(1) He suggected that atom is a positively charged sphere having electrons embedded uniformly giving an overall picture of plum pudding.
(2) This model failed to explain the line spectrum of an element and the scattering experiment of Rutherford.
Atomic spectrum
Spectrum is the impression produced on a photographic film when the radiation (s) of particular wavelength (s) is (are) analysed through a prism or diffraction grating.
Types of spectrum
(1) Emission spectrum : Spectrum produced by the emitted radiation is known as emission spectrum. This spectrum corresponds to the radiation emitted (energy evolved) when an excited electron returns back to the ground state.
(i) Continuous spectrum : When sunlight is passed through a prism, it gets dispersed into continuous bands of different colours. If the light of an incandescent object resolved through prism or spectroscope, it also gives continuous spectrum of colours.
(ii) Line spectrum : If the radiation?s obtained by the excitation of a substance are analysed with help of a spectroscope a series of thin bright lines of specific colours are obtained. There is dark space in between two consecutive lines. This type of spectrum is called line spectrum or atomic spectrum.
(2) Absorption spectrum : Spectrum produced by the absorbed radiations is called absorption spectrum. Hydrogen spectrum
(1) Hydrogen spectrum is an example of line emission spectrum or atomic emission spectrum.
(2) When an electric discharge is passed through hydrogen gas at low pressure, a bluish light is emitted.
(3) This light shows discontinuous line spectrum of several isolated sharp lines through prism.
(4) All these lines of H-spectrum have Lyman, Balmer, Paschen, Barckett, Pfund and Humphrey series. These spectral series were named by the name of scientist discovered them.
(5) To evaluate wavelength of various H-lines Ritz introduced the following expression, \[\bar{\nu }=\frac{1}{\lambda }=\frac{\nu }{c}=R\left[ \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right]\]
Where R is universal constant known as Rydberg?s constant its value is 109, 678\[c{{m}^{-1}}\].
This is a special type of covalent bond where the shared pair of electrons are contributed by one species only but shared by both. The atom which contributes the electrons is called the donor (Lewis base) while the other which only shares the electron pair is known as acceptor (Lewis acid). This bond is usually represented by an arrow \[(\,\to \,)\] pointing from donor to the acceptor atom.
\[B{{F}_{3}}\]molecule, boron is short of two electrons. So to complete its octet, it shares the lone pair of nitrogen in ammonia forming a dative bond.
Examples : \[CO,\text{ }{{N}_{2}}O,\text{ }{{H}_{2}}{{O}_{2}},\text{ }{{N}_{2}}{{O}_{3}},\text{ }{{N}_{2}}{{O}_{4}},\text{ }{{N}_{2}}{{O}_{5}},\text{ }HN{{O}_{3}},\] \[NO_{3}^{-}\], \[S{{O}_{2}},\text{ }S{{O}_{3}},\text{ }{{H}_{2}}S{{O}_{4}},\] \[SO_{4}^{2-},SO_{2}^{2-},\] \[{{H}_{3}}P{{O}_{4}},\]\[{{H}_{4}}{{P}_{2}}{{O}_{7}},\] \[{{H}_{3}}P{{O}_{3}},A{{l}_{2}}C{{l}_{6}}(\text{Anhydrous),}{{O}_{3}},S{{O}_{2}}C{{l}_{2}},SOC{{l}_{2}},HI{{O}_{3}},HCl{{O}_{4}},\]\[HCl{{O}_{3}},C{{H}_{3}}NC,{{N}_{2}}H_{5}^{+}\], \[C{{H}_{3}}N{{O}_{2}},NH_{4}^{+},\ {{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] etc.
Characteristics of co-ordinate covalent compound
(1) Their melting and boiling points are higher than purely covalent compounds and lower than purely ionic compounds.
(2) These are sparingly soluble in polar solvent like water but readily soluble in non-polar solvents.
(3) Like covalent compounds, these are also bad conductors of electricity. Their solutions or fused masses do not allow the passage to electricity.
(4) The bond is rigid and directional. Thus, coordinate compounds show isomerism.
