Class 12 Physics Theory

Chapter 1

Electric Charges and Field

Coulomb’s Law

The electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them

Electric Flux

The number of electric field lines passing normally in a given area

Gauss Law

The total electric flux over a closed surface equals 1/ε_o times the net charge enclosed by the surface

Chapter 2

Electrostatic Potential and Capacitance

Electric Potential

The work done to bring a unit positive charge from infinity to a point against electrostatic force

Equipotential surfaces

Draw equipotential surfaces :

i. In the case of the single point charge and

ii. In a constant electric field in Z-direction. Why the equipotential surfaces about a single charge are not equidistant ?

iii. Can electric field exist tangential to an equipotential surface? Give reason.

Surface in which all points have same potential

A: http://sarthaks.com/178602/define-an-equipotential-surface-draw-equipotential-surfaces

Electrostatics of Conductors

What is electrostatic shielding? How is this property used in actual practice? Is the potential in the cavity of a charged conductor zero?

• At the surface of a charged conductor (E = σ/ε_o), the electrostatic field must be normal to the surface at every point

• Under static conditions, all the charges in a conductor lie on the outer surface, ensuring that the electrostatic field inside is zero

• The electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface because the electric field inside the conductor is zero

• Inside a cavity, the electric field is zero and protected from the external electric field. This is known as electrostatic shielding. Eg: A car

Sensitive instruments are shielded from outside electrical influence by enclosing them in a hollow conductor.
It is safest to be inside a car, rather than near a tree during lightning. The metallic body of a car becomes an electrostatic shield from lightning.
The potential inside the cavity is not zero. The potential is constant.

Dipole and Ideal Dipole

• A pair of equal and opposite charges separated by a small vector distance is called an electric dipole.

• An ideal dipole consists of two very very large charges q and –q separated by a very very small distance. An ideal dipole has almost no size.

Dielectrics

Compare the individual dipole moment and the specimen dipole moment for H₂O molecule and O₂ molecule when placed in

(a) Absence of external electric field.

(b) Presence of external electric field. Justify your answer

Insulating materials that have bound charges.

Two types:

• Polar molecule: +ve and -ve charged centres don’t coincide; permanent dipole

  moment. Eg: HCl, H₂O

• Non-polar molecule: +ve and -ve charge centres coincide; induced dipole moment. Eg: H₂, O_2, CO₂, CH₄

Answer in image

Last point correction: The net dipole moment is parallel to the electric field E

Polarisation

The phenomenon in which a polar molecule orients itself along the direction of the external electric field or the non-polar molecules become temporary dipoles in presence of an external electric field

Chapter 3

Current Electricity

Drift Velocity and Relaxation Time and Mobility

• The velocity with which the free electrons move towards the positive terminal when an electric field is applied

• Relaxation time is the gap of time between two consecutive collisions of electrons in a conductor.

• Electron mobility is defined as the drift velocity of electrons per unit electric field.

Ohm’s Law

The current flowing through a conductor is directly proportional to the potential difference across it when the temperature is constant

Limitations of Ohm’s Law

• Does not hold good for all materials. Devices which do not obey Ohm’s law are called non-ohmic or non-linear devices

Temperature Dependence on Resistivity

• For conductors: T increases; ρ increases

• For semiconductors/insulators: T increases; ρ decreases

• In conductors, average relaxation time decreases with increase in temperature, resulting in an increase in resistivity. In semiconductors, the increase in number density (with an increase in temperature) is more than the decrease in relaxation time; the net result is, therefore, a decrease in resistivity

• Metals have low resistivity and α is +ve and high

• Nichrome has higher resistivity than metals and α is positive but low. Nichrome is used as a heating element since it has high resistivity

• Manganin has higher resistance than metals but α is 0 and is used to make standard resistors

• Semiconductors have high resistivity but α is -ve

Write two differences between the emf and terminal potential difference of a cell. What is the most important precaution that one should take while drawing current from a cell?

• Electromotive force or emf of a cell is the potential difference across its terminals when no electric current is flowing through it or it is in an open circuit.

• Terminal voltage V of a cell is the potential difference across its terminals when some electric current is flowing through it or it is in a closed circuit.

