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Therefore, scattering experiments that are currently 2. The experimental values have attracted can be calculated using the Lorentz factor from attention because the predicted value is shifted the invariant mass m0. However, Einstein has approximately 3. The total energy of the object increases with the addition of kinetic energy [12], 1. Below these distances, the force follows an inverse-fourth law. In If this increased kinetic energy pc is by contrast, the mass in the energy-mass interpretation 2 [11] a gravitational mass then the equivalence equation [9] has two interpretations mass associated with the total energy is also a [10].

Interpretation 1 is that energy and mass are gravitational mass M. The inertial mass m is the not exactly the same; the energy of an object mass of the combined action of the change in changes depending on velocity whereas the gravitational mass with the energy increase invariant mass does not change in any way. That is, mass, but retains the essential equivalence principle of energy and momentum.

Using Eq. Ratios among quantum size, nuclear force and gravity The pink solid line is the surface density line of 1 kg of substance. The pink dotted line is the line, obtained by dividing the pink solid line with the universal gravitational constant. The red horizontal dotted line is the proton line, scaled to a proton mass of 1 kg at one meter.

This line represents the strength of the proton force relative to 40 10 gravity. Model of the internal relationships among the structures of a ground-state hydrogen atom The blue area denotes the region occupied by the hydrogen atom model in its ground state. The red area indicates the protons residing at the center, where they spin at the speed of light.

The orbital angular velocity particle speed and spin angular velocity wave speed move at light speed at right angles to each other so a complex representation is appropriate. It increases calculation results. However, the reason why the proton affected, even if the precision of a local radius is reduced is not known, nor why p is anomalous magnetic moment is high. We believe smaller by this mechanism. Table 1. Physical parameters of a ground-state hydrogen atom —2 Mag. Blue quantities, such as fermion masses and physical constants appearing in Fig. E p Coulomb force 2 1.

The Role of the Atomic Number in the Periodic Table

E ep Coulomb force 2 2 1. The gravitational mass is generated when photons are confined, and To summarize, the inertial mass is the degree of diverges to infinity if the photons are not confined. The inertial mass and of the energy confined. All gravitational mass is determined by the strength energy has a mass equal to the vacuum of the universal gravitational force experienced expectation value generated by the gravitational by an object in the local gravitational field.

The mass determined from confinement. Hence, all two masses are separate physical quantities. This paper presented a between elementary particles. This is achieved new way to integrate general relativity and without relying on extra dimensions, which to quantum theory by the separation of the scalable 4 date have not been observed. When the long-range and We thank Professor Nyanpan deceased and short-range forces of such a vacuum mechanism the scholars who discovered the new proton act differentially through coupling, the divergence radius in the muonic hydrogen experiment.

If this energy mechanism editorial assistance. We have been using the gravitational Author has declared that no competing interests mass of a stationary object as a measure of its exist. Under most definitions the radii of isolated neutral atoms range between 30 and pm trillionths of a meter , or between 0. For many purposes, atoms can be modeled as spheres.

Atomic radius

This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the density of liquids and solids, the diffusion of fluids through molecular sieves , the arrangement of atoms and ions in crystals , and the size and shape of molecules. Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease along each period row of the table, from the alkali metals to the noble gases ; and increase down each group column.

The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii and of various other chemical and physical properties of the elements can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory.

The atomic radii decrease across the Periodic Table because as the atomic number increases, the number of protons increases across the period, but the extra electrons are only added to the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons increases, drawing the outermost electrons closer.

Ionization Energy Trends

As a result, the electron cloud contracts and the atomic radius decreases. In , shortly after it had become possible to determine the sizes of atoms using X-ray crystallography , it was suggested that all atoms of the same element have the same radii. The following table shows empirically measured covalent radii for the elements, as published by J. Slater in The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data.

The way the atomic radius varies with increasing atomic number can be explained by the arrangement of electrons in shells of fixed capacity. The shells are generally filled in order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic number increases along each row of the periodic table, the additional electrons go into the same outermost shell; whose radius gradually contracts, due to the increasing nuclear charge.