(1) Light and other forms of radiant energy propagate without any medium in the space in the form of waves are known as electromagnetic radiations. These waves can be produced by a charged body moving in a magnetic field or a magnet in a electric field. e.g. \[\alpha -\]rays, \[\gamma -\]rays, cosmic rays, ordinary light rays etc.
(2) Characteristics
(i) All electromagnetic radiations travel with the velocity of light.
(ii) These consist of electric and magnetic fields components that oscillate in directions perpendicular to each other and perpendicular to the direction in which the wave is travelling.
(3) A wave is always characterized by the following five characteristics,
(i) Wavelength : The distance between two nearest crests or nearest troughs is called the wavelength. It is denoted by \[\lambda \](lambda) and is measured is terms of centimeter(cm), angstrom(Å), micron(\[\mu \]) or nanometre (nm).
\[1{\ AA}={{10}^{-8}}\,cm={{10}^{-10}}m\];\[1\mu ={{10}^{-4}}cm={{10}^{-6}}m\];
\[1nm={{10}^{-7}}cm={{10}^{-9}}m\]; \[1cm={{10}^{8}}{\ AA}={{10}^{4}}\mu ={{10}^{7}}nm\]
(ii) Frequency : It is defined as the number of waves which pass through a point in one second. It is denoted by the symbol \[\nu \](nu) and is expressed in terms of cycles (or waves) per second (cps) or hertz (Hz).
\[\lambda \nu =\]distance travelled in one second = velocity =c
\[\nu =\frac{c}{\lambda }\]
(iii) Velocity : It is defined as the distance covered in one second by the wave. It is denoted by the letter ?c?. All electromagnetic waves travel with the same velocity, i.e., \[3\times {{10}^{10}}cm/\sec .\]
\[c=\lambda \nu =3\times {{10}^{10}}\ cm/\sec \]
(iv) Wave number : This is the reciprocal of wavelength, i.e., the number of wavelengths per centimetre. It is denoted by the symbol \[\bar{\nu }\](nu bar). It is expressed in \[c{{m}^{-1}}\,\text{or}\,{{m}^{-1}}\].
\[\bar{\nu }=\frac{1}{\lambda }\]
(v) Amplitude : It is defined as the height of the crest or depth of the trough of a wave. It is denoted by the letter ?A?. It determines the intensity of the radiation.
The arrangement of various types of electromagnetic radiations in the order of their increasing or decreasing wavelengths or frequencies is known as electromagnetic spectrum.
(1) Atomic number or Nuclear charge
(i) The number of protons present in
the nucleus of the atom is called atomic number (Z).
(ii) It was determined by Moseley
as,
\[\sqrt{\nu }=a(Z-b)\] or \[aZ-ab\]
Where, \[\nu =X-\]ray?s frequency
Z= atomic number of the metal \[a\And
b\] are constant.
(iii) Atomic number = Number of
positive charge on nucleus = Number of protons in nucleus = Number of electrons
in nutral atom.
(iv) Two different elements can
never have identical atomic number.
(2) Mass number
Mass number (A) = Number of protons or
Atomic number (Z) + Number of neutrons or Number of neutrons = A ?
Z .
(i) Since mass of
a proton or a neutron is not a whole number (on atomic weight scale), weight is
not necessarily a whole number.
(ii) The atom of an element X having
mass number (A) and atomic number (Z) may be represented by a symbol,\[_{Z}{{X}^{A}}\].
Different types of atomic species
Atomic species
Similarities
Differences
Examples
Isotopes
(Soddy)
(i) Atomic No. (Z)
(ii) No. of protons
(iii) No. of electrons
(iv) Electronic configuration
(v) Chemical properties
(vi) Position in the periodic table
(i) Mass No. (A)
(ii) No. of neutrons
(iii) Physical properties
(i) \[_{1}^{1}H,\,_{1}^{2}H,\,_{1}^{3}H\]
(ii) \[_{8}^{16}O,\,_{8}^{17}O,\,_{8}^{18}O\]
(iii) \[_{17}^{35}Cl,\,_{17}^{37}Cl\]
Isobars
(i) Mass No. (A)
(ii) No. of nucleons
(i) Atomic No. (Z)
(ii) No. of protons, electrons and
neutrons
(iii)Electronic configuration
(iv) Chemical properties
(v) Position in the perodic table.
