Effective atomic number

Effective atomic number has two different meanings: one that is the effective nuclear charge of an atom, and one that calculates the average atomic number for a compound or mixture of materials. See also List of elements by atomic number In Chemistry and Physics, the atomic number (also known as the proton Both are abbreviated Z_eff.

For an atom

The effective atomic number Z_eff', (sometimes referred to as the effective nuclear charge) of an atom is the number of protons an electron in the element effectively 'sees' due to screening by inner-shell electrons. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom It is a measure of the electrostatic interaction between the negatively charged electrons and positively charged protons in the atom. One can view the electrons in an atom as being 'stacked' by energy outside the nucleus; the lowest energy electrons (such as the 1s and 2s electrons) occupy the space closest to the nucleus, and electrons of higher energy are located further from the nucleus.

The binding energy of an electron, or the energy needed to remove the electron from the atom, is a function of the electrostatic interaction between the negatively charged electrons and the positively charged nucleus. Binding energy is the Mechanical energy required to disassemble a whole into separate parts Electrostatics is the branch of Science that deals with the Phenomena arising from what seems to be stationary Electric charges Since Classical In Iron, atomic number 26, for instance, the nucleus contains 26 protons. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The electrons that are closest to the nucleus will 'see' nearly all of them. However, electrons further away are screened from the nucleus by other electrons in between, and feel less electrostatic interaction as a result. The 1s electron of Iron (the closest one to the nucleus) sees an effective atomic number (number of protons) of 25. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom The reason why it is not 26 is because some of the electrons in the atom end up repelling the others, giving a net lower electrostatic interaction with the nucleus. One way of envisioning this effect is to imagine the 1s electron sitting on one side of the 26 protons in the nucleus, with another electron sitting on the other side; each electron will feel less than the attractive force of 26 protons because the other electron contributes a repelling force. The 4s electrons in Iron, which are furthest from the nucleus, feel an effective atomic number of only 5. 43 because of the 25 electrons in between it and the nucleus screening the charge.

Effective atomic numbers are useful not only in understanding why electrons further from the nucleus are so much more weakly bound than those closer to the nucleus, but also because they can tell us when to use simplified methods of calculating other properties and interactions. For instance, Lithium, atomic number 3, has two electrons in the 1s shell and one in the 2s shell. Lithium (ˈlɪθiəm is a Chemical element with the symbol Li and Atomic number 3 Because the two 1s electrons screen the protons to give an effective atomic number for the 2s electron close to 1, we can treat this 2s valence electron with a hydrogenic model.

Mathematically, the effective atomic number Z_effcan be calculated using methods known as "self-consistent field" calculations, but in simplified situations is just taken as the atomic number minus the number of electrons between the nucleus and the electron being considered. In Computational physics and Computational chemistry, the Hartree-Fock ( HF) method is an approximate method for the determination of the ground-state

For a compound or mixture

Effective atomic number is a term that is similar to atomic number but is used for compounds (e. A chemical compound is a substance consisting of two or more different elements chemically bonded together in a fixed proportion by Mass. g. water) and mixtures of different materials (such as tissue and bone) rather than for atoms. The effective atomic number is calculated by taking the fractional proportion of each atom in the compound and multiplying that by the atomic number of the atom. The formula for the effective atomic number, Z_eff, is as follows:

$Z_{eff} = \sqrt[2.94]{f_{1} \times (Z_{1})^{2.94} + f_{2} \times (Z_{2})^{2.94} + f_{3} \times (Z_{3})^{2.94} + ...}$

where

f n

is the fraction of the total number of electrons associated with each element, and

Z n

is the atomic number of each element.

An example is that of water (H₂O), made up of two hydrogen atoms (Z=1) and one oxygen atom (Z=8), the total number of electrons is 1+1+8 = 10, so the fraction of electrons for the two hydrogens is (2/10) and for the one oxygen is (8/10). So the Z_eff for water is:

$Z_{eff} = \sqrt[2.94]{0.2 \times 1^{2.94} + 0.8 \times 8^{2.94}} = 7.42$

Effective atomic number is important for predicting how X-rays interact with a substance, as certain types of x-ray interactions depend on the atomic number. X-radiation (composed of X-rays) is a form of Electromagnetic radiation.

References

Webelements
Eisberg and Resnick, Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles.
R. C. Murty, "Effective atomic numbers of heterogeneous materials", Nature 207, 398-399 (24 July 1965)

Nature is a prominent Scientific journal, first published on 4 November 1869

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