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Modern and Nuclear Physics近代物理与核物理

Practice Questions · AP-Feeder · ON / BC / AB Provincial & Diploma Styles练习题集 · AP 衔接 · 安 / 卑 / 阿省考与毕业考风格

EASY易 MEDIUM中 HARD难 🇺🇸 US美 🇨🇦 ON安 🇨🇦 BC卑 🇨🇦 AB阿 AP-style MCQAP 风格选择题 AP-feeder FRQAP 衔接简答题 ON Provincial-style安大略省考风格 BC Provincial-style卑诗省考风格 AB Diploma-style阿尔伯塔毕业考风格 Honors荣誉级
Name:姓名：Date:日期：
PART I  ·  SHORT RESPONSE第一部分  ·  短答题AP-style MCQ + ON/BC short answer · 24 marksAP 风格选择题 + 安/卑省考短答 · 共 24 分

Section A · Short ResponseA 部分 · 短答题

Mix of multiple-choice and short-answer items. For MCQs, circle the letter; show enough work in the margin that a marker could verify. State units in every numerical answer. Constants: $h = 6.63 \times 10^{-34}\ \text{J}\cdot\text{s}$, $c = 3.00 \times 10^{8}\ \text{m/s}$, $1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$, $1\ \text{u} = 931.5\ \text{MeV}/c^2$. Calculator permitted throughout.本节包含选择题与短答题。选择题请圈出字母答案，并在空白处写下足以让阅卷人核对的过程。每个数值答案都要写出单位。常数：$h = 6.63 \times 10^{-34}\ \text{J}\cdot\text{s}$，$c = 3.00 \times 10^{8}\ \text{m/s}$，$1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}$，$1\ \text{u} = 931.5\ \text{MeV}/c^2$。全卷可用计算器。

Q1EASY易 🇺🇸 US美 AP-style MCQAP 风格选择题 §1 Photon energy光子能量 · HS-PS4-3 [3 marks][3 分]

A photon has frequency $5.0 \times 10^{14}\ \text{Hz}$. What is its energy?一个光子的频率为 $5.0 \times 10^{14}\ \text{Hz}$。它的能量是多少？

  1. (A) $3.3 \times 10^{-19}\ \text{J}$
  2. (B) $6.63 \times 10^{-34}\ \text{J}$
  3. (C) $5.0 \times 10^{14}\ \text{J}$
  4. (D) $1.3 \times 10^{-48}\ \text{J}$
Q2EASY易 🇺🇸 US美 AP-style MCQAP 风格选择题 §4 Nuclear notation核符号 · HS-PS1-8 [3 marks][3 分]

How many neutrons are in the nucleus of ${}^{16}_{8}\mathrm{O}$?${}^{16}_{8}\mathrm{O}$ 的原子核中有多少个中子？

  1. (A) $8$
  2. (B) $16$
  3. (C) $24$
  4. (D) $4$
Q3MEDIUM中 🇨🇦 ON安 ON Provincial-style安大略省考风格 §6 Half-life半衰期 · SPH3U D3.11 [6 marks][6 分]

A sample starts with $800$ radioactive nuclei. The isotope has a half-life of $T = 12\ \text{hours}$.一个样品开始时有 $800$ 个放射性核。该同位素的半衰期 $T = 12\ \text{小时}$。

(a) How many nuclei remain after $3$ half-lives? Show the halving sequence.经过 $3$ 个半衰期后剩余多少个核？写出逐次减半的过程。 [2]
(b) How many real hours have elapsed after those $3$ half-lives?那 $3$ 个半衰期对应经过了多少实际小时？ [1]
(c) Explain why the sample never reaches exactly zero nuclei in a finite number of half-lives.解释为什么样品在有限个半衰期内永远无法精确达到零个核。 [1]
(d) State whether storing the sample in a freezer would change its half-life, and justify your answer.说明把样品放入冰箱是否会改变其半衰期，并说明理由。 [2]
Q4MEDIUM中 🇺🇸 US美 AP-style MCQAP 风格选择题 §1 Photoelectric effect光电效应 · HS-PS4-3 [3 marks][3 分]

Light of a fixed frequency above threshold shines on a metal and ejects electrons. If the intensity of the light is doubled while the frequency is unchanged, what happens?高于阈值的固定频率的光照射金属并射出电子。若在频率不变的情况下将光的强度加倍，会发生什么？

