Module 8: From the Universe to the Atom Quiz

Test Your Understanding

Instructions

This quiz covers Module 8: From the Universe to the Atom. Answer all questions, then check your answers at the bottom.

Topics covered:

  • Origins of elements
  • Atomic structure
  • Quantum mechanics
  • Nuclear physics

Section A: Multiple Choice (1 mark each)

Question 1

The Geiger-Marsden experiment provided evidence for:

A. The existence of electrons B. The nuclear model of the atom C. Electron energy levels D. Neutrons in the nucleus

Question 2

In the proton-proton chain fusion reaction, the net result is:

A. 2 protons → 1 helium nucleus B. 4 protons → 1 helium nucleus + energy C. 1 helium nucleus → 4 protons D. Uranium → barium + krypton

Question 3

After 3 half-lives, what fraction of a radioactive sample remains?

A. 1/3 B. 1/4 C. 1/8 D. 1/16

Question 4

Alpha particles are:

A. High-energy electrons B. Electromagnetic radiation C. Helium-4 nuclei D. Neutrons

Question 5

The de Broglie wavelength of a particle is inversely proportional to its:

A. Energy B. Momentum C. Mass only D. Velocity only

Section B: Short Answer (3-4 marks each)

Question 6

A radioactive isotope has a half-life of 5.0 days. Initially there are \(8.0 \times 10^{20}\) atoms.

  1. Calculate the decay constant. (2 marks)

  2. Calculate the number of atoms remaining after 15 days. (2 marks)

Use: \(\lambda = \frac{\ln 2}{t_{1/2}}\), \(N = N_0 e^{-\lambda t}\) or \(N = N_0 (1/2)^{t/t_{1/2}}\)

Question 7

Calculate the de Broglie wavelength of an electron travelling at \(2.0 \times 10^6\) m/s.

Data: \(h = 6.63 \times 10^{-34}\) J·s, \(m_e = 9.11 \times 10^{-31}\) kg

Use: \(\lambda = \frac{h}{mv}\)

Question 8

Using the Rydberg formula, calculate the wavelength of light emitted when an electron in hydrogen transitions from n = 3 to n = 2.

Data: \(R = 1.097 \times 10^7\) m\(^{-1}\)

Use: \(\frac{1}{\lambda} = R\left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)\)

Section C: Extended Response (5-6 marks each)

Question 9

In a nuclear fission reaction, Uranium-235 absorbs a neutron and splits into Barium-141, Krypton-92, and neutrons.

  1. Write the nuclear equation for this reaction. (2 marks)

  2. If the mass defect is 0.186 u, calculate the energy released per fission. (2 marks)

  3. Calculate the energy released from 1.0 kg of U-235 undergoing complete fission. (2 marks)

Data: 1 u = \(1.66 \times 10^{-27}\) kg, \(c = 3 \times 10^8\) m/s, \(N_A = 6.02 \times 10^{23}\)

Question 10

Compare and contrast nuclear fission and nuclear fusion, including:

  • Definition of each process
  • Which nuclei undergo each process
  • Energy release mechanism
  • Examples of each in nature and technology
  • Challenges in achieving controlled fusion (6 marks)

Answers

  1. B - Most alphas passed through, some deflected significantly → small, dense nucleus

  2. B - 4 protons fuse to form helium-4, releasing positrons, neutrinos, and energy

  3. C - \((1/2)^3 = 1/8\)

  4. C - Alpha particles are helium-4 nuclei (2 protons + 2 neutrons)

  5. B - \(\lambda = h/p\), wavelength is inversely proportional to momentum

Q6: (a) \(\lambda = \frac{0.693}{5.0 \times 24 \times 3600} = 1.6 \times 10^{-6}\) s\(^{-1}\) (b) After 15 days = 3 half-lives: \(N = 8.0 \times 10^{20} \times (1/2)^3 = 1.0 \times 10^{20}\) atoms

Q7: \(\lambda = \frac{h}{mv} = \frac{6.63 \times 10^{-34}}{9.11 \times 10^{-31} \times 2.0 \times 10^6} = 3.6 \times 10^{-10}\) m = 0.36 nm

Q8: \(\frac{1}{\lambda} = 1.097 \times 10^7 \left(\frac{1}{4} - \frac{1}{9}\right) = 1.097 \times 10^7 \times \frac{5}{36} = 1.52 \times 10^6\) m\(^{-1}\) \(\lambda = 6.56 \times 10^{-7}\) m = 656 nm (red - H-alpha line)

Q9: (a) \(^{235}_{92}U + ^1_0n \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3^1_0n\) (b) \(\Delta m = 0.186 \times 1.66 \times 10^{-27} = 3.09 \times 10^{-28}\) kg \(E = \Delta m c^2 = 3.09 \times 10^{-28} \times (3 \times 10^8)^2 = 2.78 \times 10^{-11}\) J = 174 MeV (c) Number of atoms in 1 kg: \(N = \frac{1000}{235} \times 6.02 \times 10^{23} = 2.56 \times 10^{24}\) Total energy: \(E = 2.56 \times 10^{24} \times 2.78 \times 10^{-11} = 7.1 \times 10^{13}\) J

Q10: Key points: - Fission: Heavy nucleus splits into lighter nuclei - Fusion: Light nuclei combine to form heavier nucleus - Fission nuclei: Heavy elements (U-235, Pu-239) - Fusion nuclei: Light elements (H, He isotopes) - Energy source: Both from mass defect → binding energy - Natural examples: Fission (spontaneous decay), Fusion (stars) - Technology: Fission (reactors, weapons), Fusion (experimental, H-bomb) - Fusion challenges: Requires extreme temperature (~10⁷ K), plasma confinement, sustained reaction

Score Guide

Score Performance
90-100% Excellent - Ready for HSC
75-89% Good - Minor revision needed
60-74% Satisfactory - Review weak areas
Below 60% More study required