Nuclei: Nuclear Force, Energy and Radioactivity

Nuclei are the smaller and denser regions present at the center of atoms that consist of protons and neutrons.

• An atom consists of electrons, protons, and neutrons.
• The protons and neutrons of an atom are located at the center of the atom, called the nucleus.
• The electrons revolve around the nucleus.
• The atomic nucleus was discovered by Rutherford along with his associates in the year 1911.
• Did you know? Over 99.9% of the mass of an atom is concentrated in its nucleus.
• The size of the nucleus is of the order of 10^-15 m.

Key Terms: Atom, Radioactivity, Radioactive decay law, Atomic reactor, Atomic fusion, Mean life, Half-life, Nucleus, Nuclear energy, Nuclear fission, Nuclear fusion

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Atom

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Everything we see around us is made up of atoms. These are the building blocks of all matter.

• An atom is a tiny particle composed of a nucleus containing protons and neutrons, surrounded by a cloud of electrons bound by electromagnetic forces.
• Protons and neutrons together called nucleons are located at the center region called the nucleus of the atom.
• Atoms are extremely small, measuring around 100 picometers across.
• The nucleus contains more than 99.94% of the mass of an atom.
• The electromagnetic force attracts electrons in an atom to protons in an atomic nucleus.
• The nuclear force attracts protons and neutrons in the nucleus to each other.

Structure of an Atom

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Nuclei

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Nuclei is the plural form of the nucleus.

• The atomic nucleus is the compact, dense region at the core of an atom. It consists of protons and neutrons.
• Ernest Rutherford discovered it in 1911 based on the 1909 Geiger-Marsden gold foil experiment.
• Protons are positively charged particles.
• Neutrons don’t have any charge.
• Protons and neutrons in a nucleus are known as nucleons.
• The number of protons in a nucleus is known as the atomic number (Z).
• The sum of the number of protons and neutrons is called mass number (A).
• The nucleus contains almost all of the mass of an atom, with just a small contribution from the electron cloud.
• The nuclear force holds protons and neutrons together to form a nucleus.

Nuclei Class 12 Important Notes PDF

Nuclei Class 12 Important Notes

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Terms Related to Nucleus

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In this section, we will explore some important terms related to the nucleus.

• Atomic Number: The number of protons in the core of a particle of the component is called the atomic number (Z) of the element.
• Mass Number: The sum of the number of protons and neutrons present inside the core of an atom is called the mass number (A) of the element.
• Nuclear Size: The radius of the nucleus is given by

R = Ro A1/3

Where R_o is an empirical constant for all nuclei and equal to 1.1 x 10^-15 m or 1.5 fermi.

• Nuclear Density: The density of the nucleus is defined as the mass per unit of a nucleus and it is equivalent to 2.38 x 10¹⁷ kg/m³.
• Atomic Mass Unit: An atomic mass unit is equal to 1/12 the mass of a single carbon-12 atom of carbon-12. It is equal to 1.660538921 × 10⁻²⁴ grams.

The energy associated with 1 amu is equal to 931 MeV.

• Isotopes: The atoms of a particular chemical element having the same atomic number but different mass numbers are called isotopes.

Examples: ₆C¹⁰, ₆C¹¹. ₆C¹², ₆C¹⁴ and ₁H¹(Hydrogen), ₁H²(Deuterium), ₁H³(Tritium)

• Isobars: The atoms of the different chemical elements having the same mass number but different atomic numbers are called Isobars.

Examples: ₁H³ and ₂He³; ₃Li⁷ and ₄Be⁷; ₇N¹⁵ and ₈O¹⁵

• Isotones: The atoms of different chemical elements having the same number of neutrons but different atomic numbers are called Iostones.

Example: ₄Be⁹ and ₅B¹⁰; ₆C¹³ and ₇N¹⁴; ₉F¹⁹ and ₁₀Ne²⁰

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Nuclear Binding Energy

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The total energy required to disintegrate the nucleus into its constituent particles (i.e. neutrons) is called nuclear binding energy.

This energy is equivalent to the energy associated with the mass defect. It is given by

\(E_b=\Delta m \times 931 MeV\)

Where Δm is the mass defect.

Nuclear Binding Energy Per Nucleon

The average energy required to release a nucleon from a nucleus is called binding energy per nucleon. It is given by

\(E_{bn}=\frac{\Delta m \times931 MeV}{Mass\ number (A)}\)

• Binding energy per nucleon determines the stability of a nucleus.
• If it is less, the nucleus is less stable.
• If it is higher, the nucleus is more stable.

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Nuclear Force

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Nuclear force is a strong attractive force between nucleons in the atomic nucleus that holds the nucleons together.

• It arises due to the exchange of particles known as π-mesons between the nucleons.
• The nuclear force is 100 times the electrostatic force and 10³⁶ times the gravitational force.
• It is charge-independent.
• These are non-central forces.
• It is a short-range force i.e. of the order of 10^-15 m.

Nuclear Force

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Radioactivity

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The phenomenon of spontaneous emission of radiation by heavy elements is called Radioactivity.

• The elements that show this phenomenon are called radioactive elements.
• Natural elements with atomic numbers more than 82 are unstable and thus radioactive.
• Uranium ores contain traces of Polonium and Radium and these elements were much more radioactive than uranium itself.

Radiations Emitted by a Radioactive Element

Three kinds of radiation are produced by radioactive components

• α-rays: They are comprised of α-particles, which are doubly ionized helium particles.
• β-rays: These are comparable to fast-moving electrons.
• γ-rays: These are the high-energy packets of electromagnetic radiation i.e. high energy photons.

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Radioactive Decay Law

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The rate of disintegration of a radioactive substance at an instant is directly proportional to the number of nuclei in the radioactive substance at that time.

