The Bohr Model of Atomic Structure

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AP Physics 2 › The Bohr Model of Atomic Structure

Questions 1 - 10
1

In the Bohr model, an electron can occupy only discrete orbits $n=1,2,3,4$; all other energies are forbidden. Which statement best describes photon emission?

It occurs when the electron jumps from higher $n$ to lower $n$.

It occurs when the electron moves within a continuous band of energies.

It occurs when the electron spirals into the nucleus from any orbit.

It occurs whenever the electron remains in a single allowed orbit.

Explanation

This question tests understanding of the Bohr model of atomic structure. In Bohr's atomic model, electrons occupy only specific, quantized orbits (n = 1, 2, 3, 4), and photon emission occurs specifically when an electron transitions from a higher energy level to a lower one. During this downward jump, the electron releases a photon with energy equal to the difference between the initial and final energy levels. Choice B incorrectly suggests continuous energy bands exist, choice C violates the discrete orbit principle with continuous spiraling, and choice D is wrong because remaining in a single orbit involves no energy change and thus no photon emission. Remember: photon emission requires a downward transition between discrete allowed levels.

2

In the Bohr model of hydrogen, electrons occupy only allowed energies $n=1,2,3$ and cannot exist between them; an electron is initially at $n=3$. Which transition results in photon emission?

The electron moves from $n=3$ to $n=2$ only

The electron moves from $n=2.5$ to $n=2$ smoothly

The electron spirals continuously into the nucleus

The electron moves from $n=2$ to $n=3$ only

Explanation

This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons can only exist in specific, quantized energy levels (n=1, 2, 3, etc.) and cannot exist between these levels. When an electron transitions from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels. Since the electron starts at n=3, it can only emit a photon by dropping to a lower level like n=2 or n=1. Choice B incorrectly suggests the electron can exist at n=2.5, which violates the quantization principle that only integer values of n are allowed. To solve Bohr model problems, remember that electrons can only occupy discrete energy levels and photon emission occurs only during downward transitions.

3

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?

The electron moves from $n=4$ to $n=1$ only

The electron moves from $n=4$ to $n=2.7$ smoothly

The electron moves from $n=4$ to $n=3$ only

The electron spirals from $n=4$ toward the nucleus continuously

Explanation

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.

4

In the Bohr model, electrons occupy only allowed orbits $n=1,2,3,4$ and forbidden energies between; an electron drops from $n=3$ to $n=1$. What happens to the energy difference?

It is radiated continuously as the electron spirals inward

It is lost because the electron can occupy forbidden energies

It is emitted as a single photon with energy $elta E$

It is converted into orbital radius without photon emission

Explanation

This question tests understanding of the Bohr model of atomic structure. In the Bohr model, when an electron transitions between allowed energy levels, the energy difference is conserved by emission or absorption of a photon. When dropping from n=3 to n=1, the electron loses energy equal to the difference between these levels, and this energy is carried away by a single photon. The transition is instantaneous, with no intermediate states or continuous radiation. Choice B incorrectly suggests continuous radiation during spiraling, which contradicts the discrete nature of Bohr transitions. The fundamental principle is that energy differences between levels are always converted to photons with matching energy.

5

In a Bohr atom, only $n=1,2,3,4$ are allowed and energies between are forbidden; an electron is at $n=2$. Which change requires absorption of a photon?

The electron moves from $n=2$ to $n=3$ only

The electron spirals inward while radiating continuously

The electron shifts to any radius between $n=2$ and $n=3$

The electron moves from $n=2$ to $n=1$ only

Explanation

This question tests understanding of the Bohr model of atomic structure. In the Bohr model, electrons occupy only specific, quantized energy levels and cannot exist between them. When an electron absorbs a photon, it must gain exactly the right amount of energy to jump from its current level to a higher allowed level. Starting from n=2, the electron can absorb a photon to jump to n=3 or n=4, but it cannot jump down to n=1 (which would require emission, not absorption). Choice D incorrectly suggests the electron can shift to any radius between levels, which violates the fundamental principle that only discrete orbits are allowed. To identify absorption transitions, look for movements from lower to higher n values.

6

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 can occupy any orbit radius without losing energy

It loses energy and spirals into the nucleus slowly

It radiates continuously but cannot reach the nucleus

It does not radiate while in an allowed orbit

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.

7

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 spirals inward and emits continuously

The electron moves from $n=2$ to $n=4$ only

The electron drifts to any radius between $n=2$ and $n=4$

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.

8

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?

Emission occurs only when the electron drops to a lower allowed level

Emission occurs as the electron moves through all intermediate radii

Emission occurs because the electron must spiral into the nucleus

Emission occurs while the electron remains in an allowed orbit

Explanation

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.

9

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?

The electron moves from $n=3$ to $n=2.2$ smoothly

The electron moves from $n=3$ to $n=2$ only

The electron spirals inward while emitting a continuum

The electron moves from $n=3$ to $n=1$ only

Explanation

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.

10

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?

The electron spirals into the nucleus after absorbing energy

The electron moves to $n=3$ in a single jump

The electron spreads into a continuum of orbit radii

The electron moves to $n=2.4$ and stays there

Explanation

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.

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