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Topic E.1 · HL only

Structure of the Atom: notes and practice questions

3 min read Jump to 5 practice questions
Summary
  • This topic explores the relationship between nuclear radius and nucleon number, discrete energy levels in the Bohr model, and quantized angular momentum.
  • The nuclear radius RR is related to the nucleon number AA by R=R0A1/3R = R_0A^{1/3}, where R0R_0 is a constant.
  • The discrete energy levels in the Bohr model for hydrogen are given by En=−13.6n2E_n = -\frac{13.6}{n^2} eV.
  • The angular momentum of an electron in the Bohr model is quantized as mvr=nh2πmvr = \frac{nh}{2\pi}.
  • Deviations from Rutherford scattering at high energies and the calculation of the distance of closest approach are also covered.

How it is examined

Both papers, with the scattering and Bohr content HL only. May 2025 HL Paper 2 TZ1 question 3(a) asked, in two parts, explain why alpha scattering deviates from the Rutherford model at high energy (1 mark: the alpha is within range of the strong nuclear force) and explain how an initial energy E0E_0 estimates the nuclear radius (2 marks: recognize that the nuclear radius is approximately the distance of closest approach, then set initial kinetic energy equal to kQq/rkQq/r). The mark scheme said explicitly that using r in an algebraic expression is not enough for the first marking point, which is a good illustration of how tightly "explains" is read.

Given in the booklet

SL: E=hfE = hf, Planck's constant, the electronvolt conversion. HL adds R=R0A1/3R = R_0 A^{1/3} with R0R_0, the Bohr energy-level formula and mvr=nh/2πmvr = nh/2\pi. Chemical symbols are explicitly not required, so a question that depends on knowing that Au is gold should name the element in words.

Key ideas
  • the Geiger-Marsden-Rutherford experiment and the discovery of the nucleus
  • nuclear notation ZAX^{A}_{Z}\text{X}, where A is the nucleon number, Z the proton number and X the chemical symbol
  • that emission and absorption spectra provide evidence for discrete atomic energy levels
  • that photons are emitted and absorbed during atomic transitions
Not assessed

Recall of chemical symbols is not required.

Guiding questions

  • What is the current understanding of the nature of an atom?
  • What is the role of evidence in the development of models of the atom?
  • In what ways are previous models of the atom still valid despite recent advances in understanding?

Linking questions

  • How can emission spectra allow for the properties of stars to be deduced?
  • How is the distance of closest approach calculated using conservation of energy?
  • How can emission spectra be used to calculate the distances and velocities of celestial bodies?
  • Under what circumstances does the Bohr model fail? (NOS)
  • How have observations led to developments in the model of the atom? (NOS)

Practice questions

5 questions · 5 medium
Showing 5 of 5

Question 1

MediumPaper 2 · calculator5 marks
(a)

The fine-structure constant, α\alpha, is a fundamental physical constant that characterizes the strength of the electromagnetic interaction. It is given by the expression α=e24πϵ0ℏc\alpha = \frac{e^2}{4\pi\epsilon_0 \hbar c}.

(a) Show that the quantity e24πϵ0\frac{e^2}{4\pi\epsilon_0} has units of energy multiplied by distance.

[2]
(b)

(b) Hence, show that the fine-structure constant α\alpha is dimensionless.

[3]

Question 2

MediumPaper 2 · calculator6 marks
(a)

In a hypothetical experiment simulating Rutherford scattering, alpha particles are accelerated towards a thin foil of Uranium. The alpha particles, with a mass of 6.64×10−27 kg6.64 \times 10^{-27} \text{ kg}, approach the Uranium nuclei with an initial speed of 1.8×107 m s−11.8 \times 10^7 \text{ m s}^{-1}. The atomic number for Uranium is 9292.

(a) Calculate the closest distance of approach for these alpha particles to a Uranium nucleus.

[4]
(b)

(b) State two assumptions made in this calculation regarding the interaction between the alpha particle and the nucleus.