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In a noble gas, the outermost shell is completely filled; therefore, the additional electron of next alkali metal will go into the next outer shell, accounting for the sudden increase in the atomic radius. The increasing nuclear charge is partly counterbalanced by the increasing number of electrons, a phenomenon that is known as shielding ; which explains why the size of atoms usually increases down each column.

However, there is one notable exception, known as the lanthanide contraction : the 5d block of elements are much smaller than one would expect, due to the weak shielding of the 4f electrons. This similarity arises because these elements have the same number and same distribution of electrons in their outermost orbitals. We can classify the elements into four blocks viz.

This is illustrated in Fig. We notice two exceptions to this categorisation. Strictly, helium belongs to the s-block but its positioning in the p-block along with other group 18 elements is justified because it has a completely filled valence shell 1s 2 and as a result, exhibits properties characteristic of other noble gases. The other exception is hydrogen.

It has a lone s-electron and hence can be placed in group 1 alkali metals. It can also gain an electron to achieve a noble gas arrangement and hence it can behave similar to a group 17 halogen family elements. Because it is a special case, we shall place hydrogen separately at the top of the Periodic Table as shown in Fig. We will briefly discuss the salient features of the four types of elements marked in the Periodic Table.

More about these elements will be discussed later. During the description of their features certain terminology has been used which has been classified in section 3. They are all reactive metals with low ionization enthalpies. The metallic character and the reactivity increase as we go down the group. Because of high reactivity they are never found pure in nature. The compounds of the s-block elements, with the exception of those of lithium and beryllium are predominantly ionic. The p-Block Elements comprise those belonging to Group 13 to 18 and these together with the s-Block Elements are called the epresentative Elements or Main Group Elements.

At the end of each period is a noble gas element with a closed valence shell ns2np6 configuration. All the orbitals in the valence shell of the noble gases are completely filled by electrons and it is very difficult to alter this stable arrangement by the addition or removal of electrons. The noble gases thus exhibit very low chemical reactivity.

Preceding the noble gas family are two chemically important groups of non-metals. They are the halogens Group 17 and the chalcogens Group These two groups of elements have high negative electron gain enthalpies and readily add one or two electrons respectively to attain the stable noble gas configuration. The non-metallic character increases as we move from left to right across a period and metallic character increases as we go down the group. These are the elements of Group 3 to 12 in the centre of the Periodic Table. These are characterised by the filling of inner d orbitals by electrons and are therefore referred to as d-Block Elements.

These elements have the general outer electronic configuration n-1 d ns They are all metals. They mostly form coloured ions, exhibit variable valence oxidation states , paramagnetism and oftenly used as catalysts. The last electron added to each element is filled in f- orbital. Within each series, the properties of the elements are quite similar.

Computational Chemistry 1.7 - Covalent Radius

The chemistry of the early actinoids is more complicated than the corresponding lanthanoids, due to the large number of oxidation states possible for these actinoid elements. Actinoid elements are radioactive. Many of the actinoid elements have been made only in nanogram quantities or even less by nuclear reactions and their chemistry is not fully studied. The elements after uranium are called Transuranium Elements. We see from Fig. In addition to displaying the classification of elements into s-, p-, d-, and f-blocks, Fig. The elements can be divided into Metals and Non-Metals.

Metals are usually solids at room temperature [mercury is an exception; gallium and caesium also have very low melting points K and K, respectively ]. Metals usually have high melting and boiling points. They are good conductors of heat and electricity. They are malleable can be flattened into thin sheets by hammering and ductile can be drawn into wires. In contrast, non-metals are located at the top right hand side of the Periodic Table.

In fact, in a horizontal row, the property of elements change from metallic on the left to non-metallic on the right. Non-metals are usually solids or gases at room temperature with low melting and boiling points boron and carbon are exceptions. They are poor conductors of heat and electricity. Most nonmetallic solids are brittle and are neither malleable nor ductile.

The elements become more metallic as we go down a group; the nonmetallic character increases as one goes from left to right across the Periodic Table.

Atomic radius - Wikipedia

The change from metallic to non-metallic character is not abrupt as shown by the thick zig-zag line in Fig. The elements e. These elements are called Semi-metals or Metalloids. Considering the atomic number and position in the periodic table, arrange the following elements in the increasing order of metallic character : Si, Be, Mg, Na, P. Metallic character increases down a group and decreases along a period as we move from left to right.

