden between). Which choice correctly links orbit change and photon behavior?
    Answer: Higher $n$ occurs when a photon is absorbed and energy increases This question tests understanding of the Bohr model of atomic structure. In the Bohr model, the relationship between orbit changes and photon behavior follows strict rules based on energy conservation and quantization. When an electron absorbs a photon, it gains energy and moves to a higher energy level (larger n value), moving farther from the nucleus. Conversely, when an electron emits a photon, it loses energy and falls to a lower level (smaller n value). The photon energy always equals the exact energy difference between the two levels. Choice D incorrectly suggests energies are continuous, which represents the classical misconception that Bohr's model rejects through quantization. The key principle is that absorption always increases n (and energy) while emission always decreases n.
11. A Bohr atom has allowed levels $n=1,2,3$ and forbidden energies between; an electron is excited to $n=3$. Which statement correctly describes photon emission?
    Answer: Emission occurs only when the electron drops to a lower allowed level This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons in allowed orbits are stable and do not radiate energy; photon emission occurs only during transitions between allowed levels. When an electron drops from a higher level to a lower one, it emits a single photon with energy equal to the difference between the two levels. The electron cannot emit while remaining in the same orbit, nor does it spiral or move through intermediate radii. Choice B incorrectly suggests continuous emission through intermediate positions, which contradicts the discrete nature of allowed orbits. The key principle is that photons are emitted only during quantum jumps between allowed states.
12. A Bohr energy-level diagram shows allowed levels $n=1,2,3,4$ and forbidden gaps. An electron transitions from $n=4$ to $n=2$. Which best describes the light involved?
    Answer: A photon is emitted with energy $E_4-E_2$. This question addresses the Bohr model of atomic structure. In the Bohr model, when an electron transitions from a higher energy level (n=4) to a lower one (n=2), it must emit a photon to conserve energy. The photon's energy equals the difference between the initial and final energy levels: E₄ - E₂. This downward transition results in light emission, which is how atoms produce discrete spectral lines. Choice B incorrectly suggests absorption during a downward transition, choice C violates the quantization principle by implying continuous motion, and choice D contradicts the discrete nature of allowed orbits. The fundamental rule: downward transitions emit photons with energy equal to the level difference.
13. A hydrogen atom has allowed energies $n=1,2,3,4$ only (no energies between). Which statement best explains atomic stability in this model?
    Answer: Electrons in allowed orbits do not radiate energy, preventing collapse This question tests understanding of the Bohr model of atomic structure. The Bohr model revolutionized atomic theory by proposing that electrons can only exist in specific, quantized orbits with discrete energy levels, solving the classical problem of atomic instability. In classical physics, an accelerating charged particle (like an orbiting electron) should continuously radiate energy and spiral into the nucleus, but Bohr postulated that electrons in allowed orbits do not radiate energy. This quantization prevents the continuous energy loss that would lead to atomic collapse. Choice A represents the classical physics prediction that Bohr's model specifically contradicts—the misconception that electrons must continuously lose energy. The fundamental principle to remember is that electrons in stationary states (allowed orbits) do not radiate energy.
14. An electron occupies discrete allowed levels $n=1,2,3,4$ (energies between are forbidden). Which transition requires absorption of a photon?
    Answer: An electron moves from $n=2$ to $n=4$ This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons occupy quantized energy levels, and transitions between these levels require the absorption or emission of photons with specific energies. When an electron moves from a lower energy level (smaller n) to a higher energy level (larger n), it must absorb a photon whose energy exactly matches the difference between the two levels. This upward transition increases the electron's energy and moves it farther from the nucleus. Choice C incorrectly suggests the electron can drift to an intermediate radius, which violates the fundamental principle of quantization—electrons cannot exist between allowed levels. The key strategy is to recognize that absorption occurs during upward transitions (increasing n values).
15. In a Bohr-model ion, allowed energies correspond to $n=1,2,3,4$ and energies between are forbidden. An electron is excited from $n=2$ to $n=4$. What must occur?