Kirchoff’s Laws

• First Law (Current Law): The sum of all the currents entering the junction is equal to the sum of the currents leaving the junction

• Second Law (Voltage Law): The algebraic sum of the change in the potential for a closed loop involving resistors and cells in that group is zero

Chapter 4

Moving Charges and Magnetism

Biot Savart’s Law

The magnetic field due to a small current carrying element is directly proportional to:

• Current element

• sine of angle between the element and the point

and inversely proportional to:

• Square of the distance between the element and the point

Note: B always acts perpendicular to velocity

Ampere’s Circuital Law

The closed integral of magnetic flux over a loop equals μ_o times the current enclosed by the loop

Lorentz Force

• The force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B is called the Lorentz Force

  It is given by F = qE + qvB

Path of Charge

• θ = 90^o : circle

• θ = 0^o or 180^o : straight line

• θ ≠ 0^o or 90^o or 180^o : helical

1 Ampere

1 Ampere is that value of steady current which, on flowing in each of two parallel infinitely long conductors of negligible cross-section, placed in vacuum at a distance of 1 meter from each other, produces a force of 2 × 10^-7N/m of their length.

Chapter 5

Magnetism and Matter

Properties of Bar Magnets

• Has 2 equal and opposite poles

• If a magnet is cut into two pieces, it splits into two magnets with each having its own north and south pole

• There is no magnetic monopole

• When a bar magnet is cut laterally (along its length), pole strength decreases and when it is cut transversely, pole strength remains the same

Magnetic Field Lines

Imaginary lines that represent the magnetic field around a magnet

Properties of Magnetic Field Lines

1. Form continuous curves that originate at the north pole and end at the south pole outside. Inside, they go from south to north

2. They never cross each other

3. They are closer together in areas of stronger magnetic field and spread out in areas of weaker magnetic field

4. The density of field lines at a point is directly proportional to the strength of the magnetic field at that point

5. If magnetic field lines are parallel - uniform

6. The direction of the magnetic field is given by the tangent to the field lines at that point

Gauss Law for Magnetism

State Gauss’s law in magnetism. How it is different from Gauss’s law in electrostatics and why?

The closed integral of magnetic flux over a closed surface is zero

Gauss’s Law in magnetism: The net magnetic flux through any closed surface is zero.

Gauss’s Law in electrostatics: The net electric flux through any closed surface is 1/ε₀ times the net charge.

The difference between Gauss’s law of magnetism and that of electrostatics is reflected in the fact that magnetic monopoles do not exist; i.e., magnetic poles always exist in pairs.

Magnetic Induction (B)

The total number of magnetic lines of force crossing per unit area normally through a material

Magnetic Field Intensity or Magnetic Intensity (H)

The ability of the magnetising field to magnetise a material medium

Magnetisation or Intensity of Magnetisation (M)

The net magnetic moment developed per unit volume of a material when placed in a magnetising field

Magnetic Permeability (μ)
Relative Permeability (μ_r)

Magnetic Susceptibility (χ_m)

• The ratio of its magnetic induction (B) to the magnetic intensity (H)

• The ratio of the permeability of a medium to the permeability of free space

• The ratio of magnetisation to the magnetic field intensity

Diamagnetic Materials

1. Exhibit negative magnetism i.e align themselves opposite to the aligned magnetic field

2. Have no unpaired electrons

3. Negative susceptibility

4. Relative permeability less than 1

5. When freely placed in an external magnetic field, it goes from a stronger to a weaker region

6. They are weakly repelled in the presence of an external field

7. When not allowed to move in an external magnetic field, field lines expel out of it

8. Superconducting materials are diamagnetic and hence expel all magnetic field lines out of it

   Ex: Bismouth, Pb, Cu, N₂, Si, H₂O, NaCl

Paramagnetic Materials

1. In the presence of an external field, the molecules align themselves in the direction of the field

2. Have unpaired electron(s)

3. Positive susceptibility

4. Relative Permeability greater than 1

5. When freely placed in an external magnetic field, it goes from a weaker to a stronger regions

6. They are weakly attracted in the presence of an external field

7. The molecules have thermal agitation as the temperature increases, so the net magnetic moment decreases. Hence the susceptibility of a paramagnet depends on temperature (inversely proportional)

   Eg: Al, Na, Ca, O₂, CuCl₂

Ferromagnetic Materials

Why is soft iron used in electromagnets?

1. They are paramagnetic and form domains

2. Domains: groups of atoms/molecules that behave as a single unit

3. The susceptibility of ferro magnets is very high

4. Relative Permeability is a lot greater than 1

5. As temperature increases over the curie temperature the domain will break and ferro magnets will become para magnets

6. Ferro magnets can be classified as:

   Hard: Retain magnetic property even after removing from an external field

   Eg: Alnico, loadstone

   Soft: Does not retain magnetic property

   Eg: Fe, Ni, Co, Gadolinium

A: Because it doesn’t retain magnetic property

Chapter 6

Electromagnetic Induction

Faraday’s Law of Induction

The induced emf developed is directly proportional to the rate of change of magnetic flux linked with the closed circuit

Lenz’s Law

Induced current always flows in a direction that opposes the rate of change of flux.

