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AP Physics 2: Algebra-Based Practice Quiz: Quantum Theory and Wave-Particle Duality

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

According to the provided text, why was quantum theory developed?

All Questions (10)

According to the provided text, why was quantum theory developed?

A) To confirm the predictions made by classical mechanics.

B) To explain observations of matter and energy that classical mechanics could not.

C) To describe the motion of large-scale objects like planets.

D) To unify the theories of gravity and electromagnetism.

Correct Answer: B

The text explicitly states, 'Quantum theory was developed to explain observations of matter and energy that could not be explained using classical mechanics.'

Based on the provided information, which of the following is a correct description of a photon?

A) A particle with a positive charge and significant mass.

B) A massless, electrically neutral particle.

C) A particle whose energy is inversely proportional to its frequency.

D) A massive particle that carries a negative charge.

Correct Answer: B

The text describes a photon as a 'massless, electrically neutral particle.' The other options contradict this description.

The energy of a photon is directly proportional to its frequency, as described by the equation E = hf. If the frequency of a photon is doubled, how does its energy change?

A) Its energy is halved.

B) Its energy is doubled.

C) Its energy is quadrupled.

D) Its energy remains the same.

Correct Answer: B

The equation E = hf shows a direct linear relationship between energy (E) and frequency (f). Therefore, if the frequency is doubled, the energy must also be doubled.

According to the de Broglie relation, what is the relationship between a particle's wavelength and its momentum?

A) The wavelength is directly proportional to the momentum.

B) The wavelength is inversely proportional to the momentum.

C) The wavelength is proportional to the square of the momentum.

D) There is no relationship between wavelength and momentum.

Correct Answer: B

The text states that the de Broglie wavelength 'increases as the momentum of a particle decreases.' This describes an inverse relationship, which is also shown by the equation λ = h/p.

If the momentum of a particle is reduced to one-third of its original value, what will happen to its de Broglie wavelength?

A) It will be reduced to one-third of its original value.

B) It will remain unchanged.

C) It will triple.

D) It will increase by a factor of nine.

Correct Answer: C

Based on the equation λ = h/p, wavelength (λ) and momentum (p) are inversely proportional. If momentum (p) becomes p/3, the new wavelength will be h/(p/3), which simplifies to 3 * (h/p), or three times the original wavelength.

Two photons are detected. Photon A has a higher frequency than Photon B. Which statement correctly compares their energies?

A) Photon A has less energy than Photon B.

B) Photon A has the same energy as Photon B.

C) Photon A has more energy than Photon B.

D) The energy of the photons cannot be determined from their frequency.

Correct Answer: C

The relationship E = hf indicates that energy is directly proportional to frequency. Since Photon A has a higher frequency, it must have more energy than Photon B.

An electron and a proton are moving such that the electron has less momentum than the proton. How does the de Broglie wavelength of the electron compare to that of the proton?

A) The electron has a shorter wavelength.

B) The electron has a longer wavelength.

C) The electron and the proton have the same wavelength.

D) The wavelength depends on charge, not momentum.

Correct Answer: B

The de Broglie wavelength (λ) is inversely proportional to momentum (p), as given by λ = h/p. Since the electron has less momentum, it will have a longer de Broglie wavelength.

A scientist wishes to increase the de Broglie wavelength of a moving particle. Based on the provided principles, which action should be taken?

A) Increase the momentum of the particle.

B) Decrease the momentum of the particle.

C) Add electric charge to the particle.

D) Keep the momentum of the particle constant.

Correct Answer: B

The provided text and equation (λ = h/p) state that the de Broglie wavelength increases as the momentum of a particle decreases. Therefore, to increase the wavelength, the momentum must be decreased.

Which of the following scenarios is best explained by the concept that an object can exhibit both particle-like and wave-like behavior?

A) A baseball following a parabolic trajectory when thrown.

B) A planet orbiting the sun due to gravitational forces.

C) An electron with a specific momentum also having a quantifiable wavelength.

D) The constant energy of a photon regardless of its frequency.

Correct Answer: C

The concept of wave-particle duality, as described in the text, means an object has both particle properties (like momentum) and wave properties (like wavelength). An electron having both momentum and a de Broglie wavelength is the prime example of this among the choices. Options A and B are described by classical mechanics.

A researcher is studying two different phenomena. Phenomenon 1 involves calculating the energy of a photon of light. Phenomenon 2 involves calculating the wavelength of a moving electron. Which equations are appropriate for these calculations?

A) Phenomenon 1: λ = h/p, Phenomenon 2: E = hf

B) Both phenomena are described by E = hf.

C) Phenomenon 1: E = hf, Phenomenon 2: λ = h/p

D) Both phenomena are described by λ = h/p.

Correct Answer: C

The text explicitly links the energy of a photon to its frequency with E = hf. It links the wave model of matter (like an electron) to its momentum with the de Broglie wavelength equation, λ = h/p. Therefore, C correctly matches each phenomenon with its corresponding equation.