75.4 and 24.6 per cent, respectively. Thus, the average mass of a chlorine atom is obtained by the weighted average of the masses of the two isotopes, which works out to be 75.4 × 34.98 + 24.6 × 36.98 = 100 = 35.47 u which agrees with the atomic mass of chlorine. Even the lightest element, hydrogen has three isotopes having masses 1.0078 u, 2.0141 u, and 3.0160 u. The nucleus of the lightest atom of hydrogen, which has a relative abundance of 99.985%, is called the proton. The mass of a proton is −27 m p = 1.00727 u = 1.67262 × 10 kg (13.2) This is equal to the mass of the hydrogen atom (= 1.00783u), minus the mass of a single electron (me = 0.00055 u). The other two isotopes of hydrogen are called deuterium and tritium. Tritium nuclei, being unstable, do not occur naturally and are produced artificially in laboratories. The positive charge in the nucleus is that of the protons. A proton carries one unit of fundamental charge and is stable. It was earlier thought that the nucleus may contain electrons, but this was ruled out later using arguments based on quantum theory. All the electrons of an atom are outside the nucleus. We know that the number of these electrons outside 307the nucleus of the atom is Z, the atomic number. The total charge of the Reprint 2025-26 Physics atomic electrons is thus (–Ze), and since the atom is neutral, the charge of the nucleus is (+Ze). The number of protons in the nucleus of the atom is, therefore, exactly Z, the atomic number. Discovery of Neutron Since the nuclei of deuterium and tritium are isotopes of hydrogen, they must contain only one proton each. But the masses of the nuclei of hydrogen, deuterium and tritium are in the ratio of 1:2:3. Therefore, the nuclei of deuterium and tritium must contain, in addition to a proton, some neutral matter. The amount of neutral matter present in the nuclei of these isotopes, expressed in units of mass of a proton, is approximately equal to one and two, respectively. This fact indicates that the nuclei of atoms contain, in addition to protons, neutral matter in multiples of a basic unit. This hypothesis was verified in 1932 by James Chadwick who observed emission of neutral radiation when beryllium nuclei were bombarded with alpha-particles (a-particles are helium nuclei, to be discussed in a later section). It was found that this neutral radiation could knock out protons from light nuclei such as those of helium, carbon and nitrogen. The only neutral radiation known at that time was photons (electromagnetic radiation). Application of the principles of conservation of energy and momentum showed that if the neutral radiation consisted of photons, the energy of photons would have to be much higher than is available from the bombardment of beryllium nuclei with a-particles. The clue to this puzzle, which Chadwick satisfactorily solved, was to assume that the neutral radiation consists of a new type of neutral particles called neutrons. From conservation of energy and momentum, he was able to determine the mass of new particle ‘as very nearly the same as mass of proton’. The mass of a neutron is now known to a high degree of accuracy. It is m n = 1.00866 u = 1.6749×10–27 kg (13.3) Chadwick was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron. A free neutron, unlike a free proton, is unstable. It decays into a proton, an electron and a antineutrino (another elementary particle), and has a mean life of about 1000s. It is, however, stable inside the nucleus. The composition of a nucleus can now be described using the following terms and symbols: Z - atomic number = number of protons [13.4(a)] N - neutron number = number of neutrons [13.4(b)] A - mass number = Z + N = total number of protons and neutrons [13.4(c)] One also uses the term nucleon for a proton or a neutron. Thus the number of nucleons in an atom is its mass number A. Nuclear species or nuclides are shown by the notation ZA X where X is the chemical symbol of the species. For example, the nucleus of gold is denoted by 19779 Au . It contains 197 nucleons, of which 79 are protons 308 and the rest118 are neutrons. Reprint 2025-26 Nuclei The composition of isotopes of an element can now be readily explained. The nuclei of isotopes of a given element contain the same number of protons, but differ from each other in their number of neutrons. Deuterium, 12 H, which is an isotope of hydrogen, contains one proton and one neutron. Its other isotope tritium, 13 H, contains one proton and two neutrons. The element gold has 32 isotopes, ranging from A =173 to A = 204. We have already mentioned that chemical properties of elements depend on their electronic structure. As the atoms of isotopes have identical electronic structure they have identical chemical behaviour and are placed in the same location in the periodic table. All nuclides with same mass number A are called isobars. For example, the nuclides 13 H and 32He are isobars. Nuclides with same neutron number N but different atomic number Z, for example 19880 Hg and 19779 Au , are called isotones.

