Hydrogen (H)

atom with a single proton which carries a spin of forming the basis of MR imaging and proton MR spectroscopy. The understanding of the physical properties of the hydrogen atom and consequently the table of chemical elements (see periodic table of elements) is one of the major accomplishments of quantum theory.

Hydrogen isotopes are H-1 (hydrogen proper), H-2 containing also a neutron, called deuterium, and H-3 containing two neutrons and called tritium (Table 1). Tritium decays with a beta minus decay and a half life of 12.26 years. It is frequently used in labelling experiments and in autoradiography.

Hydrogen (H), Table 1

Properties of hydrogen isotopes

The quantum theoretical analysis of the hydrogen atom yields the following result. The stable orbits of the electron are quantized and are characterized by four quantum numbers.

The first quantum number is associated with the energetic state of the proton-electon system, the second and third with the magnitude and the z-component of the angular momentum of the system and the fourth with the spin of the electron. The first quantum number, called the principal quantum number, is related to the orbit energy of the electron and characterizes the atomic shell, to which the electron belongs (Fig.1:levels 1 through n, shown up to 5). While normally, the hydrogen electron is in the lowest energetic state (ground state) corresponding to the shell closest to the proton nucleus, the other shells are potential states into which the electron "jumps" if excited by input of energy. In hydrogen the energy differences between the first few shells are in the range of an electron volt EV . If the electron acquires more than 13.6 eV, it will become unbound and enter a continuum of states which are not quantized, corresponding to a free electron. The energy of 13.6 eV is the ionization energy of the hydrogen atom, i.e. the energy with which the electron is bound to the proton (electron binding energy). If we imagine an atom with a larger number of protons than one, the shell structure shown in the Figure is maintained, but the shells move closer to the atomic nucleus because of the stronger electrostatic attraction: the difference between 1s and 2s states increases into the range of 100 or more keV in a substance like tungsten (see periodic table of elements) used as anode material in an X-ray tube. If we add the necessary electrons to arrive at a neutral atom, the shells are filled one by one, thereby producing the rows in the table of atomic elements (n=1: H, He; n = 2: Li, Be, B, C, N, O, F, Ne; n=3: Na, Mg, Al, etc). The shells are termed k-, l- , m- etc. shells. If an electron is ejected from its shell, i .e. by bombarding an atom like tungsten with electrons, an unoccupied energetic state in a deep shell w and generates the so called s- (l=0), p- (l=1), d- (l=2), f- (l=3) etc. orbitals (Fig. 1) and the value of the angular momentum is Öl(l+1) (: Plancks constant). While s-orbitals are spherically symmetrical, p-orbitals are dumb-bell-like and d-orbitals have a more complex structure.

The third quantum number m characterizes the value of the z-component of the angular momentum, which has the value mh. m = 0 for l=0, m = 0, ±1 for l=0, m = 1, ±1 , ±2 for l=2 etc, i. e. 1 is the maximum absolute value of m.

The fourth quantum number, s, stems from the observation that the electron behaves such as if it had an intrinsic angular momentum (spin), the z-component of which can only take two discrete values, which turn out to be±1/2.

GvS

GvS

Fig.1

Hydrogen (H), Fig.1