IB Physics HL | Unit E1: Structure of the Atom

Show all working in the space below each question. Marks are awarded for correct reasoning as well as final answers. When asked what an observation "shows", give a cause-and-effect statement, not a description. State units and round to an appropriate number of significant figures.在每题下方空白处写出全部解题过程。推理与最终答案同等给分。被问及某观测"说明"什么时，给出因果陈述而非描述。注明单位并保留适当的有效数字。

Q1MEDIUM Paper 1 alpha-scattering evidenceα 散射证据 [4 marks]

In the Geiger-Marsden experiment, a beam of alpha particles is fired at a thin gold foil. Two observations are made: (i) the vast majority of alpha particles pass straight through the foil almost undeflected; (ii) a very small fraction are deflected through angles greater than $90^{\circ}$.在盖革-马斯登实验中，一束 α 粒子射向薄金箔。观测到两件事：(i) 绝大多数 α 粒子几乎不偏转地直穿金箔；(ii) 极少数被偏转超过 $90^{\circ}$。

(a) State what each observation (i) and (ii) shows about the structure of the atom.写出观测 (i) 与 (ii) 分别说明了原子结构的什么。 [2]

(b) A typical nucleus has radius $\sim 10^{-15}\ \mathrm{m}$ and a typical atom $\sim 10^{-10}\ \mathrm{m}$. Estimate the ratio of the atomic radius to the nuclear radius, and use it to explain why so few alpha particles are deflected through large angles.典型原子核半径 $\sim 10^{-15}\ \mathrm{m}$，典型原子 $\sim 10^{-10}\ \mathrm{m}$。估算原子半径与原子核半径之比，并用它解释为何只有极少 α 粒子被大角度偏转。 [2]

Q2MEDIUM Paper 1 nuclear notation, isotopes, the u核素符号、同位素、原子质量单位 [6 marks]

Consider the nuclide $^{35}_{17}\mathrm{Cl}$.考虑核素 $^{35}_{17}\mathrm{Cl}$。

(a) State the number of protons, neutrons and nucleons in this nuclide.写出该核素的质子数、中子数与核子数。 [2]

(b) Write down the nuclear symbol of one isotope of chlorine and explain, in terms of $Z$ and $N$, why it is an isotope of $^{35}_{17}\mathrm{Cl}$.写出氯的一个同位素的核素符号，并用 $Z$ 与 $N$ 解释它为何是 $^{35}_{17}\mathrm{Cl}$ 的同位素。 [2]

(c) Estimate the mass of the $^{35}_{17}\mathrm{Cl}$ nucleus in kilograms, taking each nucleon as $1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg}$.取每个核子为 $1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg}$，估算 $^{35}_{17}\mathrm{Cl}$ 原子核的质量（kg）。 [2]

Q3MEDIUM Paper 1 photon energy and wavelength光子能量与波长 [6 marks]

A photon is emitted when an electron in an atom makes a transition, releasing $4.00\ \mathrm{eV}$ of energy. ($h = 6.63\times10^{-34}\ \mathrm{J\,s}$, $c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$, $1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$.)原子中一个电子发生跃迁，释放 $4.00\ \mathrm{eV}$ 能量并发射一个光子。（$h = 6.63\times10^{-34}\ \mathrm{J\,s}$，$c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$，$1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$。）

(a) Calculate the energy of the photon in joules.计算该光子的能量（焦耳）。 [2]

(b) Using $E = hc/\lambda$, calculate the wavelength of the photon.用 $E = hc/\lambda$ 计算该光子的波长。 [2]

(c) State which region of the electromagnetic spectrum this photon belongs to, and justify your answer with reference to the wavelength found in (b).说明该光子属于电磁波谱的哪个区域，并结合 (b) 求得的波长说明理由。 [2]

Q4HARD Paper 1 emission vs absorption spectra发射与吸收光谱 [4 marks]