It is based on conservation of energy

Self Inductance and Mutual Inductance

The phenomenon in which the rate of change of current in a coil creates an induced EMF in the same coil/in another coil

The glow of the light bulb will be decreased when an iron rod is inserted in the solenoid because the inductive reactance increases, so impedance increases, so current decreases, so the glow of the bulb decreases.

1 Henry

Self: 1 Henry is the self-inductance of a coil which creates 1 Webber of magnetic flux when 1A current is passed through it

Mutual: 1 Henry is the mutual inductance between two coils if 1A current passing through 1 coil creates a magnetic flux of 1 Wb in another coil

Chapter 7

Alternating Current

Phasor Diagrams

see cw

Wattless Current

In case of a pure inductor or capacitor, the average power dissipated over a complete cycle is zero. Thus, the current flowing through it is known as wattless current

Energy Loss in Transformers

Flux loss:

Cause: Flux created in primary coil is not completely linked with secondary coil

Minimisation: Keep the coils together

Heat Loss:

Cause: Heat loss in primary and secondary bindings due to resistance

Minimsation: Thick wires can be used

Eddy Current Loss:

Cause: Induced current in the core causes heat loss

Minimsation: Using laminated cores

Hysterisis Loss:

Cause: Repeated magnetisation and demagnetisation of the core created energy loss

Minimsation: Using materials with less hysterisis loss: Ex: Soft iron

Chapter 8

Electromagnetic Waves

Displacement Current
(Differentiate between conduction current and displacement current)

Maxwell’s Equations

EM Spectrum

Chapter 9

Ray Optics and Optical Instruments

Applications of TIR

• Optical fibre cables

• Mirage and Looming

• Circle of illumination

• TIR in prism

Optical Fibres

• The basic principle of optical fibre is total internal reflection

• When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflections along the length of the fibre and finally comes out at the other end

Microscope

Used to achieve linear magnification of very small objects (uses convex lens)

Simple Microscope

Uses a convex lens of small focal length

Compound Microscope

2 convex lenses:

1. Objective lens: Real, inverted, enlarged image, small focal length

2. Eyepiece: Virtual, erect, enlarged image, large focal length

Telescope

• A device that provides angular magnification to see distant objects

• Has 2 convex lenses:

  • Objective Lens: Real, inverted, enlarged image, larger focal length and aperture

  • Eye piece: Virtual, erect, enlarged image, smaller focal length and aperture

• Two types:

  • Astronomical

  • Terrestrial

Drawbacks of Refracting Telescopes

• The lens can only be supported at the edges

• Lenses have chromatic aberration

Advantages and Disadvantages of Reflecting Telescopes

Advantages:

• The mirror can be supported at the back

• Don’t have chromatic aberration

• Spherical aberration is reduced

Disadvantages:

• Some rays of the object will be blocked by the observer

Chapter 10

Wave Optics

Wavefront

Depict the shape of a wavefront in each of the following cases.

(i) Light diverging from a point source.

(ii) Light emerging out of a convex lens when a point source is placed at its focus.

Wavefront is the locus of all points in the same phase of vibration

Huygen’s Principle

Each point of the wavefront is a source of secondary disturbances called wavelets. These secondary wavelets propagate with the speed of the wave and their common tangent at a later time gives the new wavefront

Coherent Sources and Conditions

• Two sources are said to be coherent if they have same phase or constant phase difference

• The light waves emitted by the sources must have the same frequency and wavelength

• Two independent sources of light can never be coherent

Incoherent Sources

• Incoherent sources emit light waves having a different frequency, wavelength and phase

Interference of Light

The phenomenon of redistribution of energy in a medium due to superimposition of waves from two coherent sources of light is called Interference of light.

• Constructive Interference: When crests or troughs of both waves align, the amplitude and intensity become maximum.

• Destructive Interference: When a crest meets a trough, the amplitude and intensity become minimum.

Energy Conservation: No energy is lost—energy reduced at destructive points appears as increased intensity at constructive points.

Conditions for Sustained Interference:

• The sources must be coherent (constant phase difference).

• The light waves should have the same frequency and wavelength.

• Two sources must be very close to each other.

