--- title: "AP Physics 2 Unit 15 Practice Test" description: "A timed AP Physics 2 Unit 15 (Modern Physics) practice test in the AP format, drawn from 1,399 multiple-choice questions and 36 FRQs written for the unit. The standard version takes about 88 minutes." canonical: "https://fiveable.me/ap-physics-2-revised/unit-test/15" type: "unit-test" subject: "AP Physics 2" unit: "Unit 15" --- # AP Physics 2 Unit 15 Practice Test ## Overview A timed AP Physics 2 Unit 15 (Modern Physics) practice test in the AP format, drawn from 1,399 multiple-choice questions and 36 FRQs written for the unit. The standard version takes about 88 minutes. ## Test Format - 20 Multiple Choice Questions (40 minutes) - 1 FRQ – FRQ 1 – Mathematical Routines (24 minutes) - 1 FRQ – FRQ 2 – Translation Between Representations (24 minutes) ## Unit FRQs by Type - [FRQ 1 – Mathematical Routines](/ap-physics-2-revised/frqs/mathematical-routines?unit=15): 6 questions - [FRQ 2 – Translation Between Representations](/ap-physics-2-revised/frqs/translation-between-representations?unit=15): 7 questions - [FRQ 3 – Experimental Design](/ap-physics-2-revised/frqs/experimental-design?unit=15): 9 questions - [FRQ 4 – Qualitative/Quantitative Translation](/ap-physics-2-revised/frqs/qualitative-quantitative-translation?unit=15): 14 questions ## Practice Questions ### Question 1 A hydrogen atom's electron transitions from the ground state (n=1) to the first excited state (n=2). Which statement correctly compares the electron's orbital speed in the n=2 state to its speed in the n=1 state? - (A) The speed in the n=2 state is one-half the speed in the n=1 state. - (B) The speed in the n=2 state is one-fourth the speed in the n=1 state. - (C) The speed in the n=2 state is two times the speed in the n=1 state. - (D) The speed in the n=2 state is four times the speed in the n=1 state. **Answer: (A)** From the Bohr quantization condition $L=mvr=n\hbar$, the speed is $v=n\hbar/(mr)$. Since $r\propto n^2$, this gives $v\propto n/n^2=1/n$, so the speed at $n=2$ is half the speed at $n=1$. ### Question 2 Consider the ground state (n=1) of a hydrogen atom (Z=1) and the ground state (n=1) of a singly ionized helium atom (Z=2). How does the ionization energy of the helium ion compare to the ionization energy of the hydrogen atom? - (A) The helium ionization energy is four times that of hydrogen. - (B) The helium ionization energy is two times that of hydrogen. - (C) The helium ionization energy is one-half that of hydrogen. - (D) The helium ionization energy is one-fourth that of hydrogen. **Answer: (A)** Comparing ionization energies requires applying the Bohr energy formula E∝Z²/n². Since both atoms are in the ground state (n=1), the energy depends only on the square of the atomic number (Z), resulting in a factor of 2²=4. ### Question 3 According to the Bohr model, an electron's orbit circumference must equal an integer multiple of its de Broglie wavelength. How does the electron's wavelength in the n=3 state compare to its wavelength in the n=1 state? - (A) The wavelength in the n=3 state is three times the wavelength in the n=1 state. - (B) The wavelength in the n=3 state is nine times the wavelength in the n=1 state. - (C) The wavelength in the n=3 state is one-third the wavelength in the n=1 state. - (D) The wavelength in the n=3 state is one-ninth the wavelength in the n=1 state. **Answer: (A)** Comparing wavelengths requires connecting the standing wave condition nλ=2πr with the orbital radius relationship r∝n². Substituting r∝n² into the circumference equation yields nλ∝n², which simplifies to λ∝n. ### Question 4 In the Bohr model, the electric force between the nucleus and the electron provides the necessary centripetal force. How does the magnitude of this electric force in the n=2 state compare to the magnitude in the n=1 state? - (A) The force in the n=2 state is one-sixteenth the force in the n=1 state. - (B) The force in the n=2 state is one-fourth the force in the n=1 state. - (C) The force in the n=2 state is one-eighth the force in the n=1 state. - (D) The force in the n=2 state is one-half the force in the n=1 state. **Answer: (A)** Comparing electric forces requires applying Coulomb's Law F∝1/r² and the Bohr radius relationship r∝n². Combining these dependencies shows that force is proportional to 1/(n²)² = 1/n⁴, resulting in a factor of 1/2⁴ = 1/16. ### Question 5 An electron of mass m and charge -e moves in a stable circular orbit of radius r around a nucleus of charge +Ze. Coulomb's constant is k. Which of the following expressions correctly represents the speed v of the electron derived from the balance of forces? - (A) $v = \sqrt{\frac{kZe^2}{mr}}$ - (B) $v = \sqrt{\frac{kZe}{mr}}$ - (C) $v = \sqrt{\frac{kZe^2}{mr^2}}$ - (D) $v = \sqrt{\frac{kZ^2e}{mr}}$ **Answer: (A)** Deriving this expression requires equating the electric force (kZe²/r²) to the centripetal force (mv²/r). Solving for v yields v² = kZe²/(mr), so v = √(kZe²/mr). ### Question 6 An electron of mass m orbits a nucleus of charge +Ze at a distance r. Assuming the electric force provides the centripetal acceleration, which expression represents