  1. (A) The number of electrons ejected per second doubles; each electron's kinetic energy is unchanged每秒射出的电子数加倍；每个电子的动能不变
  2. (B) The kinetic energy of each ejected electron doubles每个被射出电子的动能加倍
  3. (C) No electrons are ejected because intensity is below threshold没有电子射出，因为强度低于阈值
  4. (D) The kinetic energy of each ejected electron halves每个被射出电子的动能减半
Q5MEDIUM中 🇨🇦 BC卑 🇨🇦 AB阿 BC Provincial-style卑诗省考风格 §5 Radioactive decay放射性衰变 · 30-D3.2k [9 marks][9 分]

Radium-226 (${}^{226}_{88}\mathrm{Ra}$) undergoes alpha decay; carbon-14 (${}^{14}_{6}\mathrm{C}$) undergoes beta-minus decay.镭-226（${}^{226}_{88}\mathrm{Ra}$）发生 alpha 衰变；碳-14（${}^{14}_{6}\mathrm{C}$）发生 beta 负衰变。

(a) Write the balanced nuclear equation for the alpha decay of Ra-226, identifying the daughter's $A$ and $Z$.写出 Ra-226 alpha 衰变的配平核方程，并指出子核的 $A$ 和 $Z$。 [3]
(b) Write the balanced nuclear equation for the beta-minus decay of C-14 (include the antineutrino).写出 C-14 beta 负衰变的配平核方程（包含反中微子）。 [3]
(c) Rank alpha, beta and gamma radiation from least to most penetrating, naming a material that stops each.将 alpha、beta、gamma 辐射按穿透力从弱到强排序，并各举一种能阻挡它的材料。 [3]
PART II  ·  EXTENDED RESPONSE第二部分  ·  简答题AP-feeder FRQ + honors · 31 marksAP 衔接简答题 + 荣誉级 · 共 31 分

Section B · Extended ResponseB 部分 · 简答题

Show every step of reasoning. State the formula used before substituting values, and write units in every final answer. Constants as in Part I. Calculator permitted on Q6-Q9.每一步推理都要写出。代入数值前先写出所用公式，并在每个最终答案中写出单位。常数同第一部分。Q6-Q9 可用计算器。

Q6MEDIUM中 🇺🇸 US美 AP-feeder FRQAP 衔接简答题 §1 Photoelectric effect光电效应 · HS-PS4-3 [8 marks][8 分]

A clean metal surface has a work function $\phi = 2.30\ \text{eV}$. Light of frequency $9.0 \times 10^{14}\ \text{Hz}$ is shone onto it.一块洁净金属表面的逸出功 $\phi = 2.30\ \text{eV}$。频率为 $9.0 \times 10^{14}\ \text{Hz}$ 的光照射其上。

(a) Find the threshold frequency $f_0$ of the metal.求该金属的阈频 $f_0$。 [2]
(b) State, with a reason, whether electrons are ejected by this light.说明该光是否能射出电子，并给出理由。 [1]
(c) Find the maximum kinetic energy of an ejected electron, in joules.求被射出电子的最大动能，以焦耳为单位。 [3]
(d) Express that maximum kinetic energy in electronvolts.将该最大动能用电子伏特表示。 [2]
Q7MEDIUM中 🇨🇦 ON安 🇨🇦 AB阿 ON Provincial-style安大略省考风格 §3 Atomic spectra原子光谱 · 30-D2.5k [7 marks][7 分]

In a hydrogen atom an electron drops from the $n=2$ level at $-3.40\ \text{eV}$ to the $n=1$ level at $-13.60\ \text{eV}$, emitting a single photon.在氢原子中，一个电子从能级 $-3.40\ \text{eV}$（$n=2$）跃迁到 $-13.60\ \text{eV}$（$n=1$），发射一个光子。

(a) Find the energy of the emitted photon in eV.求发射光子的能量，以 eV 为单位。 [2]
(b) Convert that energy to joules.将该能量换算为焦耳。 [1]
(c) Find the frequency of the photon.求该光子的频率。 [2]
(d) Find the wavelength of the photon and state which region of the spectrum it lies in.求该光子的波长，并指出它位于光谱的哪个区域。 [2]
Q8HARD难 🇨🇦 AB阿 AB Diploma-style阿尔伯塔毕业考风格 §4 Binding energy结合能 · 30-D3.6k [8 marks][8 分]

