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Atoms of an element with different mass number are called Isotopes. 

Ex : Hydrogen has three types of atoms, 

1. ₁H¹ (protium) 

2. ₁H² (deuterium) 

3. ₁H³ (tritium)

In 1803 English chemist Dalton put forward his atomic theory. 

The main postulates of the theory are as follows. 

1. Elements are made up of very small indivisible particles called atoms. 

2. All atoms of a particular element are identical in shape, mass and other properties, but are different from the atom of other elements. 

3. Atom of one element can not be converted into that of another element. 

4. Atoms of an element combine in integral ratio with those of other elements to form a compound 

5. An atom can neither be created nor destroyed.

The characteristics of anode rays are: 

1. They consists of positively charged particles. 

2. They are deflected by electrical and magnetic fields. The deflection is very little when compared to the deflection of cathode rays because they consists of heavy particles 

3. The deflection of the anode rays depends on the nature of the rays in the discharge tube. Heavier the gas lower the depletion.

(i) IT could not explain the origin of the spectral lines of hydrogen and other atoms,

(ii) It failed to explain scattering of a - particles in Rutherford’s scattering experiment.

1. The mass number of potassium (A)= 40 

2. The atomic number of potassium (Z)=19 

3. The electronic configuration of potassium

 = 1S² , 2S²2Ps 3S²3P⁶, 4S₁

Canal rays are positively charged radiations that can pass through perforated cathode plate. These rays consist of positively charged particles known as protons.

Any Substance made up of same kind of atom is called element. 118 elements are known to us.

The positive particles of hydrogen atoms are the lightest hence the deflection will be maximum.

Mass of particles of cathode rays is not constant.

by using uncertainty principal calculated value of uncertainty in velocity is more than the velocity of light.

The characteristics of cathode rays are: 

1. They consists of negatively charged particles. 

2. cathode rays are also called as electrons. 

3. electrons are lighter than Hydrogen atom. 

4. electrons mass is very small or less.

(a) Calculation of the wave number

\(\lambda\) = 5800 Å = 5800 × 10^-10 m

\(\bar{v}\) = \(\frac{1}{\lambda}\) = \(\frac{1}{5800\times10^{-10}}\)

= 1.724 × 10⁶ m⁻¹

= 1.724 × 10⁴ cm¹

(b) Calculation of frequency (v)

v = \(\frac{c}{\lambda}\) = \(\frac{3\times10^8ms^{-1}}{5800\times10^{-10}m}\)

= 5.172 × 10⁻¹⁴ s⁻¹

ʎ=h/mv derive from this equation for an electron and proton 

V1/v2 =m2/m1 

=1.6725 x 10^-27/9.1095 x 10^-31 

=1836

 Velocity of electron= velocity of proton x 1836 

(1). He was unable to explain the stability of Atom. 

(2). He could not explain the line spectrum.

The space around the nucleus where the probability of finding electrons is maximum is called orbital.

Types of atomic species

•  Isotopes : Atoms of same element having same atomic number but different mass number. For example, isotopes of Hydrogen are ₁¹H, ²₁H, ³₁H
• Isobars : Atoms of different elements having the same mass number but different atomic number, e.g., ⁴⁰₁₈Ar, ⁴⁰₁₉K, ⁴⁰₂₀Ca
• Isotones : Atoms of different elements which contain the same number of neutrons. e.g., ¹⁴₆C, ¹⁵₇N, ¹⁶₈O
• Isoelectronic Species : Atoms or ions containing the same number of electrons. For example, N^3- , O^2- , F^- , Na⁺ , Mg²⁺ , Al³⁺ and Ne, having 10 electrons each are isoelectronic

1.Photoelectric effect 2. Black Body radiation  

Some properties of light can be explained only by considering the wave nature (differaction and interference) while some could be explained by the particle nature (photoelectric effect).

Atomic line spectra arise because of the absorption/emission of certain frequencies of light energy.

The complete range of electromagnetic waves in the increasing order of wavelength (decreasing order of frequency) is known as electromagnetic spectra.

Increasing order of wave length > Cosmic rays > Gamma rays < X-rays < U.V. rays < Visible rays < IR rays < Microwave rays < Radio waves (i.e, decreasing order of frequency).

Wave nature of light: According to Newton, light is a stream of particles which are also known as corpuscles of light. This could not account for the phenomena of interference and deflection (as Rutherford’s model) but justified reflection and refraction. 

Hygen suggested in his wave theory that the fight travels in the form of waves, later James Maxwell proposed that fight and other radiations are transmitted, these waves are associated with oscillating electric and magnetic field.

Correct option is  D) pm

Dual nature of electron – de Broglie's matter-wave equation 

According to Einstein’s mass-energy relation, E = mc² … (1) 

Where m and c are the mass and velocity of an electron respectively. 

According to quantum theory, Energy E = hv = (he) / λ … (2) 

Where h is Plank’s constant = 6.626 × 10^-34 Js, u is the frequency of moving electron. 

Comparing(1) and (2) me² = (hc)/λ >me = h/λ > = λ = h /me … (3) 

Equation (3) is called de-Broglie’s equation. 

For an electron its velocity is given as V, So the de-Broglie’s equation for an electron is given by, 

λ = h / mv (mv = p = momentum of electron) 

λ = h / p is called de-Broglie’s matter – wave equation

de Broglie’s equation :

• de Broglie proposed (in 1924) that matter should exhibit a dual behaviour. That is, every object which possesses a mass and velocity behaves both as a particle and as a wave. An electron has mass and velocity. This means that an electron should have momentum (p), a property of particle as well as wavelength (λ), a property of wave.
• According to de Broglie, the wavelength λ of a particle of mass m moving with a velocity v is λ = \(\frac{h}{mv}\) where, h is Planck’s constant.
• The quantity mv gives the momentum of the particles. λ = \(\frac{h}{p}\) where, p represents the momentum of the particle.
• de Broglie’s prediction was confirmed by diffraction experiments (a wave property).