Diffraction of Light

• The phenomenon in which light bends around the sharp edges of obstacles

• Diffraction is only evident if the wavelength and the size of the obstacle is almost the same

Draw the intensity pattern for single slit diffraction and double slit interference. Hence, state two differences between interference and diffraction patterns

Difference :

• Interference fringes are of the same intensity whereas diffraction fringes are of different intensity.

• Fringe width is of the same size in interference whereas it is not so in diffraction

Explain the following giving reasons:

(i) When monochromatic light is incident on a surface separating two media, the reflected and refracted light both have the same frequency as the incident frequency.

(ii) When light travels from a rarer to a denser medium, the speed decreases. Does this decrease in speed imply a reduction in the energy carried by the wave?

• This is because the frequency of light is determined by the source and remains constant regardless of the medium through which it travels. The interaction of light with the surface does not change the frequency but can change the direction of propagation through reflection and refraction

• The energy of a photon is given by E=hν remains constant during refraction. Since energy depends only on frequency and not on speed or wavelength, the reduction in speed does not affect the energy carried by the light wave.

What kind of fringes do you expect to observe if white light is used instead of monochromatic light?

If instead of monochromatic light, white light is used, then the central fringe will be white and the fringes on either side will be coloured. Blue colour will be nearer to central fringe and red will be farther away.

Chapter 11

Dual Nature of Radiation of Matter

Work Function

The minimum energy required to remove an electron from the surface of a metal

Photoelectric Effect

• The phenomenon in which electrons are emitted from the surface of a metal when light of suitable radiation falls on it

• Ex:

  • Zn, Cd, Mg - These will emit electrons only under UV light

  • Na, Li, K, Cs, Rb - Alkali metal will respond to visible light

Threshold Frequency or Cut-Off Frequency

• The minimum frequency of incident radiation below which no photoemission takes place is called the threshold frequency

• For frequency less than threshold frequency, emission of photo electrons is not possible even if intensity of light is increasing

Stopping Potential or Cut-Off Voltage

The minimum negative potential given to anode plate w.r.t. to cathode plate at which the photoelectric current becomes zero is known as stopping potential or cut off potential

Effect of Intensity and Potential on Photocurrent

• The photocurrent is directly proportional to the intensity of light if the frequency is greater than the threshold frequency

• The saturation current is independent of the applied voltage. It depends on the intensity of the light

Effect of Frequency on Stopping Potential and Max Kinetic energy

• Stopping potential and max kinetic energy increase linearly with frequency and are independent of intensity

Einstein’s Photoelectric Equation

• K_max = hν - Φ_o

• If ν<νo, then the maximum kinetic energy is negative, which is impossible. Hence, photoelectric emission does not take place for the incident radiation below the threshold frequency. Thus, the photoelectric emission can take place if ν>νo.

• The maximum kinetic energy of emitted photoelectrons is directly proportional to the frequency of the incident radiation. This means that the maximum kinetic energy of a photoelectron depends only on the frequency of incident light.

Why photoelectric effect cannot be explained on the basis of the wave nature of light?

• Instantaneous Emission: Electrons are emitted immediately as soon as light of sufficient frequency strikes the surface, without any delay. Wave theory predicts that energy would gradually accumulate over time before electrons are ejected, but this is not observed.

• Threshold Frequency: Photo emission occurs only if the light's frequency is above a certain the threshold frequency, regardless of how intense the light is. Wave theory suggests that increasing intensity should eventually supply enough energy to eject electrons, but this does not happen.

• Kinetic Energy Dependence on Frequency: The maximum kinetic energy of the emitted electrons depends only on the frequency of the incident light and not on its intensity. According to wave theory, a more intense light should transfer more energy to the electrons, but experiments show that only higher frequency light increases their kinetic energy.

Properties of Photons

• On interaction with matter, light behaves as particles called photons

• The energy of the photon, E = hv

• They do have momentum and are moving particles.

  Momentum, p = E/C = h/λ

• Intensity, I = nhv/At

  For a given frequency, the intensity of light in the photon picture is determined by the number of photons crossing a unit area per unit time.

• The energy of a photon is independent of intensity and only depends upon the frequency

• Photons are electrically neutral and not affected by electric and magnetic fields

• The total momentum and total energy are conserved in a photon-particle collision.

• They have zero mass and rest energy.

• It is a stable particle and does not decay on its own.