1.6 Dalton’s Atomic Theory 1.7.1 Atomic Mass Although the origin of the idea that matter is The atomic mass or the mass of an atom is composed of small indivisible particles called actually very-very small because atoms are ‘a-tomio’ (meaning, indivisible), dates back extremely small. Today, we have sophisticated to the time of Democritus, techniques e.g., mass spectrometry for a Greek Philosopher (460– determining the atomic masses fairly 370 BC), it again started accurately. But in the nineteenth century, emerging as a result of several scientists could determine the mass of one experimental studies which atom relative to another by experimental led to the laws mentioned means, as has been mentioned earlier. above. Hydrogen, being the lightest atom was arbitrarily assigned a mass of 1 (without In 1808, Dalton published John Dalton any units) and other elements were assigned‘A New System of Chemical (1776–1884) masses relative to it. However, the presentPhilosophy’, in which he system of atomic masses is based onproposed the following : carbon-12 as the standard and has been1. Matter consists of indivisible atoms. agreed upon in 1961. Here, Carbon-12 is2. All atoms of a given element have identical one of the isotopes of carbon and can be properties, including identical mass. Atoms represented as 12C. In this system, 12C is of different elements differ in mass. assigned a mass of exactly 12 atomic mass 3. Compounds are formed when atoms of unit (amu) and masses of all other atoms are different elements combine in a fixed ratio. given relative to this standard. One atomic 4. Chemical reactions involve reorganisation mass unit is defined as a mass exactly equal of atoms. These are neither created nor to one-twelfth of the mass of one carbon – 12 destroyed in a chemical reaction. atom. Reprint 2025-26 Some Basic Concepts of Chemistry 17 And 1 amu = 1.66056×10–24 g 1.7.3 Molecular Mass Mass of an atom of hydrogen Molecular mass is the sum of atomic masses of the elements present in a molecule. It is = 1.6736×10–24 g obtained by multiplying the atomic massThus, in terms of amu, the mass of each element by the number of its atoms and adding them together. For example,of hydrogen atom = molecular mass of methane, which contains one carbon atom and four hydrogen atoms, = 1.0078 amu can be obtained as follows: = 1.0080 amu Molecular mass of methane, Similarly, the mass of oxygen - 16 (16O) (CH4) = (12.011 u) + 4 (1.008 u) atom would be 15.995 amu. = 16.043 u At present, ‘amu’ has been replaced by Similarly, molecular mass of water (H2O)‘u’, which is known as unified mass. = 2 × atomic mass of hydrogen + 1× atomic When we use atomic masses of elements mass of oxygen in calculations, we actually use average = 2 (1.008 u) + 16.00 uatomic masses of elements, which are explained below. = 18.02 u 1.7.2 Average Atomic Mass 1.7.4 Formula Mass Many naturally occurring elements exist Some substances, such as sodium chloride, as more than one isotope. When we take do not contain discrete molecules as their into account the existence of these isotopes constituent units. In such compounds, and their relative abundance (per cent positive (sodium ion) and negative (chloride ion) occurrence), the average atomic mass of entities are arranged in a three-dimensional that element can be computed. For example, structure, as shown in Fig. 1.10. carbon has the following three isotopes with relative abundances and masses as shown against each of them. Isotope Relative Atomic Mass Abundance (amu) (%) 12C 98.892 12 13C 1.108 13.00335 14C 2 ×10–10 14.00317 Fig. 1.10 Packing of Na+ and Cl– ions From the above data, the average atomic in sodium chloride mass of carbon will come out to be: (0.98892) (12 u) + (0.01108) (13.00335 u) + It may be noted that in sodium chloride, (2 × 10–12) (14.00317 u) = 12.011 u one Na+ ion is surrounded by six Cl– ion and Similarly, average atomic masses for vice-versa. other elements can be calculated. In the The formula, such as NaCl, is used to periodic table of elements, the atomic masses calculate the formula mass instead of mentioned for different elements actually molecular mass as in the solid state sodium represent their average atomic masses. chloride does not exist as a single entity. Reprint 2025-26 18 chemistry Thus, the formula mass of sodium chloride is This number of entities in 1 mol is so atomic mass of sodium + atomic mass of chlorine important that it is given a separate name and symbol. It is known as ‘Avogadro constant’, = 23.0 u + 35.5 u = 58.5 u or Avogadro number denoted by NA in honour Problem 1.1 of Amedeo Avogadro. To appreciate the Calculate the molecular mass of glucose largeness of this number, let us write it with (C6H12O6) molecule. all zeroes without using any powers of ten. Solution 602213670000000000000000 Hence, so many entities (atoms, molecules or Molecular mass of glucose (C6H12O6) any other particle) constitute one mole of a = 6 (12.011 u) + 12 (1.008 u) + 6 (16.00 u) particular substance. = (72.066 u) + (12.096 u) + We can, therefore, say that 1 mol of hydrogen (96.00 u) atoms = 6.022 × 1023 atoms = 180.162 u 1 mol of water molecules = 6.022 × 1023 water

12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?