The Bohr Model of Atomic Structure
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AP Physics 2 › The Bohr Model of Atomic Structure
A hydrogen electron can occupy only Bohr orbits $n=1,2,3,4$; all intermediate energies are forbidden. If the electron emits the highest-energy photon, which jump occurred?
The electron moves from $n=4$ to $n=3$.
The electron spirals inward continuously from $n=4$ to $n=1$.
The electron moves from $n=2$ to $n=1$.
The electron moves from $n=4$ to $n=1$.
Explanation
This question examines the Bohr model of atomic structure. In the Bohr model, the energy of emitted photons equals the difference between initial and final energy levels, and larger energy differences produce higher-energy photons. Since energy levels get closer together as n increases, the largest possible energy difference occurs when an electron drops from the highest level (n=4) to the lowest level (n=1). This n=4 to n=1 transition produces the highest-energy photon possible in this system. Choices B and C represent smaller energy differences and thus lower-energy photons, while choice D violates the quantization principle by suggesting continuous motion between levels. The key principle: maximum photon energy comes from the largest allowed energy level difference.
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?
The atom must emit a photon with energy $E_4-E_2$.
The atom must absorb a photon with energy $E_4-E_2$.
The electron passes through all intermediate energies continuously.
The electron spirals outward while radiating energy continuously.
Explanation
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.
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?
It is held by gravity, so radiation is unnecessary for stability.
It radiates continuously, so it slowly spirals into the nucleus.
It can have any energy, so it avoids radiating by choosing a continuous orbit.
It does not radiate energy while in an allowed orbit.
Explanation
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.
A Bohr-model atom has allowed levels $n=1,2,3$ (forbidden: all energies between levels). Why is the electron in $n=1$ stable?
It is stable because the electron cannot radiate while remaining in an allowed orbit.
It is stable because the electron continuously loses energy but never reaches the nucleus.
It is stable because the electron may occupy any radius between $n=1$ and $n=2$.
It is stable because the nucleus exerts no force on electrons in circular motion.
Explanation
This question examines the Bohr model of atomic structure. The Bohr model postulates that electrons in allowed orbits do not radiate energy, which solves the classical physics problem of accelerating charges losing energy through radiation. The n=1 level represents the ground state, the lowest allowed energy level where the electron is stable because it cannot transition to any lower state. While in this allowed orbit, the electron does not radiate energy despite its circular motion, which would classically require acceleration. Choice B incorrectly suggests the electron continuously loses energy, which contradicts Bohr's postulate of stable orbits. The key principle is that electrons in allowed orbits are stable and do not radiate energy.
A hydrogen atom is modeled with allowed orbits $n=1$ through $n=5$ and forbidden energies between. Which transition emits the highest-energy photon?
The electron moves from $n=2$ to $n=1$.
The electron moves from $n=5$ to $n=1$.
The electron moves from $n=3$ to $n=2$.
The electron moves from $n=4$ to an energy between $n=3$ and $n=4$.
Explanation
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.
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?
The electron moves from $n=4$ to $n=5$ only
The electron spirals inward while radiating at all frequencies
The electron moves from $n=4$ to $n=3$ only
The electron shifts continuously to any orbit radius
Explanation
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.
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?
It radiates continuously but cannot reach the nucleus
It does not radiate while in an allowed orbit
It loses energy and spirals into the nucleus slowly
It can occupy any orbit radius without losing energy
Explanation
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.
An electron in a Bohr atom can occupy only allowed levels $n=1,2,3,4$ (forbidden: energies between). Which transition results in photon absorption?
The electron moves from $n=2$ to $n=4$.
The electron moves from $n=4$ to $n=2$.
The electron moves from $n=3$ to any energy between $n=2$ and $n=3$.
The electron spirals from $n=2$ into the nucleus.
Explanation
This question tests the Bohr model of atomic structure. In the Bohr model, photon absorption occurs when an electron gains energy and moves from a lower allowed energy level to a higher allowed energy level. The transition from n=2 to n=4 requires the electron to absorb a photon with energy exactly equal to E₄ - E₂. This is the only option that represents an upward transition between allowed levels. Choice C incorrectly suggests the electron can move to an energy between allowed levels, which violates the quantization principle of the Bohr model. Remember: absorption requires upward transitions between allowed levels, while emission requires downward transitions.
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?
The electron moves from $n=2$ to $n=1$ only
The electron drifts to any radius between $n=2$ and $n=4$
The electron moves from $n=2$ to $n=4$ only
The electron spirals inward and emits continuously
Explanation
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.
In the Bohr model, electrons occupy discrete allowed energies $E_1<E_2<E_3<E_4$ (forbidden: energies between). Which statement best describes emission during a transition?
A photon is emitted whenever the electron moves along an orbit at constant $n$.
A photon is emitted only when the electron drops from a higher allowed level to a lower allowed level.
A photon is emitted as the electron continuously spirals toward the nucleus.
A photon is emitted when the electron occupies any energy between $E_2$ and $E_3$.
Explanation
This question examines the Bohr model of atomic structure. The Bohr model establishes that electrons occupy only discrete, allowed energy levels, and photon emission occurs exclusively during transitions from higher to lower allowed levels. When an electron drops from a higher allowed level to a lower allowed level, it emits a photon with energy equal to the difference between these levels. This is the fundamental mechanism of atomic emission in the Bohr model. Choice C incorrectly describes continuous spiraling, which would occur in classical physics but is explicitly prevented by Bohr's quantization postulates. The key principle is that emission requires discrete jumps between allowed energy levels, not continuous motion.