Wave Nature of Matter (de-Broglie’s hypothesis)

• According to de-Broglie, if light (wave) has particle nature (photon), then the particle should have wave nature

• For light momentum p = h/λ

  Then λ=h/p=h/mv

Chapter 12

Atoms

Conclusions of alpha particle experiment

In an experiment on α-particle scattering by a thin foil of gold, draw a plot showing the number of particles scattered versus the scattering angle θ. Why is it that a very small fraction of the particles are scattered at θ > 90º? Write two important conclusions that can be drawn regarding the structure of the atom from the study of this experiment

• If impact parameter ‘b’ reduces to zero, coulomb force increases, and hence alpha particles are scattered at angle θ > 90º, and only one alpha particle is scattered at angle 180º

Conclusions:

• The entire positive charge and most of the mass of the atom is concentrated in the nucleus with the electrons some distance away. 

• The size of the nucleus is about 10^-15m to 10^-14m, while the size of the atom is 10^-10m, so the electrons are at a distance 10⁴m to 10⁵m from the nucleus, and being large empty space in the atom, most a particles go through the empty space

What result do you expect if α -particle scattering experiment is repeated using a thin sheet hydrogen in place of a gold foil? Explain. (Hydrogen is a solid at temperature below 14K)

• In the alpha-particle scattering experiment, if a thin sheet of solid hydrogen is used in place of a gold foil, then the scattering angle would not be large enough.

• This is because the mass of hydrogen is less than the mass of incident α−particles

• Thus, the mass of the scattering particle is more than the target nucleus (hydrogen).

• As a result, the α−particles would not bounce back if solid hydrogen is used in the α−particle scattering experiment.

Image: Schematic Arrangement of gold foil experiment

Impact Parameter

It is the perpendicular distance of the initial velocity vector of α-particles from the centre of the nucleus

Distance of Closest Approach

In Rutherford scattering experiment, draw the trajectory traced by alpha particles in the coulomb field of the target nucleus and explain how this led to estimate the size of the nucleus

The smallest distance an α-particle can go near the nucleus

or
It is the distance of the charged particle from the centre of the target nucleus, at which the whole kinetic energy of the charged particle gets converted into potential energy

The size of the nucleus from the distance of the closest approach was found to be 10^-15 and from kinetic theory, the size of an atom was known to be 10^-10 m

Rutherford’s Model

• +ve charged nucleus at the centre of the atom and electrons revolve around the nucleus in circular orbits

• The centripetal force required for a dynamically stable orbit is given by the electrostatic force

Drawbacks of Rutherford’s Model

• Could not explain the stability of an atom: As an electron revolves around the nucleus, it should emit radiation, lose energy and spiral into the nucleus

• Could not explain line spectra: The emission of line spectra by gases could not be explained since this model predicts continuous spectra but cannot explain why

Bohr’s Postulates

• Electrons could only revolve around the nucleus in stable orbits in which no radiation is emitted

• An electron can revolve in orbits around the nucleus in which the angular momentum of the electron is the integral multiple of h/2π

• An electron might make a transition to a lower energy state during which it emits a photon whose energy equals the difference in energy of initial and final states

Drawbacks of Bohr’s Model

• Could not explain the relative intensity of spectral lines

• It is only applicable to H-like atoms. Eg: H, He⁺, Li²⁺

Ionization Energy

Define ionization energy. How would the ionization energy change when electron in hydrogen atom is replaced by a particle 200 times heavier than electron, but having the same charge?

Ionization energy is defined as the minimum energy required to remove an electron from the valence shell of an isolated gaseous atom.

Spectral Series

Large Bears Prefer Big Pies

Lyman:

• n₁ or n_f = 1

• UV region

• -13.6 eV

Balmer:

• n₁ or n_f = 2

• Visible Region

• -3.4 eV

• When 3→2 => H_α

• When 4→2=> H_β

• When 5→2=> H_γ

Parschen:

• n₁ or n_f = 3

• IR Region

• -1.51 eV

Brackett:

• n₂ or n_f = 4

• IR Region

• -0.85

Pfund:

• n₂ or n_f = 5

• IR Region

• -0.54

Note: To calculate the shortest wavelength, let’s say for the Balmer series, take n_f as 2 and n_i as infinity. For longest, n_f = 3.

de-Broglie’s explanation on Bohr’s Model (second postulate)

State Bohr’s postulate to define stable orbits in hydrogen atoms. How does de Broglie’s hypothesis explain the stability of these orbits?

According to de-Broglie, electrons can exist in orbitals where the circumference of the orbit is the integral multiple of de-Broglie’s wavelength of electron

Chapter 13

Nuclei

(a) The density of the nuclear matter is tremendously larger than the physical density of the material. Explain.