Radioactive decay obeys the following law

• Radioactive decay is a spontaneous process and is not affected by external conditions such as temperature, pressure, etc.
• At a time, a nucleus will emit one alpha particle or one beta particle. Both alpha and Beta-particles are not emitted simultaneously and Gamma-rays emission follows the emission of alpha or beta particles.
• When a radioactive decays by emitting an alpha particle, the position of the daughter element is down by two places in the periodic table.
• When a radioactive element decays by emitting a beta-particle, the position of the daughter element is raised by one place in the periodic table.
• When a radioactive element decays by emitting rays, its position remains the same in the periodic table. The radioactive element in the excited state comes to its ground state by emitting the energy in the form of a photon or gamma-rays.

Let N_o be the number of nuclei at time t = 0 and N be the number of nuclei at time t = t, then

N = N_oe^-λt

Where 

• N_o be the number of nuclei at time t = 0
• λ is known as the radioactive decay constant or disintegration constant

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Half-Life and Mean Life

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The time during which half of the nuclei of the radioactive substance disintegrate is called the half-life of a radioactive substance. It is given by

T_1/2 = 06931/λ

The average life or mean life (τ) of a radioactive component is given by the sum of the total lifetime of all nuclei divided by the total number of nuclei present.

i.e. Mean life, τ = T_Total/N_o

Also,  τ = 1/λ

The relation between half-life and mean life is given by

Mean life,  τ = 1.44 T_1/2

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Activity of a Radioactive Element

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The total decay rate of the substance is known as the activity of a radioactive substance.

Mathematically, it is given by

R = R_oe^-λt

Where

• R is the activity of the radioactive element at time t
• R_o is the original activity

Its SI unit is Becquerel (Bq)

Its different units are Curie and Rutherford.

• 1 Curie = 3.7 x10¹⁰ rot/s
• 1 Rutherford = 10⁶ rot/s

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Nuclear Energy

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The energy obtained from the conversion of nuclear mass is known as nuclear energy.

Energy can be released from radioactive elements by two processes

• Nuclear Fission
• Nuclear Fusion

Nuclear Fission

Nuclear fission is a process of splitting a heavy nucleus into two lighter nuclei releasing a large amount of energy.

• At the point when a sluggish neutron hits a uranium core (92U235), it parts into 56Ba141 and 36Kr92 alongside three neutrons and a ton of energy.
• The energy released per fission in nuclear fission is about 200 MeV.

Nuclear Fusion

A process in which two very light nuclei combine to form a nucleus with a larger mass number along with the simultaneous release of a large amount of energy is called nuclear fusion.

• Nuclear fusion can be achieved at very high temperatures (10⁸ K).
• It is also known as a Thermonuclear reaction.
• Nuclear fusion occurs in the Sun and other stars.

Nuclear Fusion

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Atomic Reactor

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An atomic reaction, also known as nulcear reactor is a device to initiate and control self-sustained nuclear chain reaction.

The principal parts of an atomic reactor are the following

• Fuel: Fissionable materials like ₉₂U²³⁵, ₉₂U²³⁸, and ₉₄^U239 are utilized as fuel.
• Moderator: Heavy water, graphite, and beryllium oxide are utilized to more slow down quick neutrons.
• Coolant: The virus water, fluid oxygen, and so on are utilized to eliminate heat produced in the parting interaction.
• Control bars: Cadmium or boron poles are an acceptable safeguard of neutrons and along these lines used to control the parting response.

Nuclear bomb working depends on uncontrolled chain response. 

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Things to Remember

• The whole charge and almost the whole mass of a particle is amassed in a little space called the core of an atom.
  The core comprises protons and neutrons. They are called nucleons.
• The power acting inside the core or acting between nucleons is called atomic power.
  Atomic powers are the most grounded powers in nature.
• The base energy needed to isolate the nucleons up to an endless separation from the core is called atomic restricting energy
• The wonder of breaking down hefty components into similarly lighter components by the discharge of radiation is called radioactivity.
• Three kinds of radiation produced by radioactive components are α-beams, β-beams, and γ-beams.
• The action of a radioactive component is equivalent to its pace of deterioration.
• The way toward joining two lighter cores to frame one hefty core is called atomic combination.
• The energy delivered during atomic combination is known as nuclear energy.

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Previous Year Questions

1. A 280 day old radioactive substance shows an activity of 6000 dps, 140 days later its activity becomes 3000 dps. What was its initial activity?
2. A radioactive element 90X238 decays into 83Υ222. The number of P-particle emitted are:
3. The ratio of number of nuclei of A to those of B will be (1e)2 after a time interval
4. If 92U206 emits 8 α-particles and 6 β-particles, then the resulting nucleus is
5. The half-life of a ratio-isotope is 4 h. If initial mass of the isotope was 200 g, then mass remaining after 24 h will be​
6. The half-life of a radioactive substance is 3.6 How much of 20mg of this radioactive substance will remain after 36 days ?
7. Due to ? decay, what is the effect on neutron and proton numbers?
8. In radioactive decay process, the negatively charged emitted β− particles are
9. An atom bomb is based on the principle of
10. Fission of nuclei is possible because the binding energy per nucleon in them​
11. Hydrogen bomb is based upon​
12. In gamma ray emission from a nucleus​
13. If 200 MeV of energy is released in the fission of nucleus of 92U235,92U235, the number of nuclei that undergo fission to produce energy of 10 kWh in 1 s​
14. ln the nuclear reaction 147N+X→146C+11H,714N+X→614C+11H, the XX will be​
15. A luminous body radiates energy at a rate 3.6×10283.6×1028 J/s, then loss of mass of the body per second is​