(i) \[_{18}^{40}Ar,\,_{19}^{40}K,\,_{20}^{40}Ca\]
(ii) \[_{52}^{130}Te,\,_{54}^{130}Xe,\,_{56}^{130}Ba\].
Isotones
No. of neutrons
(i) Atomic No.
(ii) Mass No., protons and
electrons.
(iii) Electronic configuration
(iv) Physical and chemical
properties
(v) Position in the periodic table.
In any \[\Delta \,A\,B\,C\] with sides \[\overrightarrow{a},\,\overrightarrow{b},\,\overrightarrow{c}\] \[\frac{\sin \alpha }{a}=\frac{\sin \beta }{b}=\frac{\sin \gamma }{c}\]
i.e.for any triangle the ratio of the sine of the angle containing the side to the length of the side is a constant. For a triangle whose three sides are in the same order we establish the Lami's theorem in the following manner. For the triangle shown
\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\] [All three sides are taken in order] ?
(i) \[\Rightarrow \]\[\overrightarrow{a}+\overrightarrow{b}=-\overrightarrow{c}\] ?
(ii) Pre-multiplying both sides by \[\overrightarrow{a}\]\[\overrightarrow{a}\times (\overrightarrow{a}+\overrightarrow{b})=-\overrightarrow{a}\times \overrightarrow{c}\]
\[\Rightarrow \]\[\overrightarrow{0}+\overrightarrow{a}\times \overrightarrow{b}=-\overrightarrow{a}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{a}\] ?(iii) Pre-multiplying both sides of
(ii) by \[\overrightarrow{b}\] \[\overrightarrow{b}\times (\overrightarrow{a}+\overrightarrow{b})=-\,\overrightarrow{b}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,\overrightarrow{b}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{b}=-\overrightarrow{b}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,-\overrightarrow{a}\times \overrightarrow{b}=-\overrightarrow{b}\times \overrightarrow{c}\]\[\Rightarrow \,\,\,\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{b}\times \overrightarrow{c}\] ?
(iv) From (iii) and (iv), we get \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{c}\times \overrightarrow{a}\] Taking magnitude, we get \[|\overrightarrow{a}\times \overrightarrow{b}|\,=\,|\overrightarrow{b}\times \overrightarrow{c}|\,=\,|\overrightarrow{c}\times \overrightarrow{a}|\] \[\Rightarrow \,\,\,ab\sin (180-\gamma )=bc\sin (180-\alpha )=ca\sin (180-\beta )\] \[\Rightarrow \,\,\,ab\sin \gamma =bc\sin \alpha =ca\sin \beta \] Dividing through out byabc,we have \[\Rightarrow \,\,\,\,\frac{\sin \alpha }{a}=\frac{\sin \beta }{b}=\frac{\sin \gamma }{c}\]
Limiting reagent or reactant
In many situations, an excess of one or more substance is available for chemical reaction. Some of these excess substances will therefore be left over when the reaction is complete; the reaction stops immediately as soon as one of the reactant is totally consumed.
The substance that is totally consumed in a reaction is called limiting reagent because it determines or limits the amount of product. The other reactant present in excess are called as excess reagents.
Let us consider a chemical reaction which is initiated by passing a spark through a reaction vessel containing 10 mole of H2 and 7 mole of O2.
\[2\underset{{}}{\mathop{\,{{H}_{2}}\,}}\,(g)\,\,+\,\,\underset{{}}{\mathop{{{O}_{2}}\,}}\,(g)\,\xrightarrow{{}}\,\,2\,\,\underset{{}}{\mathop{{{H}_{2}}O}}\,\,(v)\]
Moles before reaction
10
7
0
Moles after reaction
0
2
10
The reaction stops only after consumption of 5 moles of O2 as no further amount of H2 is left to react with unreacted O2. Thus H2 is a limiting reagent in this reaction.