the kinetic energy K of the electron? - (A) $K = \frac{kZe^2}{2r}$ - (B) $K = \frac{kZe^2}{r}$ - (C) $K = -\frac{kZe^2}{2r}$ - (D) $K = -\frac{kZe^2}{r}$ **Answer: (A)** Deriving this requires starting with the force balance mv²/r = kZe²/r², which simplifies to mv² = kZe²/r. Since kinetic energy K = ½mv², substituting mv² yields K = kZe²/(2r). ### Question 7 An electron of charge -e and mass m orbits a nucleus of charge +Ze in a circle of radius r. Which expression represents the equivalent electric current I generated by this orbiting electron? - (A) $I = \frac{e^2}{2\pi} \sqrt{\frac{kZ}{mr^3}}$ - (B) $I = \frac{e}{2\pi} \sqrt{\frac{kZ}{mr^3}}$ - (C) $I = \frac{e^2}{2\pi} \sqrt{\frac{kZ}{mr}}$ - (D) $I = \frac{e}{2\pi} \sqrt{\frac{kZ}{mr}}$ **Answer: (A)** Deriving this involves defining current as charge/period (I = e/T) and substituting T = 2πr/v. Using the velocity v = √(kZe²/mr), the expression simplifies to I = (e²/2π)√(kZ/mr³). ### Question 8 An electron of mass m moves with speed v in a circular orbit around a nucleus. Assuming the potential energy is zero at infinity, which expression represents the total mechanical energy E of the system? - (A) $E = -\frac{1}{2}mv^2$ - (B) $E = \frac{1}{2}mv^2$ - (C) E = -mv^2 - (D) E = mv^2 **Answer: (A)** Deriving this requires summing kinetic (K = ½mv²) and potential (U = -mv²) energies. The virial theorem for inverse-square forces implies U = -2K, so E = K - 2K = -K = -½mv². ### Question 9 A student claims that a perfect mirror exerts no force on a light beam because light has no mass. Which of the following evaluates this claim using physical principles of reflection? - (A) Incorrect, because the change in momentum of the reflecting light results in a force on the mirror. - (B) Incorrect, because the light energy is absorbed by the mirror and converted into mechanical force. - (C) Correct, because force requires mass and acceleration, neither of which applies to photons. - (D) Correct, because the speed of light remains constant before and after reflection from the surface. **Answer: (A)** Justifying the existence of radiation pressure requires the impulse-momentum theorem. Although photons have no mass, they carry momentum ($$p=E/c$$). Reflection reverses the direction of this momentum, and the rate of change of momentum constitutes a force exerted on the mirror. ### Question 10 A physicist compares a photon of ultraviolet light with frequency $$f_{UV}$$ to a photon of infrared light with frequency $$f_{IR}$$, where $$f_{UV} = 100 f_{IR}$$. Which statement correctly compares the energy $$E_{UV}$$ of the ultraviolet photon to the energy $$E_{IR}$$ of the infrared photon? - (A) $$E_{UV}$$ is $$100$$ times $$E_{IR}$$ because energy is directly proportional to frequency. - (B) $$E_{UV}$$ is $$0.01$$ times $$E_{IR}$$ because energy is inversely proportional to frequency. - (C) $$E_{UV}$$ is $$10$$ times $$E_{IR}$$ because energy is proportional to the square root of frequency. - (D) $$E_{UV}$$ is equal to $$E_{IR}$$ because photon energy depends only on the speed of light. **Answer: (A)** Connecting photon energy to frequency requires applying the Planck relation $$E = hf$$. Since energy is directly proportional to frequency, a photon with 100 times the frequency will possess 100 times the energy. ## Review the Unit - [15.1 Quantum Theory and Wave-Particle Duality](/ap-physics-2-revised/unit-15/1-quantum-theory-and-wave-particle-duality/study-guide/LU54fgTuvW1xw63V) - [15.2 The Bohr Model of Atomic Structure](/ap-physics-2-revised/unit-15/2-the-bohr-model-of-atomic-structure/study-guide/gzEFr1ron8hpACPx) - [15.3 Emission and Absorption Spectra](/ap-physics-2-revised/unit-15/3-emission-and-absorption-spectra/study-guide/QvJsunuWugAm3bOk) - [15.4 Blackbody Radiation](/ap-physics-2-revised/unit-15/4-blackbody-radiation/study-guide/jcWRJUVghpDEK71c) - [15.5 The Photoelectric Effect](/ap-physics-2-revised/unit-15/5-the-photoelectric-effect/study-guide/OLYoFyn8nutvrlZD) - [15.6 Compton Scattering](/ap-physics-2-revised/unit-15/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf) - [15.7 Fission, Fusion, and Nuclear Decay](/ap-physics-2-revised/unit-15/7-fission-fusion-and-nuclear-decay/study-guide/nVULWHgdGjkiGhbI) - [15.8 Types of Radioactive Decay](/ap-physics-2-revised/unit-15/8-types-of-radioactive-decay/study-guide/yQriAHMZEcNvi6kE) ## Other Unit Tests - [Unit 9: Thermodynamics](/ap-physics-2-revised/unit-test/9) - [Unit 10: Electric Force, Field, and Potential](/ap-physics-2-revised/unit-test/10) - [Unit 11: Electric Circuits](/ap-physics-2-revised/unit-test/11) - [Unit 12: Magnetism and Electromagnetism](/ap-physics-2-revised/unit-test/12) - [Unit 13: Geometric Optics](/ap-physics-2-revised/unit-test/13) - [Unit 14: Waves, Sound, and Physical Optics](/ap-physics-2-revised/unit-test/14) ## About This Document Canonical Fiveable pages are available as Markdown at the same path plus `.md`. - [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns - [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing - [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`) - [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)