    Answer: The atom must absorb a photon with energy $E_4-E_2$. This question tests the Bohr model of atomic structure. In Bohr's theory, electrons occupy only discrete energy levels, and transitions between levels require the absorption or emission of photons with specific energies. To move from n=2 to n=4, the electron must jump to a higher energy level, which requires absorbing a photon with energy exactly equal to E₄ - E₂. The electron cannot exist at intermediate energies between allowed levels, making instantaneous transitions necessary. Choice B incorrectly suggests emission during an upward transition, while choices C and D violate the quantization principle by proposing continuous energy changes. Remember: upward transitions require photon absorption with energy matching the level difference.
16. A Bohr-model atom has allowed electron orbits only at $n=1,2,3$ and forbidden energies between them. Why is the electron stable in a fixed orbit?
    Answer: It does not radiate energy while in an allowed orbit. This question examines the Bohr model of atomic structure. According to Bohr's postulates, electrons in allowed orbits (n = 1, 2, 3) do not radiate energy despite their circular motion, which contradicts classical physics. This stability in allowed orbits is a fundamental assumption that prevents electrons from spiraling into the nucleus. Electrons only emit or absorb photons when transitioning between allowed levels, not while remaining in a single orbit. Choice A represents the classical physics prediction that Bohr's model specifically addresses, choice B incorrectly suggests continuous energy values, and choice D incorrectly invokes gravity instead of electromagnetic forces. The key principle: electrons in allowed Bohr orbits are stable and do not radiate energy.
17. A Bohr energy-level diagram shows allowed levels $n=1,2,3,4$ (no energies between). Which arrow corresponds to photon absorption?
    Answer: Arrow from $n=1$ up to $n=3$ This question tests understanding of the Bohr model of atomic structure. In energy-level diagrams, transitions are represented by arrows between allowed energy levels, with the arrow direction indicating whether energy is absorbed or emitted. Photon absorption occurs when an electron gains energy and moves to a higher energy level, which is shown by an upward arrow from a lower n value to a higher n value. During absorption, the photon's energy must exactly match the energy difference between the two levels. Choice D incorrectly shows an arrow to a point between levels, which represents the misconception that electrons can exist at intermediate energies—this violates the quantization principle. The strategy for reading energy diagrams is that upward arrows always represent photon absorption.
18. In a Bohr atom, only $n=1,2,3,4$ are allowed (forbidden between). Which statement about emitted photon energies is correct?
    Answer: Photon energies are discrete because only certain energy levels exist This question tests understanding of the Bohr model of atomic structure. The Bohr model's revolutionary insight was that electrons can only occupy specific, quantized energy levels, which directly determines the nature of emitted photons. Since only certain energy levels exist, transitions between these levels produce photons with discrete, specific energies equal to the difference between the initial and final states. This explains why atomic spectra show distinct lines rather than continuous bands. Choice A incorrectly assumes continuous orbit radii, which represents the classical physics misconception that Bohr's model specifically rejects. The key principle is that quantized energy levels necessarily produce discrete photon energies.
19. In a Bohr-model hydrogen atom, only $n=1,2,3,4$ are allowed and energies between are forbidden; an electron is at $n=4$. Which transition emits a photon?
    Answer: The electron moves from $n=4$ to $n=3$ only This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only occupy specific energy levels, and photon emission occurs when an electron transitions from a higher to a lower energy level. From n=4, the electron can emit a photon by dropping to n=3, n=2, or n=1, but not by moving up to n=5 (which would require absorption). The emitted photon carries away the exact energy difference between the initial and final levels. Choice C incorrectly suggests the electron can shift to any orbit radius, violating the quantization principle. To identify emission, look for transitions from higher to lower n values.
20. An electron in a Bohr atom may occupy only the discrete levels shown (forbidden energies between): it is initially at $n=3$. Which transition emits a photon with the smallest energy?
    Answer: The electron moves from $n=3$ to $n=2$ only This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons occupy only discrete energy levels, and the energy of emitted photons equals the energy difference between initial and final levels. The smallest energy photon corresponds to the smallest energy drop, which occurs between adjacent levels. From n=3, the smallest drop is to n=2, producing the lowest-energy photon compared to a drop to n=1. Choice C incorrectly suggests the electron can move to n=2.2, which violates the quantization principle requiring integer values of n. To find the smallest-energy photon emission, look for transitions between adjacent energy levels.

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