[2]

Question 3

MediumPaper 1A · calculator1 mark

The energy levels of a hydrogen atom are given by the formula En=−13.6n2E_n = -\frac{13.6}{n^2} eV, where nn is the principal quantum number.

Consider two transitions in a hydrogen atom:

Transition P: An electron moves from the n=2n=2 energy level to the n=4n=4 energy level.

Transition Q: An electron moves from the n=1n=1 energy level to the n=3n=3 energy level.

What is the ratio energy absorbed in transition Penergy absorbed in transition Q\frac{\text{energy absorbed in transition P}}{\text{energy absorbed in transition Q}}?

A. 27128\frac{27}{128}

B. 12827\frac{128}{27}

C. 11

D. 22

Question 4

MediumPaper 1A · calculator1 mark

An alpha particle (4He^4\text{He}) with an initial kinetic energy of 6.0 MeV6.0 \text{ MeV} is directed towards the center of a stationary lead nucleus (208Pb^{208}\text{Pb}). The alpha particle approaches the nucleus head-on.

What is the distance of closest approach of the alpha particle to the lead nucleus?

A. 2.1×10−14 m2.1 \times 10^{-14} \text{ m}

B. 3.9×10−14 m3.9 \times 10^{-14} \text{ m}

C. 7.8×10−14 m7.8 \times 10^{-14} \text{ m}

D. 1.6×10−13 m1.6 \times 10^{-13} \text{ m}

Question 5

MediumPaper 1A · calculator1 mark

An electron in a hydrogen-like ion absorbs a photon of energy 96 eV96\text{ eV} to make a transition from the n=1n = 1 to the n=3n = 3 state. The energy levels of the ion are given by E=−kn2E = -\frac{k}{n^2}.

What photon energy is required for a transition from the n=2n = 2 to the n=3n = 3 state?

A. 81 eV81\text{ eV}

B. 48 eV48\text{ eV}

C. 24 eV24\text{ eV}

D. 15 eV15\text{ eV}

Every Structure of the Atom question, marked for you

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Where marks are lost

  • Stopping one step short of the conclusion. Two numbers and no sentence is two marks out of three.
  • Answering a procedure question with a platitude.
  • Losing precision in Paper 1B. Uniquely to this paper, quoting the right number badly loses marks.
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What does Structure of the Atom cover in IB Physics?

This topic explores the relationship between nuclear radius and nucleon number, discrete energy levels in the Bohr model, and quantized angular momentum. The nuclear radius R is related to the nucleon number A by R = R_0A^1/3, where R_0 is a constant. The discrete energy levels in the Bohr model for hydrogen are given by E_n = -(13.6)/(n^2) eV.

Is Structure of the Atom SL or HL?

Structure of the Atom is HL only. SL students are not examined on it.

How do I revise Structure of the Atom for IB Physics?

Start from the core idea: this topic explores the relationship between nuclear radius and nucleon number, discrete energy levels in the Bohr model, and quantized angular momentum. In the exam: both papers, with the scattering and Bohr content HL only. May 2025 HL Paper 2 TZ1 question 3(a) asked, in two parts, explain why alpha scattering deviates from the Rutherford model at high energy (1 mark: the alpha is within range of the strong nuclear force) and explain how an initial energy E_0 estimates the nuclear radius (2 marks: recognize that the nuclear radius is approximately the distance of closest approach, then set initial kinetic energy equal to kQq/r). Then practise exam-style questions, easiest first, writing out every step of your working before you check it.

How does FourtyFive help me practise Structure of the Atom?

FourtyFive has 5 Structure of the Atom questions. Every answer you write is marked mark by mark, IB-style, and you see where each mark was won or lost. Every part has a hint, the AI tutor helps you through the step you are stuck on, and your Study Profile picks what to practise next.

Is FourtyFive free for Structure of the Atom practice?

Yes. A free account gives you 50 marked answers a month, and you do not need a card to sign up.

Can I handwrite Structure of the Atom answers on an iPad?

Yes. In the FourtyFive iPad app you write your working by hand with Apple Pencil, the way you would on paper, and it is marked the same way.

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