Percentage composition & Molecular formula
(1) Percentage composition of a compound
Percentage composition of the compound is the relative mass of each of the constituent element in 100 parts of it. If the molecular mass of a compound is M and B is the mass of an element in the molecule, then
\[\text{Percentage of element }=\frac{\text{Mass of element }}{\text{Molecular mass}}\times 100=\frac{X}{M}\times 100\]
(2) Determination of empirical formula : The empirical formula of a molecule is determined using the % of elements present in it. Following method is adopted.
Element
% Relative no. of atoms = %/at. wt.
Simplest Ratio
Empirical Formula
Relative no. of atoms : Divide the percentage of each element present in compound by its at. weight. This gives the relative no. of atoms of element in molecule.
Simplest ratio : Find out lowest value of relative no. of atoms and divide each value of relative no. of atoms by this value to estimate simplest ratio of elements.
It the simplest ratio obtained are not complete integers, multiply them by a common factor to get integer values of simplest ratio.
Empirical formula : Write all constituent atoms with their respective no. of atoms derived in simplest ratio. This gives empirical formula of compound.
Molecular formula : Molecular formula \[=n\times \]empirical formula where \['n'\] is the whole no. obtained by
\[n=\frac{\text{molecular weight of compound}}{\text{empirical formula weight of compound}}\]
(2) This model failed to explain the line spectrum of an element and the scattering experiment of Rutherford. 
Examples : \[CO,\text{ }{{N}_{2}}O,\text{ }{{H}_{2}}{{O}_{2}},\text{ }{{N}_{2}}{{O}_{3}},\text{ }{{N}_{2}}{{O}_{4}},\text{ }{{N}_{2}}{{O}_{5}},\text{ }HN{{O}_{3}},\] \[NO_{3}^{-}\], \[S{{O}_{2}},\text{ }S{{O}_{3}},\text{ }{{H}_{2}}S{{O}_{4}},\] \[SO_{4}^{2-},SO_{2}^{2-},\] \[{{H}_{3}}P{{O}_{4}},\]\[{{H}_{4}}{{P}_{2}}{{O}_{7}},\] \[{{H}_{3}}P{{O}_{3}},A{{l}_{2}}C{{l}_{6}}(\text{Anhydrous),}{{O}_{3}},S{{O}_{2}}C{{l}_{2}},SOC{{l}_{2}},HI{{O}_{3}},HCl{{O}_{4}},\]\[HCl{{O}_{3}},C{{H}_{3}}NC,{{N}_{2}}H_{5}^{+}\], \[C{{H}_{3}}N{{O}_{2}},NH_{4}^{+},\ {{[Cu{{(N{{H}_{3}})}_{4}}]}^{2+}}\] etc.
Characteristics of co-ordinate covalent compound
(1) Their melting and boiling points are higher than purely covalent compounds and lower than purely ionic compounds.
(2) These are sparingly soluble in polar solvent like water but readily soluble in non-polar solvents.
(3) Like covalent compounds, these are also bad conductors of electricity. Their solutions or fused masses do not allow the passage to electricity.
(4) The bond is rigid and directional. Thus, coordinate compounds show isomerism. 
\[1{\ AA}={{10}^{-8}}\,cm={{10}^{-10}}m\];\[1\mu ={{10}^{-4}}cm={{10}^{-6}}m\];
\[1nm={{10}^{-7}}cm={{10}^{-9}}m\]; \[1cm={{10}^{8}}{\ AA}={{10}^{4}}\mu ={{10}^{7}}nm\]
(ii) Frequency : It is defined as the number of waves which pass through a point in one second. It is denoted by the symbol \[\nu \](nu) and is expressed in terms of cycles (or waves) per second (cps) or hertz (Hz).
