Binding Energy Curve

Binding Energy Curve :

A graph is plotted for different nuclei between the binding energy per nucleon and the atomic mass number. This graph gives a curve which is called " binding energy curve".

There are following discussion point obtained from the binding energy curve :

1.) For Nuclei with $A=50$ TO $A=80$:

For nuclei with atomic mass number $A = 50 - 80$ , the B.E./ nucleon (i.e. binding energy per nucleon) is approximately $8.5 MeV$.

The curve is almost flat in this and indicate the highly stability of the nucleus.

2.) For Nuclei with $A \geq 80$:

For heavier nuclei with $A \gt 80$, the B.E. /nucleon ( i.e. binding energy per nucleon) decreases slowly and reaching about $7.6 MeV$ for uranium ($U \: A = 238$).

The lower value of binding energy per nucleon fails to counteract the Coulombian repulsion among protons in nuclei having large number of protons resulting instability

Consequently, the nuclei of heavier atoms beyond $_{83}Bi^{209}$ are radioactive.

3.) For Nuclei with $A \leq 50$:

For nuclei with atomic mass number below $50$ , the B.E./ nucleon decreases, with a sharp drop below $A=20$.

For example: Heavy hydrogen (i.e $_{1}H^{2}$), it is only about $1.1 MeV$. it indicates that lower stability for nuclear with mass number below $20$.

4.) Subsidiary Peak for $A \lt 50$:

Below $A = 50$, the curve does not fall continuously, but the subsidiary peaks at $_{8}O^{16}, _{6}C^{12},_{2}He^{4}$.

These peak indicate that such even-even nuclear are more stable compared to the immediate neighbours .

5.) Nuclear fusion and Nuclear fission process release energy:

From curve, it shows that drops down in curve at both high and low mass number and lower binding energy per nucleon.

For example:

A very high amount of energy is released in the process of nuclear fission and fusion because of Lo binding energy causes instability of the nucleus.

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Nuclear Fission and Nuclear Fusion

Nuclear Fission:

When a heavy nucleus breaks into two or more smaller, lighter nuclei and produces high energy, this process is called as nuclear fission.

Example:

$_{92}U^{235} + _{0}n^{1} (Neutron) \rightarrow _{92}U^{236} \rightarrow _{56}Ba^{141} + _{36}Kr^{92} +3 _{0}n^{1} + \gamma$

Nuclear Fusion:

When two or more very light nuclei move with a very high speed then these nuclei are fused and form a single nucleus. This process is called as nuclear fusion.

Example: Two deuterons can be fused to form a triton(tritium nucleus) as reaction is shown below:

$_{1}H^{2} + _{1}H^{2} \rightarrow _{1}H^{3} + _{1}H^{1} + 4.0 \: MeV \:(Energy)$

$_{1}H^{3} (Tritium) + _{1}H^{2} \rightarrow _{2}He^{4} + _{0}n^{1} + 17.6.0 \: MeV \:(Energy)$

The total result of the above two equations is the fusion of deuterons and produces an $\alpha - $ particle $(_{2}He^{4})$, a neutron $(_{0}n^{1})$ and a proton $(_{1}H^{1})$. The total released energy is $21.6 MeV$.

Alternatively, the fusion of three deutrons $(_{1}H^{2})$ into $\alpha -$ partice can takes place as follows:

$_{1}H^{2} + _{1}H^{2} \rightarrow _{2}He^{3} + _{0}n^{1} + 3.3 \: MeV \:(Energy)$

$_{2}He^{3} + _{1}H^{2} \rightarrow _{2}He^{4} + _{1}H^{1} + 18.3 \: MeV \:(Energy)$

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Mass Defect, Binding Energy and Binding Energy per nucleon

Binding Energy:

The difference between the total mass of individual nucleons (i.e. total number of proton and neutron) and actual mass of nucleus of that energy is called binding energy.