The lithium-7 nucleus ${}^{7}_{3}\mathrm{Li}$ has a measured mass of $7.01600\ \text{u}$. Use $m_p = 1.00728\ \text{u}$, $m_n = 1.00867\ \text{u}$.锂-7 原子核 ${}^{7}_{3}\mathrm{Li}$ 的测得质量为 $7.01600\ \text{u}$。取 $m_p = 1.00728\ \text{u}$，$m_n = 1.00867\ \text{u}$。

(a) State how many protons and how many neutrons the nucleus contains.写出该原子核含有多少个质子和多少个中子。 [1]
(b) Find the total mass of the free nucleons.求自由核子的总质量。 [2]
(c) Find the mass defect $\Delta m$ of the nucleus.求该原子核的质量亏损 $\Delta m$。 [2]
(d) Find the binding energy in MeV.求结合能，以 MeV 为单位。 [2]
(e) Find the binding energy per nucleon.求每核子结合能。 [1]
Q9HARD难Honors荣誉级 🇺🇸 US美 AP-feeder FRQAP 衔接简答题 §2 Wave-particle duality波粒二象性 · HS-PS4-3 (above NGSS floor)（超出 NGSS 基准） [8 marks][8 分]

An electron ($m = 9.11 \times 10^{-31}\ \text{kg}$) moves at $v = 2.0 \times 10^{6}\ \text{m/s}$.一个电子（$m = 9.11 \times 10^{-31}\ \text{kg}$）以 $v = 2.0 \times 10^{6}\ \text{m/s}$ 运动。

(a) Find the magnitude of the electron's momentum.求该电子动量的大小。 [2]
(b) Find the de Broglie wavelength of the electron.求该电子的德布罗意波长。 [3]
(c) Explain why an electron beam can be diffracted by a crystal lattice (spacing $\sim 0.1$ nm).解释为什么电子束能被晶格（间距约 $0.1$ nm）衍射。 [1]
(d) A tennis ball moving at the same speed has a de Broglie wavelength near $10^{-34}\ \text{m}$. Explain why matter waves are never observed for everyday objects.以相同速率运动的网球，其德布罗意波长约为 $10^{-34}\ \text{m}$。解释为什么日常物体观察不到物质波。 [2]
PART III  ·  MODELING / APPLIED第三部分  ·  建模与应用AB Diploma + Universal · 25 marks阿省毕业考 + 通用题型 · 共 25 分

Section C · Modeling and ApplicationsC 部分 · 建模与应用

Define symbols (with units) at the start of each question. State the formula used before substituting. Conclude each question with a one-sentence answer in context. Constants as in Part I. Calculator permitted throughout Part III.每题开始时定义符号（含单位）。代入数值前先写出所用公式。每题以一句结合情境的完整句子作答。常数同第一部分。第三部分全程可用计算器。

Q10MEDIUM中 🇨🇦 AB阿 AB Diploma-style阿尔伯塔毕业考风格 §6 Half-life (applied)半衰期（应用） · 30-D3.3k [9 marks][9 分]

Iodine-131 (${}^{131}_{53}\mathrm{I}$) is used to treat thyroid cancer. Its half-life is $T = 8.02\ \text{days}$. A patient receives a dose containing $N_0 = 1.60 \times 10^{12}$ atoms.碘-131（${}^{131}_{53}\mathrm{I}$）用于治疗甲状腺癌，半衰期 $T = 8.02$ 天。患者接受含 $N_0 = 1.60 \times 10^{12}$ 个原子的剂量。

(a) How many I-131 atoms remain after $24.06$ days? (Use $N = N_0 (1/2)^{t/T}$.)$24.06$ 天后剩余多少个 I-131 原子？（用 $N = N_0 (1/2)^{t/T}$。） [3]
(b) What fraction of the original activity remains after $32.08$ days?$32.08$ 天后原始活度的多少分数仍存在？ [2]
(c) Explain why the activity is considered clinically negligible after about $5$ half-lives.解释为什么约 $5$ 个半衰期后活度在临床上被视为可忽略。 [2]
(d) A nurse suggests warming the sample to speed up its decay. Explain why this will not work.一名护士建议把样品加热以加快其衰变。解释为什么这行不通。 [2]
Q11MEDIUM中 🇨🇦 AB阿 AB Diploma-style阿尔伯塔毕业考风格 §7 Fusion & mass-energy聚变与质能 · 30-D3.5k [9 marks][9 分]