A sample of cool atomic hydrogen gas is studied in two ways: first, white light is passed through the gas and the transmitted light is examined; second, the same gas is excited in a discharge tube and the light it emits is examined directly.对一份低温原子氢气以两种方式研究：其一，让白光穿过气体并检查透射光；其二，将同种气体在放电管中激发，直接检查它发出的光。

(a) Describe the appearance of the spectrum observed in each case.描述两种情形下所观测到的光谱外观。 [2]

(b) Explain why the dark lines of the first spectrum occur at exactly the same wavelengths as the bright lines of the second.解释为何第一种光谱的暗线恰好出现在第二种光谱亮线相同的波长处。 [2]

Q5HARD Paper 1 strong force, nuclear energy levels强核力与核能级 [6 marks]

Protons in a nucleus exert a Coulomb repulsion on one another, yet stable nuclei do not fly apart.原子核中的质子彼此施加库仑斥力，但稳定的原子核并不飞散。

(a) State three properties of the strong nuclear force, and explain how they allow it to hold the nucleus together.写出强核力的三条性质，并解释它们如何使强核力把原子核束缚在一起。 [3]

(b) An excited nucleus de-excites by emitting gamma photons of only certain discrete energies. State what this discreteness shows about the nucleus, and compare the energy scale of nuclear transitions with that of atomic electron transitions.某激发态原子核通过发射仅具某些分立能量的 γ 光子退激。说明这种分立性揭示了原子核的什么，并比较核跃迁与原子电子跃迁的能量尺度。 [3]

Data and Diagram Questions数据与图表题

These items reward careful reading of energy-level diagrams and graphs. Decide whether to work in eV or joules before substituting, and quote photon energies as positive differences $E_{\text{high}} - E_{\text{low}}$.这些题考查对能级图与图线的细致读取。代入前先决定用 eV 还是焦耳，并把光子能量写成正的能级差 $E_{\text{high}} - E_{\text{low}}$。

Q6HARD Paper 1B energy-level diagram to spectral lines由能级图到谱线 [10 marks]

An atom has just three energy levels, with energies measured relative to the ionised state ($E = 0$):某原子仅有三个能级，能量相对电离态（$E = 0$）测量：

Level能级	$E_1$	$E_2$	$E_3$
Energy / eV能量 / eV	$-6.00$	$-3.40$	$-1.50$

(a) Three downward transitions are possible between these levels. State which one emits the photon of longest wavelength, and calculate that wavelength.这些能级间可能有三种向下跃迁。指出哪一种发射波长最长的光子，并计算该波长。 [3]

(b) Calculate the wavelength of the photon of shortest wavelength emitted by this atom.计算该原子发射的波长最短的光子的波长。 [3]

(c) Calculate the minimum energy, in joules, needed to ionise this atom from its ground state.计算把该原子从基态电离所需的最小能量（焦耳）。 [2]

(d) The atoms are now kept cool, so they sit in the ground state, and white light is passed through the gas. State which transitions give rise to dark lines in the absorption spectrum, and justify your answer.现把原子保持低温使其处于基态，并让白光穿过该气体。指出哪些跃迁会在吸收光谱中产生暗线，并说明理由。 [2]

Q7HARD Paper 1B HL ONLY mass defect and binding energy质量亏损与结合能 [12 marks]

The helium-4 nucleus $^{4}_{2}\mathrm{He}$ is made of 2 protons and 2 neutrons. The relevant masses are: proton $m_p = 1.00728\ \mathrm{u}$, neutron $m_n = 1.00867\ \mathrm{u}$, helium-4 nucleus $m(^{4}_{2}\mathrm{He}) = 4.00150\ \mathrm{u}$. ($1\ \mathrm{u} = 931.5\ \mathrm{MeV\,c^{-2}}$.)氦-4 原子核 $^{4}_{2}\mathrm{He}$ 由 2 个质子和 2 个中子组成。相关质量为：质子 $m_p = 1.00728\ \mathrm{u}$、中子 $m_n = 1.00867\ \mathrm{u}$、氦-4 原子核 $m(^{4}_{2}\mathrm{He}) = 4.00150\ \mathrm{u}$。（$1\ \mathrm{u} = 931.5\ \mathrm{MeV\,c^{-2}}$。）