$\Delta m = \left (P \times m_{P} + N \times m_{N} \right) - m_{actual} \qquad (1)$

Where
$\Delta m \rightarrow$ Mass Defect
$P \rightarrow$ Number of Proton
$N \rightarrow$ Number of Neutron
$m_{actual} \rightarrow$ Actual mass of nucleus
$m_{P} \rightarrow$ Mass of a Proton
$m_{N} \rightarrow$ Mass of a Neutron

We know that

$Z=P=e \\ N=A-Z \qquad (2)$

Where
$Z \rightarrow $ Atomic Number
$A \rightarrow $ Atomic Mass Number
$ e \rightarrow $ Number of Electrons

From above two equation $(1)$ and equation $(2)$

$\Delta m = \left [ Z \times m_{P} + \left ( A-Z \right) \times m_{N} \right] - m_{actual} \qquad (1)$

Binding Energy:

The energy require to form or break a nucleous is called the binding energy of nucleous.

$B.E= \Delta m \times c^{2} Joule$

Where $B.E.\rightarrow$ Binding Energy

$B.E= \Delta m (in \: a.m.u.) \times 931.5 \: MeV$

Where $1 \: a.m.u. = 1.67377 \times 10^{-27} kilograms$

Binding energy per nucleon:

The energy require to emit one nucleon from the nucleous is called binding energy per nucleon.

$B.E. \: per \: nucleon = \frac{B.E.}{ Total \: No. \: of \: Nucleons}$

Where $B.E.\rightarrow$ Binding Energy

Note: Higher binding energy per nucleon shows higher stability of the nucleus.

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Radioactive Decay and its types

Definition:

When the unstable atom (called radionuclide) loses its energy through ionizing radiation, this process is known as radioactive decay.

Types of radioactive decay:

There are 3- types of radioactive decay

1. Alpha Decay
2. Beta Decay
3. Gamma Decay

1. Alpha Decay: A helium nuclei which contain two protons and two neutrons is known as an alpha particle. The $\alpha$- particles are commonly emitted by the heavier radioactive nuclei. When the $\alpha$- particle is emitted from the nucleus then the atomic number is reduced by two (i.e. $Z-2$) or the atomic mass number is reduced by 4 (i.e. $A-4$).

Example:

The decay of $Pu^{239}$ into fissionable $U^{235}$ by the emission of $alpha$- particle

$_{94}Pu^{214} \rightarrow _{92}U^{235} + _{2}He^{4} \left(\alpha - particle \right)$

2. Beta Decay: The emission of $\beta$-particle occurs due to the conversion of a neutron into a proton or vice versa in the nucleus. The $\beta$-decay is commonly accompanied by the emission of neutrino ($\nu$) radiation. There are two types of $\beta$-decay.

i.) Beta Minus: When a neutron is converted into a proton then an electron ($_{-1}e^{\circ}$) i.e.$\beta$-minus particle is emitted. When the $\beta$- minus particle is emitted from the nucleus then the atomic number is increased by one (i.e. $Z+1$) and no change in atomic mass number ($A$).

Example:

$_{6}C^{14} \rightarrow _{7}N^{14} + _{-1}e^{\circ} + \overline{\nu}_{e} \: (anti\:neutrino)$

ii.) Beta Plus: When a proton is converted into a neutron then a positron ($_{+1}e^{\circ}$) $\beta$- plus partice is emitted. When the $\beta$- plus particle is emitted from the nucleus then the atomic number is decreased by one (i.e. $Z-1$) and no change in atomic mass number ($A$). It is also known as positron decay. Positron decay is caused when the radioactive nucleus contains an excess of protons.

Example:

$_{12}Mg^{23} \rightarrow _{11}Na^{23} + _{+1}e^{\circ} + \nu_{e}\: (neutrino)$

The penetrating power of $_{-1}\beta^{\circ}$ particles is small compared to $\gamma$-rays, however it is larger than that of $\alpha$-particles.

Note:

Electron Capture: The nucleus captures the electron from orbits and combines with a proton to form a neutron and emits a neutrino.

Example:

$_{26}Fe^{55} + _{-1}e^{\circ} \rightarrow _{25}Mn^{55} + \nu_{e}\: (neutrino)$

3. Gamma (y) Decay: $\gamma$-particles are electromagnetic radiation of extremely short wavelength and high frequency resulting in high energy. The $\gamma$-rays originate from the nucleus while X-rays come from the atom. $\gamma$-wavelength are on average, about one-tenth those of X-rays, though energy ranges overlap somewhat. There is no alternation of atomic or mass numbers due to $\gamma$ decay.

