Atoms

Atoms traces how our picture of the atom developed from experiments, and how that picture explains the sharp spectral lines emitted by gases. In this chapter you will study the Geiger-Marsden alpha particle scattering experiment, in which most alpha particles passed straight through a thin gold foil but a few were deflected through large angles. From this, Rutherford concluded that the positive charge and almost all the mass of an atom are concentrated in a tiny nucleus. You will learn about impact parameter and distance of closest approach, and why Rutherford's model cannot explain the stability of atoms or their line spectra. You will then study Bohr's model of the hydrogen atom: stationary orbits, quantisation of angular momentum, mvr = nh/(2 pi), and emission or absorption of a photon when the electron jumps between levels. You will derive the radius and energy of the nth orbit, use E = -13.6/n^2 eV to draw energy level diagrams, explain the Lyman, Balmer and Paschen series, and see how de Broglie's waves explain Bohr's quantisation condition.

Detailed Worksheet: Atoms Section A - Definitions (10 marks) 1. State two main observations of the Geiger-Marsden alpha scattering experiment and the conclusions drawn from them. (2 marks) 2. Define impact parameter. How is the scattering angle related to it? (2 marks) 3. State Bohr's three postulates for the hydrogen atom. (2 marks) 4. Define ionisation energy and excitation energy of an atom. What is the ionisation energy of a hydrogen atom in its ground state? (2 marks) 5. Why does Rutherford's model fail to explain the stability of an atom? (2 marks) Section B - Calculations and Applications (15 marks) 6. The radius of the first Bohr orbit of hydrogen is 0.53 x 10^-10 m. Find the radii of the second and third orbits. (3 marks) 7. Using E = -13.6/n^2 eV, find the energies of the n = 2 and n = 3 levels of hydrogen and the energy needed to ionise an atom in the n = 2 state. (3 marks) 8. Calculate the wavelength of the photon emitted when an electron in a hydrogen atom jumps from n = 3 to n = 2 (hc = 1240 eV nm). Name the series and the region of the spectrum. (3 marks) 9. In a Geiger-Marsden experiment, an alpha particle of kinetic energy 7.7 MeV is directed at a gold nucleus (Z = 79). Calculate the distance of closest approach (1/(4 pi epsilon0) = 9 x 10^9 N m^2 C^-2, e = 1.6 x 10^-19 C). (3 marks) 10. Using R = 1.097 x 10^7 m^-1, calculate the shortest and longest wavelengths of the Lyman series. (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled schematic diagram of the Geiger-Marsden alpha scattering experiment, and a sketch of the paths of alpha particles with different impact parameters near a nucleus. (4 marks) 12. Draw the energy level diagram of the hydrogen atom for n = 1 to n = 5 and n = infinity, marking the energies. Show transitions for the Lyman, Balmer and Paschen series. (3 marks) 13. Draw a diagram showing a standing de Broglie wave in the n = 3 orbit, with three wavelengths fitting the circumference. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Show that in a Bohr orbit the total energy of the electron is negative and equal to minus its kinetic energy, and that the potential energy is twice the total energy. Find KE, PE and total energy in the ground state of hydrogen. (5 marks) 15. Hydrogen atoms are excited to the n = 4 level. How many spectral lines can be emitted as they return to the ground state? Identify each line by series and calculate the wavelength of the line with the least energy. (5 marks) 16. Explain how de Broglie's hypothesis justifies Bohr's second postulate. Verify that the de Broglie wavelength of the electron in the first orbit equals the circumference of the orbit (speed 2.18 x 10^6 m/s, m = 9.1 x 10^-31 kg, h = 6.63 x 10^-34 J s). State two limitations of Bohr's model. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use the given constants and show units. Draw neat energy level diagrams.