(a) Define the mass defect of a nucleus, and calculate the mass defect of $^{4}_{2}\mathrm{He}$ in unified atomic mass units.定义原子核的质量亏损，并计算 $^{4}_{2}\mathrm{He}$ 的质量亏损（统一原子质量单位）。 [3]

(b) Calculate the binding energy of $^{4}_{2}\mathrm{He}$ in MeV.计算 $^{4}_{2}\mathrm{He}$ 的结合能（MeV）。 [3]

(d) The binding-energy-per-nucleon curve rises steeply for light nuclei, peaks near iron ($^{56}_{26}\mathrm{Fe}$, about $8.8\ \mathrm{MeV}$ per nucleon), then falls slowly for heavy nuclei. Use the shape of this curve to explain why energy is released both when light nuclei fuse and when heavy nuclei split.每核子结合能曲线对轻核陡升，在铁（$^{56}_{26}\mathrm{Fe}$，约 $8.8\ \mathrm{MeV}$ 每核子）附近达峰，随后对重核缓降。用该曲线的形状解释为何轻核聚变与重核裂变都会释放能量。 [4]

Extended Structured Problems长结构问题

Set out each calculation step by step. Method marks dominate the longer items; carry intermediate values to extra figures and round only the final answer. Pair each piece of evidence with the conclusion it supports.逐步写出每步计算。长题中方法分占比最大；中间值多保留几位，仅在最终答案处取舍有效数字。把每条证据与它支持的结论配对。

Q8HARD Paper 2 HL ONLY Bohr model of hydrogen氢原子玻尔模型 [12 marks]

In the Bohr model the allowed energies of the electron in a hydrogen atom are $E_n = -\dfrac{13.6}{n^2}\ \mathrm{eV}$, with $n = 1, 2, 3, \dots$ ($h = 6.63\times10^{-34}\ \mathrm{J\,s}$, $c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$, $1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$.)在玻尔模型中，氢原子电子的允许能量为 $E_n = -\dfrac{13.6}{n^2}\ \mathrm{eV}$，$n = 1, 2, 3, \dots$（$h = 6.63\times10^{-34}\ \mathrm{J\,s}$，$c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$，$1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$。）

(a) Calculate the energy, in eV, of the $n = 2$ and $n = 3$ levels.计算 $n = 2$ 与 $n = 3$ 能级的能量（eV）。 [2]

(b) An electron makes the transition $n = 3 \to n = 2$. Calculate the energy of the emitted photon in joules.一个电子发生跃迁 $n = 3 \to n = 2$。计算所发射光子的能量（焦耳）。 [3]

(d) Calculate the energy, in joules, required to ionise a hydrogen atom from its ground state.计算把氢原子从基态电离所需的能量（焦耳）。 [2]

(e) Explain why the emission spectrum of hydrogen consists of discrete lines rather than a continuous band of colours.解释为何氢的发射光谱由分立谱线组成，而非连续的颜色带。 [2]

Q9HARD Paper 2 scattering evidence + gamma emission散射证据与 γ 发射 [10 marks]

The Geiger-Marsden experiment provided the evidence that led Rutherford to the nuclear model of the atom. ($h = 6.63\times10^{-34}\ \mathrm{J\,s}$, $1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$.)盖革-马斯登实验提供了引导卢瑟福建立原子核模型的证据。（$h = 6.63\times10^{-34}\ \mathrm{J\,s}$，$1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$。）

(a) Outline the experimental arrangement, and state the two main experimental observations together with the conclusion each one supports about the atom.概述实验装置，并写出两个主要实验观测以及各自支持的关于原子的结论。 [4]