Example:

$_{27}Co^{60} \rightarrow _{27}Co^{60} + \gamma \: (gamma)$

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Safety measures for nuclear power plants

Safety measures for nuclear power plants are as follows:

1.) A nuclear power plant should bė constructed away from human habitation. The 106 km radius around the plant should be excluded zone where no public habitation is permitted.

2.) The materials to be used for the construction of a nuclear power plant should be of required standards.

3.) The nuclear power plant produces the waste water that should be purified.

4.)The nuclear power plant must be provided with such a safety system which should safely shut down the plant as and when necessity arises.

5.) There must be periodic checks tó ensure that radioactivity does not exceed the permissible value in the environment.

6.) While disposing off the wastes from the nuclear plants it shoud be where these ensured that there is no pollution of water of river or sea wastes are disposed.

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Nuclear force and its properties

Nuclear Force

A forces that act between the nucleons (i.e proton and neutron) inside the nucleus. This force is called the nuclear force.

These forces are responsible to keep the nucleons bound inside the nucleus.

Properties of Nuclear Force

There are the following properties of nuclear force is given below.

(i) These are strong nuclear forces otherwise protons cannot exist in the nucleus.

(ii) The intensity of these forces is very large. The intensity of nuclear force is maximum among, so far known forces.

(iii) It is not electrical in nature. If we assume them electrical forces, then the protons cannot reside in nucleus.

(iv) These forces do not depend on charge. The force acting between the nucleons (such as proton-proton, neutron-neutron and proton-neutron) is of same nature.

(v) These are not gravitational forces because the mass of the particles inside the nucleus is very small, while the magnitude of nuclear force is very large.

(vi) These forces are short range forces. They are confined inside the nucleus (i. e., $10^{-15} m$ equal to the diameter of nucleus). There is no existence of these forces outside the nucleus.

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Construction and Working of Nuclear Reactor or Atomic Pile

A nuclear reactor is a device within which a self-sustaining controlled chain reaction is produced by fissionable material. it is thus a source of control energy that is utilized for several useful purposes. The reactor has some important part which is given below:

1. Fuel: The fassionable material such as Uranium-235 and Plutonium-239 known as fuel. These materials play an important role in operating the nuclear reactor.


2. Moderator: It slows down the neutrons to thermal energies through the elastic collision between its nuclei and fission neutrons. Thermal neutrons have a very high probability of fissioning Uranium-235 nuclei. Examples: heavy water graphite beryllium oxide. Heavy water is the best moderator.


3. Control Rods: These rods are used to control the fission rate in the reactor. these Rods are fixed in the reactor walls. These rods are made up of the material of cadmium and Boron. These materials are good absorbers of slow neutrons. Therefore when the rods are pushed into the reactor, the fission rate decreases, and when they are pulled out, the fission grows.


4. Coolant: The coolant is used to remove the heat from the reactor which is produced inside the reactor. For this purpose air-water or CO₂ is passed through the reactor.


5. Shield: various type of intense rays are emitted from the reactor, which may be injurious to the people working near the reactor. To protect them from this radiation, thick concrete walls are erected around the reactor.


6. Safety device: In case of an accident or other emergency, a special set of control rods, called " shut-off rods" enter the reactor automatically. They immediately absorb the neutrons so that the chain reaction stops entirely.

Construction:

It is made up of a large number of uranium rods which are placed in calculated geometrical lattice between layers of pure graphite ( moderator) blocks. To prevent oxidation of Uranium, the rods are covered by close-fitting aluminum cylinders. The control rods are so inserted within the lattice that they will be raised or lowered between the Uranium rods whenever necessary. The whole reactor is encircled by a concrete shield.

Working:

The actual operation of the reactor is started by pulling out the control rods so that they do not absorb many neutrons. Then, the stray neutrons, which are always present in the tractor, start fissioning the U-235 nuclei. In each fission, two or three fast neutrons are produced. These neutrons repeatedly strike the moderator and slowed down. Then, These neutrons start fissioning the U-235 nuclei. So, a chain-reaction of fission starts. The number of neutrons, which is produced in fissioning, is controlled by pushing the cadmium rods into the reactor. These rods absorb a number of the neutrons. Thus, the energy produced in the reactor is kept under control to avoid any explosion. The coolant is pond pumped through the reactor to carry away The Heat generated by the fission of uranium nuclei. the hot CO₂ passes through the heat exchanger and convert cold water into steam. This steam is used to operate turbines for generating electricity.

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