[Note : According to de Broglie’s equation, the wavelength of a moving particle is inversely proportional to its mass. Therefore, heavier particles have much smaller wavelength than lighter particles like electrons.]

λ = h/mV 

where λ – wavelength of wave, h = Plank’s constant, m = mass of the electron, V – velocity of the electron.

In order that a fuel undergoes combustion, three basic requirements are to be present

• A combustible substance: All carbon compounds are combustible, but carbon as diamond is not. Petrol is a combustible substance.

• A supporter of combustion: Atmospheric air or oxygen gas is a supporter of combustion. In their absence, combustion will not be supported. Carbon dioxide or nitrogen gases do not support combustion.

• Heating to ignition temperature: A minimum amount of temperature or heat is required to enable a fuel to catch fire. Coal has a high ignition temperature; a matchstick cannot produce enough heat to ignite it. However, a matchstick can ignite paper or LPG gas as it has low ignition temperature.

The mean life time of the nucleus is the ratio of sum or integration of life times of all nuclei to the total number nuclei present initially. The expression for mean life time, \(\tau =\frac{1}{λ}\).

when Z protons and N neutrons combine to form a nucleus, mass equal to mass defect disappears and the corresponding energy is released. This is called the binding energy of the nucleus (BE) and is equal to (∆m) c². 

BE = (Zm_p + Nm_n – M ) c²

The mass of any nucleus is always less than the sum of the mass of its individual constituents. The difference in mass Am is called mass defect.

∆m = (Zm_p + Nm_n) – M.

The average binding energy per nucleon is the energy required to separate single nucleon from the particular nucleus.

Combustion

Combustion means the burning of a substance. It is a process that is highly exothermic i.e., produces a lot of heat. The products of combustion of carbon and its compounds are heat energy, carbon dioxide and water (vapour).

Chemical Properties of Carbon Compounds

Most of the carbon-containing compounds associated with hydrogen i.e., hydrocarbons are fuels that produce heat on burning. Petroleum products like natural gas, petrol, diesel, kerosene, heavy oils etc., and in a larger sense, wood, biogas, charcoal and coke are all rich source of carbon compounds used as fuels.

• Most of the alpha particles are undeflected through the gold foil and went straight. 
• Some of the alpha particles are deflected through a small angle. 
• A few alpha particles (one in thousand) are deflected through the angle more than 90°. 
• Very few alpha particles returned back (back scattered) -that is, deflected back by 180°.

Limitations of Bohr atom model: 

The following are the drawbacks of Bohr atom model: 

1. Bohr atom model is valid only for hydrogen atom or hydrogen like-atoms but not for complex atoms.

2. When the spectral lines are closely examined, individual lines of hydrogen spectrum is accompanied by a number of faint lines. These are often called fine structure. This is not explained by Bohr atom model.

3. Bohr atom model fails to explain the intensity variations in the spectral lines.

4. The distribution of electrons in atoms is not completely explained by Bohr atom model.

The ionization energy and ionization potential are: 

1. Ionization energy: The minimum energy required to remove an electron from an atom in the ground state is known as binding energy or ionization energy.

2. Ionization potential: Ionization potential is defined as ionization energy per unit charge.

The energy required to excite an electron from lower energy state to any higher energy state is known as excitation energy.

(b) 5.6 MeV

If w = 1 u, C = 3 x 10⁸ ms^-1 

then, E = 931 MeV

1 u = 931 Mev

Binding energy = 0. 042 x 931

= 39. 10 MeV 

∴ B.E 39.10

Binding energy per nucleon = \(\frac{B.E}{A}\) = \(\frac{39.10}{7}\)

5.58 = 5.6 MeV

• Cathode rays possess energy and momentum and travel in a straight line with high speed of the order of 10⁷ m s^-1
• It can be deflected by application of electric and magnetic fields.
• When the cathode rays are allowed” to fall on matter, they produce heat.
• They affect the photographic plates and also produce fluorescence when they fall on certain crystals and minerals.
• When the cathode rays fall on a material of high atomic weight, x-rays are produced.
• Cathode rays ionize the gas through which they pass.
• The speed of cathode rays is up to (\(\frac{1}{10}\))^th

(i) Combustion:

CH₄+O₂→ CO₂+H₂O+Energy+Light

(ii) Addition

CH₂=CH₂+H₂+Ni →C₂H₆

(iii) Substitution

CH₄+Cl₂+Sunlight → CH₃Cl+HCl

(iv) Esterification

CH₃COOH+C₂H₅OH+H⁺  →CH₃COOC₂H₅+H₂O

(v) Oxidation

C₂H₅OH+alk KMnO₄  →CH₃COOH.

(c) B will decay at faster rate than A

(t _1/2)_A = (t _mean)_B

\(\frac{0.6931}{λ_A} = \frac{1}{λ_B}\)

λ_A = 0.6931 λ_B 

λ_A < λ_B

A cathode ray is a stream of electrons that are seen in vaccum tubes. It is called a “cathode ray” because the electrons are being emitted from the negative charged element in the vaccum tube called the cathode.

(b) \(\frac{A-Z-2}{Z-6}\)

(c) M (N, Z) = NM_n + ZM_p – B / c²

Binding energy, B = [ZM_p + NM_n – M (N, Z)] C² 

M(N,Z) = ZM_p + NM_n - \(\frac{B}{C^2}\)

D) fermentation

The answer is (a) Prop roots

D) Isobutane

The isomeric pair is butane and 2-methyl propane.

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n-butane and iso-butane.