Physics > Atoms and Nuclei

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  • Atom, as a whole, is electrically neutral and therefore contains equal amount of positive and negative charges.
  • In Thomson's model, an atom is a spherical cloud of positive charges with electrons embedded in it.
  • In Rutherford's model, most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus (typically one by ten thousand the size of an atom), and the electrons revolve around it.
  • Rutherford nuclear model has two main difficulties in explaining the structure of atom: (a) It predicts that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus. This contradicts the stability of matter. (b) It cannot explain the characteristic line spectra of atoms of different elements.
  • Atoms of each element are stable and emit characteristic spectrum. The spectrum consists of a set of isolated parallel lines termed as line spectrum. It provides useful information about the atomic structure.

 

The atomic hydrogen emits a line spectrum consisting of various series. The frequency of any line in a series can be expressed as a difference of two terms;

  • Lyman series:
  • Balmer Series:
  • Paschen Series:
  • Brackett Series:
  • Pfund Series:

 

To explain the line spectra emitted by atoms, as well as the stability of atoms, Niel's Bohr proposed a model for hydro genic (single electron) atoms. He introduced three postulates and laid the foundations of quantum mechanics:

  • In a hydrogen atom, an electron revolves in certain stable orbits(called stationary orbits) without the emission of radiant energy.
  • The stationary orbits are those for which the angular momentum is some integral multiple of (Bohr's quantisation condition.) That is L =, where n is an integer called a quantum number.
  • The third postulate states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency (ν) of the emitted photon is then given by

  • An atom absorbs radiation of the same frequency the atom emits, in which case the electron is transferred to an orbit with a higher value of n.

  • As a result of the quantisation condition of angular momentum, the electron orbits the nucleus at only specific radii. For hydrogen atom it is given by

    The total energy is also quantized as

 

The n = 1 state is called ground state. In hydrogen atom the ground state energy is . Higher values of n correspond to excited states  Atoms are excited to these higher states by collisions with other atoms or electrons or by absorption of a photon of right frequency.

  • De Broglie's hypothesis that electrons have a wavelengthgave an explanation for Bohr's quantised orbits by bringing in the wave particle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.
  • Bohr's model is applicable only to hydro genic (single electron) atoms. It cannot be extended to even two electron atoms such as helium. This model is also unable to explain for the relative intensities of the frequencies emitted even by hydro genic atoms.
  • An atom has a nucleus. The nucleus is positively charged. The radius of the nucleus is smaller than the radius of an atom by a factor of104. More than 99.9% mass of the atom is concentrated in the nucleus.
  • On the atomic scale, mass is measured in atomic mass units (u). By definition, 1 atomic mass unit (1u) is 1/12thmass of one atom of 12C;

  • A nucleus contains a neutral particle called neutron. Its mass is almost the same as that of proton
  • The atomic number Z is the number of protons in the atomic nucleus of an element. The mass number A is the total number of protons and neutrons in the atomic nucleus; A = Z+N; Here N denotes the numberof neutrons in the nucleus.
  • A nuclear species or a nuclide is represented as AXZ, where X is the chemical symbol of the species.
  • Nuclides with the same atomic number Z, but different neutron number N are called isotopes. Nuclides with the same A are isobars and those with the same N are isotones.
  • Most elements are mixtures of two or more isotopes. The atomic mass of an element is a weighted average of the masses of its isotopes. The masses are the relative abundances of the isotopes.
  • A nucleus can be considered to be spherical in shape and assigned a radius. Electron scattering experiments allow determination of the nuclear radius; it is found that radii of nuclei fit the formula

    where R0 = a constant = 1.2 fm. This implies that the nuclear density is independent of A. It is of the order of

  • Neutrons and protons are bound in a nucleus by the short-range strong nuclear force. The nuclear force does not distinguish between neutron and proton.
  • The nuclear mass M is always less than the total mass, Σm, of its constituents. The difference in mass of a nucleus and its constituents is called the mass defect,

    Using Einstein's mass energy relation, we express this mass difference in terms of energy as

    The energy represents the binding energy of the nucleus. In the mass number range A = 30 to 170, the binding energy per nucleon is nearly constant, about 8 MeV/nucleon.

    Energies associated with nuclear processes are about a million times larger than chemical process.

  • The Q-value of a nuclear process is

    Q = final kinetic energy – initial kinetic energy.

    Due to conservation of mass-energy, this is also,

    Q = (sum of initial masses – sum of final masses)

  • Radioactivity is the phenomenon in which nuclei of a given species transform by giving  rays; -rays are helium nuclei;-rays are electrons.-rays are electromagnetic radiation of wave lengths shorter than X-rays;
  • Law of radioactive decay where λ is the decay constant or disintegration constant.
  • The half-life  of a radionuclide is the time in which N has been reduced to one-half of its initial value. The mean life τ is the time at which N has been reduced to e–1 of its initial value.

  • Energy is released when less tightly bound nuclei are transmuted into more tightly bound nuclei. In fission, a heavy nucleus likes 92 U235 breaks into two smaller fragments.
  • The fact that more neutrons are produced in fission than are consumed gives the possibility of a chain reaction with each neutron that is produced triggering fission. The chain reaction is un controlled and rapid in a nuclear bomb explosion. It is controlled and steady in a nuclear reactor. In a reactor, the value of the neutron multiplication factor k is maintained at 1.
  • In fusion, lighter nuclei combine to form a larger nucleus. Fusion of hydrogen nuclei into helium nuclei is the source of energy of all stars including our sun.
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