RBSE Class 12 Physics Notes Chapter 13 Nuclei

These comprehensive RBSE Class 12 Physics Notes Chapter 13 Nuclei will give a brief overview of all the concepts.

RBSE Class 12 Physics Chapter 13 Notes Nuclei

Composition of Nucleus:
Nucleus was first discovered by Rutherford and his associates from the study of scattering of alpha particles from thin metal foils.

At present nucleus is considered to be a small massive core of the size of the order to 10^-14 m and contains neutrons and protons called nucleons. (Neutrons were discovered by Chadwick.)

• Mass of proton, m_p = 1.6726 × 10^-27 kg = 1.007825 amu
• Mass of neutron, m_n = 1.6749 × 10^-27 kg = 1.008665 amu.

Atomic Number (Z):
Atomic Number (Z) of an element is the number of protons present inside the nucleus of an atom.

Mass Number (A):
Mass Number (A) of an element is the total number of protons and neutrons present inside the atomic nucleus
A = Z + N.

Nuclear Size:
The volume of the nucleus is proportional to its mass number
i.e volume ∝ A
or \(\frac{4}{3}\)πR³ ∝ A
or R ∝ A^1/3
or R = R₀A^1/3

where R₀ = 1.1 × 10^-15 m is the range of nuclear force

Nuclear force:
Nuclear force is the force which binds the protons and neutrons inside the nucleus and is the strongest force in nature.
Atomic mass unit is defined as \(\frac{1}{12}\) th of the mass of ₆C¹² atom i.e. 1 a.m.u. = 1.66 × 10^-27 kg

One electron volt (eV):
One electron volt (eV) is the energy gained by an electron, when accelerated through a potential difference of one volt.
1 eV = 1.6 × 10^-19 C × 1V = 1.6 × 10^-19 CV = 1.6 × 10^-19 J.

Energy equivalent of 1 a.m.u.
From Einstein mass-energy relation
E = mc²
If m = 1 a.m.u. - 1.66 × 10^-27 kg
then E = 1.66 × 10^-27 × (3 × 10⁸)
= 1.49 × 10^-10 J.
or E = \(\frac{1.49 \times 10^{-10}}{1.6 \times 10^{-13}}\)eV = 931.25 MeVs
or E = 931 MeV.

Mass defect (Am):
Mass defect (Am) is the difference between the sum of the masses of the nucleons constituting a nucleus and the rest mass of the nucleus.
So Δm = [Z mp + (A - Z) m_n] - m_N (_ZX^A)

• Binding energy of a nucleus is the energy equivalent to the mass defect, i.e. B.E. = Δm c⁸
• Binding energy of a nucleus is also defined as the energy required to separate the nucleons an infinite distance apart, so that they cannot interact with each other.

Binding energy per nucleon:
Binding energy per nucleon is the average energy required to extract one nucleon from the nucleus.
B.E. per nucleon = \(\frac{\text { B.E. }}{\text { A }}\)

Packing fraction (f):
Packing fraction (f) of a nucleus is the mass defect per nucleon of the nucleus
f = \(\frac{\text { mass defect }}{\mathrm{A}}\)

Radioactivity:
It is the phenomenon of spontaneous emission of radiations due to disintegration of nucleus. And the substances which emit these rays (or radiations) are called radioactive substances.
Nuclear radiations. The radiations emitted by radioactive elements consists of three kinds namely

• Alpha (α) rays: They are helium nuclei and carry double the positive charge of proton and are four times as heavy.
• Beta (β) rays: They are streams of electrons.
• Gamma (γ) rays: They are electromagnetic waves and have velocity equal to that of light.

Laws of radioactive decay

• Radioactive decay is spontaneous with the emission of α, β and γ rays.
• Rate of disintegration is directly proportional to the number of radioactive atoms present at that time.
  And N = N₀e^-λt

Half life (T):
Half life (T) of a radioactive substance is the time during which, half of the total number of atoms in the element disintegrate.
And T = \(\frac{0.6931}{\lambda}\)
where λ is called decay constant

Radioactive decay constant (λ):
Radioactive decay constant (λ) is the reciprocal of the time, after which the number of atoms of a radioactive element decreases to 0.368 (i.e. 36.8%) of their number present initially.

Average or mean life:
Average or mean life of a radioactive substance is the average time for which the nuclei of the atoms exist
T_a = \(\frac{1}{λ}\)

Units of radioactivity:
(i) curie Ci: The activity (rate of disintegration of the source) of a radioactive substance is said to be 1Ci, when 3.7 × 10¹⁰ decays take place in every second.
i. e. 1Ci = 3.7 × 10⁷ decay/s.

(ii) rutherford (Rd): The activity of a radioactive substance is said to be 1 Rd, when 106 decays take place in every second.
i. e. 1 Rd = 10⁶ decay/s.

Nuclear Reaction:
It is the transformation of one nucleus into another nucleus by bombardingthe former with suitable high energy particles.
i.e _ZX^A + ₂He⁴ → _Z+2C^A+4 → _Z+1Y^A+3 + ₂H¹ + Q
e.g ₁₂Mg²⁴ + ₂He⁴ → ₁₃Al²⁷ + ₁H¹
or ₅B¹¹ + ₁H¹ → ₄Be⁸ + ₂He⁴

Conservation laws obeyed in all nuclear reactions

• Law of conservation of nudecm nambei
• Law of conservation of charge number
• Law of conservation or mass and energy
• Law of conservation of linear momentum

Nuclear Fission:
Nuclear Fission is the process of splitting of a heavy nucleus into two nuclei of nearly comparable masses with, liberation of energy.
eg:
₉₂U²³⁵ + ₀n¹ → [₉₂U²³⁶] → ₅₆Ba¹⁴¹ + ₃₆Kr⁹² + 3 ₀n¹ + Q
The energy Q released was estimated to be 200 MeV per fission (or about 0.9 MeV per nucleon)

It is not necessary that ₉₂U²³⁵ will split into ₅₆Ba¹⁴¹ and ₃₆Kr⁹², other pair of fission product e.g. ₅₆Ba¹⁴⁴ and ₃₆Kr⁸⁹ etc. are also possible depending upon the kinetic energy of neutron.

Nuclear chain reaction:
In fission reaction, on the average three neutrons are emitted These three neutrons can further produce fission of three more uranium nuclei and so on. This can lead to a chain reaction and within no time a large number of uranium can undergo fission resulting in the enormous amount of energy.

Critical mass:
A particular mass of fissionable material will sustain a chain reaction or not is determined by a factor called reproduction factor. If the rate of neutron production is equal to rate at which neutrons disappear, then the reproduction factor is one and this mass is called critical mass.

Nuclear Reactor:
Nuclear Reactor is a device in which a controlled chain reaction produces radioactive isotopes and energy.

Uses:

• A nuclear reactor is used for generation of electricity and preparation of radio-isotopes etc.
• Nuclear fusion is the process in which lighter nuclei (like ₁H¹) are fused together into heavier atom (like ₂He⁴) with the release of enormous amount of energy called thermonuclear energy, and the reaction is called thermonuclear reaction.
• Nuclear fusion takes place at very high temperature and very high density.
  e.g. ₁H² + ₁H² → ₂He⁴ + 24 MeV
• Nuclear fusion reaction takes place in the presence of about 10⁷ K temperature.