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Brock University
Physics 1P22/1P92
Winter 2015
Dr. D’Agostino
Tutorial 9 (Chapter 30: Atoms)
Questions
Purpose: To understand the role quantum ideas played in the development of current atomic
models.
1. Describe the Geiger-Marsden experiment, and the Rutherford’s resulting atomic model.
2. Describe the fatal flaw in Rutherford’s atomic model.
3. Describe Bohr’s atomic model.
4. Describe how de Broglie’s idea of matter waves provides a satisfying explanation for why
electrons can travel only in orbits of certain radii.
5. Describe how Bohr’s atomic model explains atomic emission and absorption spectra.
6. Describe the Pauli exclusion principle. How does the Pauli principle help explain the periodic
table of the elements?
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Problems
Purpose: To solve problems related to atomic structure.
1. The nucleus of the hydrogen atom has a radius of about 1.2 × 10−15 m. The electron is at a
distance of about 5.3 × 10−11 m from the nucleus. Assuming the hydrogen atom is a sphere
with a radius of 5.3 × 10−11 m, determine (a) the volume of the atom, (b) the volume of the
nucleus, and (c) the percentage of the volume of the atom that is occupied by the nucleus.
Compare these quantities to the solar system, where the Sun plays the role of the nucleus and
Earth plays the role of the electron. What do you conclude about how “empty” an atom is?
2. A hydrogen atom is in its ground state. It absorbs energy and makes a transition to the n = 4
excited state. The atom returns to its ground state by emitting two photons, one in dropping
to the n = 3 state, and one in further dropping to the ground state. What are the possible
photon wavelengths of (a) the first transition and (b) the second transition?
3. A wavelength of 656.3 nm is emitted by the hydrogen atoms in a high-voltage discharge tube.
What are the initial and final values of the quantum number n for the energy level transition
that produces this wavelength?
4. When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number n. According to
quantum mechanics, however, there is a rule that restricts the initial and final values of the
orbital quantum number `. This rule is called a selection rule and states that ∆` = ±1.
In other words, when an electron makes a transition between energy levels, the value of `
can only increase or decrease by one. The value of ` may not remain the same or increase
or decrease by more than one. According to this rule, which of the following energy level
transitions are allowed: (a) 2s to 1s, (b) 2p to 1s, (c) 4p to 2p, (d) 4s to 2p, (e) 3d to 3s?
5. In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus.
Determine the angular speed of an electron in a hydrogen atom, in revolutions per second,
when it is in (a) the ground state and (b) the first excited state.
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