There are many observable patterns in the physical and chemical properties of elements as we descend in a group or move across a period in the Periodic Table.

NCERT Class XI Chemistry Chapter 3 – Classification of Elements and Periodicity

For example, within a period, chemical reactivity tends to be high in Group 1 metals, lower in elements towards the middle of the table, and increases to a maximum in the Group 17 non-metals. Likewise within a group of representative metals say alkali metals reactivity increases on moving down the group, whereas within a group of non-metals say halogens , reactivity decreases down the group.

But why do the properties of elements follow these trends? And how can we explain periodicity? To answer these questions, we must look into the theories of atomic structure and properties of the atom. In this section we shall discuss the periodic trends in certain physical and chemical properties and try to explain them in terms of number of electrons and energy levels.

There are numerous physical properties of elements such as melting and boiling points, heats of fusion and vaporization, energy of atomization, etc. You can very well imagine that finding the size of an atom is a lot more complicated than measuring the radius of a ball. Do you know why? Secondly, since the electron cloud surrounding the atom does not have a sharp boundary, the determination of the atomic size cannot be precise. In other words, there is no practical way by which the size of an individual atom can be measured.

However, an estimate of the atomic size can be made by knowing the distance between the atoms in the combined state. For example, the bond distance in the chlorine molecule Cl 2 is pm and half this distance 99 pm , is taken as the atomic radius of chlorine. For example, the distance between two adjacent copper atoms in solid copper is pm; hence the metallic radius of copper is assigned a value of pm. For simplicity, in this book, we use the term Atomic Radius to refer to both covalent or metallic radius depending on whether the element is a non-metal or a metal. Atomic radii can be measured by X-ray or other spectroscopic methods.

The atomic radii of a few elements are listed in Table 3. Two trends are obvious. We can explain these trends in terms of nuclear charge and energy level. The atomic size generally decreases across a period as illustrated in Fig. It is because within the period the outer electrons are in the same valence shell and the effective nuclear charge increases as the atomic number increases resulting in the increased attraction of electrons to the nucleus. Within a family or vertical column of the periodic table, the atomic radius increases regularly with atomic number as illustrated in Fig.

For alkali metals and halogens, as we descend the groups, the principal quantum number n increases and the valence electrons are farther from the nucleus. This happens because the inner energy levels are filled with electrons, which serve to shield the outer electrons from the pull of the nucleus. Consequently the size of the atom increases as reflected in the atomic radii. Note that the atomic radii of noble gases are not considered here. Being monoatomic, their non-bonded radii values are very large. In fact radii of noble gases should be compared not with the covalent radii but with the van der Waals radii of other elements.

The ionic radii can be estimated by measuring the distances between cations and anions in ionic crystals. In general, the ionic radii of elements exhibit the same trend as the atomic radii. A cation is smaller than its parent atom because it has fewer electrons while its nuclear charge remains the same. The size of an anion will be larger than that of the parent atom because the addition of one or more electrons would result in increased repulsion among the electrons and a decrease in effective nuclear charge.

For example, the ionic radius of fluoride ion F — is pm whereas the atomic radius of fluorine is only 64 pm. When we find some atoms and ions which contain the same number of electrons, we call them isoelectronic species. Their radii would be different because of their different nuclear charges.

The cation with the greater positive charge will have a smaller radius because of the greater attraction of the electrons to the nucleus. Anion with the greater negative charge will have the larger radius. In this case, the net repulsion of the electrons will outweigh the nuclear charge and the ion will expand in size.

Which of the following species will have the largest and the smallest size? Atomic radii decrease across a period. Cations are smaller than their parent atoms. Among isoelectronic species, the one with the larger positive nuclear charge will have a smaller radius. A quantitative measure of the tendency of an element to lose electron is given by its Ionization Enthalpy.

It represents the energy required to remove an electron from an isolated gaseous atom X in its ground state. The ionization enthalpy is expressed in units of kJ mol We can define the second ionization enthalpy as the energy required to remove the second most loosely bound electron; it is the energy required to carry out the reaction shown in equation 3. Energy is always required to remove electrons from an atom and hence ionization enthalpies are always positive. The second ionization enthalpy will be higher than the first ionization enthalpy because it is more difficult to remove an electron from a positively charged ion than from a neutral atom.