(b) Explain why the Thomson "plum pudding" model, in which positive charge is spread uniformly throughout the atom, cannot account for the large-angle deflections.解释为何汤姆孙"葡萄干布丁"模型（正电荷均匀弥散于整个原子）无法解释大角度偏转。 [2]

(c) The same gold nucleus, when excited, can de-excite by emitting a gamma photon between two nuclear energy levels separated by $1.33\ \mathrm{MeV}$. Calculate the frequency of this gamma photon.同一金原子核被激发后，可在相距 $1.33\ \mathrm{MeV}$ 的两核能级间发射 γ 光子退激。计算该 γ 光子的频率。 [3]

(d) State what the discrete energy of the emitted gamma photon shows about the nucleus.说明所发射 γ 光子能量的分立性揭示了原子核的什么。 [1]

Q10HARD Paper 2 HL ONLY mass defect via $E = \Delta m c^2$由 $E = \Delta m c^2$ 求质量亏损 [12 marks]

The lithium-7 nucleus $^{7}_{3}\mathrm{Li}$ contains 3 protons and 4 neutrons. Masses: proton $m_p = 1.00728\ \mathrm{u}$, neutron $m_n = 1.00867\ \mathrm{u}$, lithium-7 nucleus $m(^{7}_{3}\mathrm{Li}) = 7.01436\ \mathrm{u}$. ($1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg} = 931.5\ \mathrm{MeV\,c^{-2}}$, $c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$, $1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$.)锂-7 原子核 $^{7}_{3}\mathrm{Li}$ 含 3 个质子与 4 个中子。质量：质子 $m_p = 1.00728\ \mathrm{u}$、中子 $m_n = 1.00867\ \mathrm{u}$、锂-7 原子核 $m(^{7}_{3}\mathrm{Li}) = 7.01436\ \mathrm{u}$。（$1\ \mathrm{u} = 1.66\times10^{-27}\ \mathrm{kg} = 931.5\ \mathrm{MeV\,c^{-2}}$，$c = 3.00\times10^{8}\ \mathrm{m\,s^{-1}}$，$1\ \mathrm{eV} = 1.60\times10^{-19}\ \mathrm{J}$。）

(a) Explain what is meant by the binding energy of a nucleus, and write down the expression for the mass defect of $^{7}_{3}\mathrm{Li}$ in terms of $m_p$, $m_n$ and $m(^{7}_{3}\mathrm{Li})$.解释原子核结合能的含义，并用 $m_p$、$m_n$ 与 $m(^{7}_{3}\mathrm{Li})$ 写出 $^{7}_{3}\mathrm{Li}$ 质量亏损的表达式。 [2]

(b) Calculate the mass defect of $^{7}_{3}\mathrm{Li}$ in kilograms.计算 $^{7}_{3}\mathrm{Li}$ 的质量亏损（千克）。 [3]

(c) Using $E = \Delta m\, c^2$, calculate the binding energy of $^{7}_{3}\mathrm{Li}$ in joules.用 $E = \Delta m\, c^2$ 计算 $^{7}_{3}\mathrm{Li}$ 的结合能（焦耳）。 [3]

(d) Show that this binding energy is about $39\ \mathrm{MeV}$, and calculate the binding energy per nucleon.证明该结合能约为 $39\ \mathrm{MeV}$，并计算每核子结合能。 [2]

(e) The binding energy per nucleon of $^{4}_{2}\mathrm{He}$ is about $7.1\ \mathrm{MeV}$. State, with a reason, which of $^{7}_{3}\mathrm{Li}$ and $^{4}_{2}\mathrm{He}$ is the more tightly bound nucleus.$^{4}_{2}\mathrm{He}$ 的每核子结合能约为 $7.1\ \mathrm{MeV}$。写出 $^{7}_{3}\mathrm{Li}$ 与 $^{4}_{2}\mathrm{He}$ 中哪个原子核束缚更紧，并说明理由。 [2]

Structure of the Atom原子结构

Short Structured Items短结构题

Data and Diagram Questions数据与图表题

Extended Structured Problems长结构问题