Chapter 28 Atomic Physics

28.1 Early Models of the Atom

• In the early part of the twentieth century, the “watermelon” model of the atom was widely accepted. (Figure 28.1)

• Figure 28.2 (Rutherford Scattering Experiment)

-particles were scattered by a thin metal foil and observed some were deflected at large angles.

• The idea of “Nuclear atom” is accepted: An atom consists of a small positively charged nucleus surrounded at relatively large distance by a number of electrons, whose total negative charge equals the positive nuclear charge when the atom is electrically neutral.

• The nucleus is about 10000 times smaller than the atom.

28.2 Atomic Spectra

• A line spectrum is a series of discrete electromagnetic wavelengths emitted by the atoms of a low-pressure gas that is subjected to a sufficiently high potential difference. (Neon signs, mercury vapor lamps)

• Line spectra provides an accurate mean of distinguishing between atomic species. (Figure 28.3)

• The line spectrum of atomic hydrogen includes, among others, the Lyman series, the Balmer series, and the Paschen series of wavelengths. (Figure 30.4)

Lyman series: = R_H ( - ) n = 2, 3, 4, …

Balmer series: = R_H ( - ) n = 3, 4, 5, …

Paschen series: = R_H ( - ) n = 4, 5, 6, …

Where R_H is the Rydberg constant (R = 1.097 x 10⁷ m^-1): empirical equations

• Examples

28.3 The Bohr Theory of Hydrogen

< Bohr’s Assumptions >

1. The electron moves in circular orbits about the proton under the influence of the Coulomb force of attraction.

2. Only certain electron orbits are stable. These are orbits in which the hydrogen atom does not emit energy in the form of radiation.

3. Radiation is emitted by the hydrogen atom when the electron “jumps” from a more energetic initial state to a lower state. The frequency of the emitted radiation is

E_i – E_f = hf (E_f < E_i)

Where E_i and E_f are the energy of the initial and final states, respectively, and h is Planck’s constant.

4. The allowed orbits are those for which the electron’s orbital angular momentum about the nucleus is an integral multiple of .

m_evr = n

• Angular momentum () is quantized (Bohr’s postulation)

= n = 1, 2, 3, …

where h is Planck’s constant (6.626 x 10^-34 J-s).

• The radius () of the n-th Bohr orbit is

= = (5.29 x 10^-11) , n = 1, 2, 3, …

where m is the mass of an electron (9.109 x 10^-31 kg), k is (8.988 x 10⁹ N-m²/c²), e is the charge of an electron (1.602 x 10^-19 C), and Z is the atomic number.

• The total energy () for the n-th Bohr orbit is

= - = -(2.18 x 10^-18 J)

= -(13.6 eV) , n = 1, 2, 3, …

• Figure 28.7

• The lowest energy level is called the ground state and the higher levels are excited states.

• The energy needed to remove the electron from the atom is called the ionization energy.

• Examples

• Figure 28.8

• Examples

28.4 Modification of the Bohr Theory

• Bohr’s concept of quantization of angular momentum led to the principal quantum number, n, which determines the energy of the allowed states of hydrogen. All states with the same principal quantum number form a shell identified by K, L, M, … which designated the states for which n = 1, 2, 3, ….

• The orbital quantum number, from 0 to n-1. The states with given values of n and form a subshell. The letters s, p, d, f, g,… are used to designate the states for which = 0, 1, 2, 3, 4,…

• The orbital magnetic quantum number, ranging from - to +, was introduced to explain the Zeeman effect.

• The spin magnetic quantum number

28.5 De Broglie Waves and the Hydrogen Atom

28.6 Quantum Mechanics and the Hydrogen Atom

28.7 The Spin Magnetic Quantum Number

28.8 Electron Clouds

28.9 The Exclusion Principle and the Periodic Table

• The Pauli exclusion principle states that no two electrons in an atom can have the same set of values for the four quantum numbers, (, , , ). This principle determines the way in which the electrons in multiple-electron atoms are distributed into shells () and subshells (, )

• The arrangement of the periodic table of the elements is related to the exclusion principle.

28.10 Buckyballs

28.11 Characteristic X-rays

28.12 Atomic Transitions

28.13 Lasers and Holography

• A laser (Light Amplification by Stimulated Emission of Radiation) is a device that generates electromagnetic waves via a process known as stimulated emission.

• Figure 28.18, 28.19, 28.20

Spontaneous & Stimulated emissions

• Stimulated emission

1. One photon goes in and two photons come out.

2. The emitted photon travels in the same direction as the incoming photon

3. The emitted photon is exactly in step with or has the same phase as the incoming photon (coherent).

• Processes

1. Population inversion (electrical, optical, chemical pumping)

2. Initial triggering with a right frequency photon (= )

3. Avalanche of stimulated photons

4. The process can continue as long as the population inversion is maintained.

5. The process can be enhanced by placing the medium between two mirrors, so that the light wave passed back and forth through many times.

6. One side mirror is not 100% reflecting (laser beam).

28.14 Fluorescence and Phosphorescence

• When an atom absorbs a photon and ends up in an excited state, it can return to the ground state via some intermediate states. The process of converting high frequency radiation to lower frequency radiation is called fluorescence. (Figure 28.29)