\[\lambda \nu =\]distance travelled in one second = velocity =c
\[\nu =\frac{c}{\lambda }\]
(iii) Velocity : It is defined as the distance covered in one second by the wave. It is denoted by the letter ?c?. All electromagnetic waves travel with the same velocity, i.e., \[3\times {{10}^{10}}cm/\sec .\]
\[c=\lambda \nu =3\times {{10}^{10}}\ cm/\sec \]
(iv) Wave number : This is the reciprocal of wavelength, i.e., the number of wavelengths per centimetre. It is denoted by the symbol \[\bar{\nu }\](nu bar). It is expressed in \[c{{m}^{-1}}\,\text{or}\,{{m}^{-1}}\].
\[\bar{\nu }=\frac{1}{\lambda }\]
(v) Amplitude : It is defined as the height of the crest or depth of the trough of a wave. It is denoted by the letter ?A?. It determines the intensity of the radiation.
The arrangement of various types of electromagnetic radiations in the order of their increasing or decreasing wavelengths or frequencies is known as electromagnetic spectrum.
(ii) It was determined by Moseley
as,
\[\sqrt{\nu }=a(Z-b)\] or \[aZ-ab\]
Where, \[\nu =X-\]ray?s frequency
Z= atomic number of the metal \[a\And
b\] are constant.
(iii) Atomic number = Number of
positive charge on nucleus = Number of protons in nucleus = Number of electrons
in nutral atom.
(iv) Two different elements can
never have identical atomic number.
(2) Mass number
Mass number (A) = Number of protons or
Atomic number (Z) + Number of neutrons or Number of neutrons = A ?
Z .
(i) Since mass of
a proton or a neutron is not a whole number (on atomic weight scale), weight is
not necessarily a whole number.
(ii) The atom of an element X having
mass number (A) and atomic number (Z) may be represented by a symbol,\[_{Z}{{X}^{A}}\].
Different types of atomic species
i.e.for any triangle the ratio of the sine of the angle containing the side to the length of the side is a constant. For a triangle whose three sides are in the same order we establish the Lami's theorem in the following manner. For the triangle shown
\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\] [All three sides are taken in order] ?
(i) \[\Rightarrow \]\[\overrightarrow{a}+\overrightarrow{b}=-\overrightarrow{c}\] ?
(ii) Pre-multiplying both sides by \[\overrightarrow{a}\]\[\overrightarrow{a}\times (\overrightarrow{a}+\overrightarrow{b})=-\overrightarrow{a}\times \overrightarrow{c}\]
\[\Rightarrow \]\[\overrightarrow{0}+\overrightarrow{a}\times \overrightarrow{b}=-\overrightarrow{a}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}\times \overrightarrow{a}\] ?(iii) Pre-multiplying both sides of
(ii) by \[\overrightarrow{b}\] \[\overrightarrow{b}\times (\overrightarrow{a}+\overrightarrow{b})=-\,\overrightarrow{b}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,\overrightarrow{b}\times \overrightarrow{a}+\overrightarrow{b}\times \overrightarrow{b}=-\overrightarrow{b}\times \overrightarrow{c}\]
\[\Rightarrow \,\,\,\,-\overrightarrow{a}\times \overrightarrow{b}=-\overrightarrow{b}\times \overrightarrow{c}\]\[\Rightarrow \,\,\,\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{b}\times \overrightarrow{c}\] ?
(iv) From (iii) and (iv), we get \[\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{c}\times \overrightarrow{a}\] Taking magnitude, we get \[|\overrightarrow{a}\times \overrightarrow{b}|\,=\,|\overrightarrow{b}\times \overrightarrow{c}|\,=\,|\overrightarrow{c}\times \overrightarrow{a}|\] \[\Rightarrow \,\,\,ab\sin (180-\gamma )=bc\sin (180-\alpha )=ca\sin (180-\beta )\] \[\Rightarrow \,\,\,ab\sin \gamma =bc\sin \alpha =ca\sin \beta \] Dividing through out byabc,we have \[\Rightarrow \,\,\,\,\frac{\sin \alpha }{a}=\frac{\sin \beta }{b}=\frac{\sin \gamma }{c}\] 