The deuterium-tritium fusion reaction is ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \to {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$. Masses: $m({}^{2}\mathrm{H}) = 2.01410\ \text{u}$, $m({}^{3}\mathrm{H}) = 3.01605\ \text{u}$, $m({}^{4}\mathrm{He}) = 4.00260\ \text{u}$, $m_n = 1.00867\ \text{u}$.氘-氚聚变反应为 ${}^{2}_{1}\mathrm{H} + {}^{3}_{1}\mathrm{H} \to {}^{4}_{2}\mathrm{He} + {}^{1}_{0}\mathrm{n}$。质量：$m({}^{2}\mathrm{H}) = 2.01410\ \text{u}$，$m({}^{3}\mathrm{H}) = 3.01605\ \text{u}$，$m({}^{4}\mathrm{He}) = 4.00260\ \text{u}$，$m_n = 1.00867\ \text{u}$。

(a) Find the total mass on the reactant side.求反应物一侧的总质量。 [1]
(b) Find the total mass on the product side.求产物一侧的总质量。 [1]
(c) Find the mass defect $\Delta m$ of the reaction.求该反应的质量亏损 $\Delta m$。 [2]
(d) Find the energy released, in MeV.求释放的能量，以 MeV 为单位。 [3]
(e) Explain, using the binding-energy-per-nucleon curve, why this reaction releases energy.用每核子结合能曲线解释为什么该反应释放能量。 [2]
Q12HARD难Honors荣誉级 🇺🇸 US美 AP-feeder FRQAP 衔接简答题 §7 Fission chain reaction裂变链式反应 · HS-PS1-8 (above NGSS floor)（超出 NGSS 基准） [7 marks][7 分]

A uranium-235 nucleus absorbs a slow neutron and fissions: ${}^{1}_{0}\mathrm{n} + {}^{235}_{92}\mathrm{U} \to {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + x\,{}^{1}_{0}\mathrm{n}$. The mass defect of this reaction is $\Delta m = 0.1860\ \text{u}$.一个铀-235 核吸收一个慢中子后裂变：${}^{1}_{0}\mathrm{n} + {}^{235}_{92}\mathrm{U} \to {}^{141}_{56}\mathrm{Ba} + {}^{92}_{36}\mathrm{Kr} + x\,{}^{1}_{0}\mathrm{n}$。该反应的质量亏损为 $\Delta m = 0.1860\ \text{u}$。

(a) Balance the equation: find the number $x$ of neutrons released.配平方程：求释放的中子数 $x$。 [2]
(b) Find the energy released per fission, in MeV.求每次裂变释放的能量，以 MeV 为单位。 [2]
(c) Convert that energy to joules.将该能量换算为焦耳。 [2]
(d) Explain how the released neutrons make a self-sustaining chain reaction possible.解释释放的中子如何使自持链式反应成为可能。 [1]
🇺🇸 US NGSS美国 NGSSHS-PS4-3 · HS-PS1-8
🇨🇦 Ontario安大略SPH3U D3 · D3.11 · D3.12 · SPH4U Strand F
🇨🇦 British Columbia不列颠哥伦比亚Physics 12 / Science 9: atomic models, radioactivity, half-life, nuclear energy物理 12 / 科学 9：原子模型、放射性、半衰期、核能
🇨🇦 Alberta阿尔伯塔Physics 30 Unit C/D · 30-C2.3k · 30-D2.5k · 30-D3.2k · 30-D3.6k

Full Syllabus Map lives in ../Study Guides/Unit_12_Modern_and_Nuclear_Physics.html. Note: NGSS treats the wave/particle and nuclear-decay ideas qualitatively (HS-PS4-3, HS-PS1-8); the quantitative photon, binding-energy and decay-equation items are core for Alberta Physics 30 and are honors-flagged where they sit above the NGSS-assessed floor.完整大纲对照表见 ../Study Guides/Unit_12_Modern_and_Nuclear_Physics.html。注：NGSS 对波粒与核衰变概念作定性处理（HS-PS4-3、HS-PS1-8）；定量的光子、结合能与衰变方程题目是阿尔伯塔物理 30 的核心内容，凡超出 NGSS 考查范围处均标注荣誉级。