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Topic | Discussion | Learning Aids
Nuclear atom | 30.1 RUTHERFORD SCATTERING AND THE NUCLEAR ATOM The idea of a nuclear atom originated in 1911 as a result of experiments by Ernest Rutherford in which particles were scattered by a thin metal foil. The phrase “nuclear atom” refers to the fact that an atom consists of a small, positively charged nucleus surrounded at relatively large distances by a number of electrons, whose total negative charge equals the positive nuclear charge when the atom is electrically neutral. |
Line spectrum | 30.2 LINE 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. Certain groups of discrete wavelengths are referred to as “series.” The following equations can be used to determine the wavelengths in three of the series that are found in the line spectrum of atomic hydrogen: |
Lyman series |

| (30.1)

Balmer series |

| (30.2)

Paschen series |

| (30.3)

The constant term R is called the Rydberg constant and has the value .
Stationary orbit | 30.3 THE BOHR MODEL OF THE HYDROGEN ATOM The Bohr model applies to atoms or ions that have only a single electron orbiting a nucleus containing Z protons. This model assumes that the electron exists in circular orbits that are called stationary orbits because the electron does not radiate electromagnetic waves while in them. According to this model, a photon is emitted only when an electron changes from an orbit with a higher energy Ei to an orbit with a lower energy Ef. The orbital energies and the photon frequency f are related according to |
Photon frequency |

| (30.4)

where h is Planck’s constant. The model also assumes that the magnitude Ln of the orbital angular momentum of the electron can only have the following discrete values:
Angular momentum |

| (30.8)

With these assumptions, it can be shown that the nth Bohr orbit has a radius rn and is associated with a total energy En of
Orbital radius |

| (30.10)

Total orbital energy |

| (30.13)

Ionization energy | The ionization energy is the minimum energy needed to remove an electron completely from an atom. The Bohr model predicts that the wavelengths comprising the line spectrum emitted by a hydrogen atom can be calculated from |
Line spectrum wavelengths |

| (30.14)

| 30.4 DE BROGLIE’S EXPLANATION OF BOHR’S ASSUMPTION ABOUT ANGULAR MOMENTUM Louis de Broglie proposed that the electron in a circular Bohr orbit should be considered as a particle wave and that standing particle waves around the orbit offer an explanation of the angular momentum assumption in the Bohr model. |
| 30.5 THE QUANTUM MECHANICAL PICTURE OF THE HYDROGEN ATOM Quantum mechanics describes the hydrogen atom in terms of the following four quantum numbers: |
Principal quantum number | (1) the principal quantum number n, which can have the integer values n = 1,2,3,… |
Orbital quantum number | (2) the orbital quantum number , which can have the integer values |
Magnetic quantum number | (3) the magnetic quantum number , which can have the positive and negative values |
Spin quantum number | (4) the spin quantum number ms, which, for an electron, can be either or According to quantum mechanics, an electron does not reside in a circular orbit but, rather, has some probability of being found at various distances from the nucleus. |
Use Self-Assessment Test 30.1 to evaluate your understanding of Sections 30.1, 30.2, 30.3, 30.4 and 30.5 .
Pauli exclusion principle | 30.6 THE PAULI EXCLUSION PRINCIPLE AND THE PERIODIC TABLE OF THE ELEMENTS The Pauli exclusion principle states that no two electrons in an atom can have the same set of values for the four quantum numbers n, , , and ms. This principle determines the way in which the electrons in multiple-electron atoms are distributed into shells (defined by the value of n) and subshells (defined by the value of ). |
Convention of letters | The following notation is used to refer to the orbital quantum numbers: s denotes , p denotes , d denotes , f denotes , g denotes , h denotes , and so on. The arrangement of the periodic table of the elements is related to the Pauli exclusion principle. |
X-rays Characteristic X-rays Bremsstrahlung Cutoff wavelength | 30.7 X-RAYS X-rays are electromagnetic waves emitted when high-energy electrons strike a metal target contained within an evacuated glass tube. The emitted X-ray spectrum of wavelengths consists of sharp “peaks” or “lines,” called characteristic X-rays, superimposed on a broad continuous range of wavelengths called Bremsstrahlung. The characteristic X-ray is emitted when an electron in the n = 2 level (L shell) drops into a vacancy in the n = 1 level (K shell). Similarly, the characteristic X-ray is emitted when an electron in the n = 3 level (M shell) drops into a vacancy in the n = 1 level (K shell). The minimum wavelength, or cutoff wavelength , of the Bremsstrahlung is determined by the kinetic energy of the electrons striking the target in the X-ray tube, according to |

| (30.17)

where h is Planck’s constant, c is the speed of light in a vacuum, e is the magnitude of the charge on an electron, and V is the potential difference applied across the X-ray tube.
Stimulated emission | 30.8 THE LASER, 30.9 MEDICAL APPLICATIONS OF THE LASER A laser is a device that generates electromagnetic waves via a process known as stimulated emission. In this process, one photon stimulates the production of another photon by causing an electron in an atom to fall from a higher energy level to a lower energy level. The emitted photon travels in the same direction as the photon causing the stimulation. Because of this mechanism of photon production, the electromagnetic waves generated by a laser are coherent and may be confined to a very narrow beam. |
Spontaneous emission | Stimulated emission contrasts with the process known as spontaneous emission, in which an electron in an atom also falls from a higher to a lower energy level, but does so spontaneously, in a random direction, without any external provocation. |
Use Self-Assessment Test 30.2 to evaluate your understanding of Sections 30.6, 30.7, 30.8 and 30.9 .

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