(b) The nuclear forces are not coulomb forces between nucleons. Explain

• The density of the nuclear matter is tremendously larger than the physical density of the material. This is because most of the atom is empty and its whole mass is concentrated in its nucleus.

• Coulombian force between two proton is repulsive. However, within a nucleus a number of protons and neutrons exist together within a very small space. So it is clear that nuclear force is not coulomb force but it is an extremely short range force which is attractive in nature and responsible for maintaining all the nucleons together.

Mass Defect

Why is the mass of a nucleus always less than the sum of the masses of its constituents-neutrons and protons?

The difference in the sum of the mass of individual nucleons and the mass of the actual nucleus is called mass defect

A: During the formation of a nucleus, the protons and neutrons come closer to a distance of 10^-14 m. The energy required for the purpose is spent by the nucleus at the expense of their masses. So mass of the nucleus found is less than the sum of the masses of the individual nucleons

Binding Energy of Nucleus

Why does the process of spontaneous nuclear fission occur in heavy nuclei?

• The energy required to bind the protons and neutrons inside the nucleus against the coulombic repulsion

• For 30 < A < 170: E_bn is maximum

• For A<30 and A>170 E_bn is low

• For A < 10: Nuclear fusion is energetically possible

• For A > 230: Nuclear fission is energetically possible

The above curve tells us that the binding energy per nucleus is smaller for heavier nuclei as well as for lighter nuclei than for the middle order nuclei (with mass number lying between 30 to 170). This means A: heavier nuclei are less stable thus they undergo fission and lighter nuclei undergo fusion to form the nucleus lying in the range of the mass number 30 to 170

Another point: heavy nuclei contain a large number of protons which exert strong repulsive forces on one another.

Draw a plot showing the variation of potential energy of two nucleons as a function of distances between them. Identify the regions in which the force between the nucleons is (i) attractive, and (ii) repulsive. Justify your answers.

Conclusions:

• The nuclear force is much stronger than the coulomb force acting between charges or the gravitational forces between masses.

• The nuclear force between two nucleons falls rapidly to zero as their distance is more than a few fermi.

• For a separation greater than r₀, the force is attractive and for a separation less than r₀, the force is strongly repulsive.

Properties of Nuclear Force

Which property of nuclear force explains the approximate constance of binding energy per nucleon with mass number A for nuclei in the range 30 < A < 170?

• Strongest of all fundamental forces; short-range force

• They are strongly attractive within a range of 1 fermi to 4.2 fermi. Nuclear forces above 4.2 fermi are negligible, whereas below 1 fermi, they become repulsive in nature.

• Has a saturation property. This is why B.E per nucleon is almost a constant (8 MeV)

• Charge independent; same for p-p, n-n, p-n

A: The characteristic property of nuclear force that explains the constancy of binding energy per nucleon is the saturation or short-range nature of nuclear forces. In heavy nuclei, nuclear size > range of nuclear force.

Nuclear Fission

If both the number of protons and neutrons in a nuclear reaction is conserved, in what way is mass converted into energy (or vice versa)? Explain giving one example

or

In a typical nuclear reaction, e.g. ²₁H + ²₁H → ³₂He + ¹₀n + 3.27 MeV, although the number of nucleons is conserved, yet energy is released. How? Explain.

• The process in which a heavy nucleus breaks into smaller fragments with the release of energy

• Eg: When uranium is bombarded by a neutron

A: In a nuclear reaction both the number of protons and neutrons remains conserved, yet total mass of products is not same as the total mass of reactants. There is some loss/gain in mass, which is converted into energy. Alternately we can say that total binding energy of products is not same as the total binding energy of reactants and the difference in these binding energies appears as energy released or absorbed in a nuclear reaction.

Example: Ba Kr reaction (image) or reaction in second question

or

In a nuclear reaction, the sum of the masses of the target nucleus (²₁H) and the bombarding particle (²₁H) may be greater than the product nucleus (³₂He) and the outgoing neutron (¹₀n). So from the law of conservation of mass energy, some energy (3.27 MeV) is evolved due to mass defect in the nuclear reaction. This energy is called the Q-value of the nuclear reaction.

Nuclear Fusion

• The process in which two or more lighter nuclei join together to form a nucleus with the release of energy

• Required very high temperatures (10⁸ K) to overcome the coulombic repulsion and fuses. So it is called a thermonuclear reaction

Briefly describe the multi-step process involved in the generation of energy in the