In the same way the third ionization enthalpy will be higher than the second and so on. The first ionization enthalpies of elements having atomic numbers up to 60 are plotted in Fig. The periodicity of the graph is quite striking. You will find maxima at the noble gases which have closed electron shells and very stable electron configurations. On the other hand, minima occur at the alkali metals and their low ionization enthalpies can be correlated with their high reactivity. In addition, you will notice two trends the first ionization enthalpy generally increases as we go across a period and decreases as we descend in a group.

These trends are illustrated in Figs. You will appreciate that the ionization enthalpy and atomic radius are closely related properties. To understand these trends, we have to consider two factors : i the attraction of electrons towards the nucleus, and ii the repulsion of electrons from each other. For example, the 2s electron in lithium is shielded from the nucleus by the inner core of 1s electrons. In general, shielding is effective when the orbitals in the inner shells are completely filled.

This situation occurs in the case of alkali metals which have a lone ns-outermost electron preceded by a noble gas electronic configuration. When we move from lithium to fluorine across the second period, successive electrons are added to orbitals in the same principal quantum level and the shielding of the nuclear charge by the inner core of electrons does not increase very much to compensate for the increased attraction of the electron to the nucleus. Thus, across a period, increasing nuclear charge outweighs the shielding.

Consequently, the outermost electrons are held more and more tightly and the ionization enthalpy increases across a period. As we go down a group, the outermost electron being increasingly farther from the nucleus, there is an increased shielding of the nuclear charge by the electrons in the inner levels.

In this case, increase in shielding outweighs the increasing nuclear charge and the removal of the outermost electron requires less energy down a group. From Fig. When we consider the same principal quantum level, an s-electron is attracted to the nucleus more than a p-electron. In beryllium, the electron removed during the ionization is an s-electron whereas the electron removed during ionization of boron is a p-electron.

The penetration of a 2s-electron to the nucleus is more than that of a 2p-electron; hence the 2p electron of boron is more shielded from the nucleus by the inner core of electrons than the 2s electrons of beryllium. Therefore, it is easier to remove the 2p-electron from boron compared to the removal of a 2s- electron from beryllium. Thus, boron has a smaller first ionization enthalpy than beryllium. Consequently, it is easier to remove the fourth 2p-electron from oxygen than it is, to remove one of the three 2p-electrons from nitrogen. Justify your answer. It will be more close to kJ mol The value for Al should be lower than that of Mg because of effective shielding of 3p electrons from the nucleus by 3s-electrons.

Electron gain enthalpy provides a measure of the ease with which an atom adds an electron to form anion as represented by equation 3. Depending on the element, the process of adding an electron to the atom can be either endothermic or exothermic. For many elements energy is released when an electron is added to the atom and the electron gain enthalpy is negative. For example, group 17 elements the halogens have very high negative electron gain enthalpies because they can attain stable noble gas electronic configurations by picking up an electron. On the other hand, noble gases have large positive electron gain enthalpies because the electron has to enter the next higher principal quantum level leading to a very unstable electronic configuration.

It may be noted that electron gain enthalpies have large negative values toward the upper right of the periodic table preceding the noble gases. The variation in electron gain enthalpies of elements is less systematic than for ionization enthalpies. As a general rule, electron gain enthalpy becomes more negative with increase in the atomic number across a period.

New tolerance factor to predict the stability of perovskite oxides and halides

The effective nuclear charge increases from left to right across a period and consequently it will be easier to add an electron to a smaller atom since the added electron on an average would be closer to the positively charged nucleus. We should also expect electron gain enthalpy to become less negative as we go down a group because the size of the atom increases and the added electron would be farther from the nucleus.


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  4. This is generally the case Table 3. However, electron gain enthalpy of O or F is less negative than that of the succeeding element. If energy is released when an electron is added to an atom, the electron affinity is taken as positive, contrary to thermodynamic convention. If energy has to be supplied to add an electron to an atom, then the electron affinity of the atom is assigned a negative sign.

    Which of the following will have the most negative electron gain enthalpy and which the least negative? P, S, Cl, F. Explain your answer.