# AP Inter 2nd Year Physics Notes Chapter 14 Nuclei

Students can go through AP Inter 2nd Year Physics Notes 14th Lesson Nuclei will help students in revising the entire concepts quickly.

## AP Inter 2nd Year Physics Notes 14th Lesson Nuclei

→ No. of protons inside the nucleus is called atomic number.

→ The total number of protons and neutrons inside the nucleus is called mass number.

→ Both protons and neutrons in a nucleus are called nucleons. The nucleus was first discovered by Rutherford.

→ The size of atom is in the order of 10-10 m.

→ The size of nucleus is in the order of 10-15 m.

→ The radius of nucleons is directly proportional to A1/3, where A is the mass number.
R∝ A 1/3
∴ R = R0A1/3
R0 = 1.1 × 10-15 m.

→ The mass defect is the difference of the sum of the individual masses of the protons and neutrons to the actual mass of the nucleus. It is customary to use the atomic mass unit (u). while dealing with nuclear masses. 1 atomic mass unit is equal to $$\frac{1}{12}$$ of a mass of $${ }_6^{12} \mathrm{C}$$ atom. One atomic mass unit has a mass of 1.660565 × 10-27 kg which is equivalent to an energy of 931.5 MeV.

→ The binding energy of a nucleus is the energy required to separate the “nucleus into its constituent parts – protons and neutrons. The binding energy is equal to (∆M.c2, where c is the speed of the light in a vacuum and Am is the mass defect in the nucleus.

→ Natural radioactivity is a process by which unstable nuclei spontaneously emit α, β, γ- rays in order to acquire stability.

→ α – rays consist of positively charged particles, each particle being nucleus of helium. β rays consist of negatively charged particles, the electrons, γ – rays are high – energy photons.

→ The half-life T of a radioactive isotope is the time required for one-half of the original nuclei present to disintegrate. T = 0.693/λ, where λ is disintegration constant.

→ The activity of a radioactive substance is the number of disintegrations per second.

→ The average life time τ of a radioactive substance is equal to the total life time of all the nuclei present initially divided by the total number of nuclei that were present initially, τ = 1/λ.

→ The nuclear force is the force of attraction between nucleons. This force balances the electrostatic repulsion between protons and holds the nucleons in the nucleus together.

→ The conversion of one element into another by artificial means is called artificial transmutation. It was discovered by Rutherford.

→ The nuclear reaction that led to the discovery of neutron by Chadwick is
$${ }_4^9 \mathrm{Be}+{ }_2^4 \mathrm{He} \rightarrow{ }_6^{12} \mathrm{C}+{ }_0^1 \mathrm{n}+\mathrm{Q}$$

→ The breaking of a heavy nucleus into two fragments or intermediate mass nuclei is called nuclear fission.

235U undergoes fission with thermal neutrons as well as fast neutrons. 238U undergoes fission with fast neutrons only. 232Th undergoes fission with fast neutron only. 239Pu undergoes fission with both thermal and fast neutrons.

→ Chain reaction: The neutrons produced in the fission of a nucleus can cause fission in other neighbouring nuclei producing more and more neutrons to continue the fission until the whose fissionable material is disintegrated. This is called chain reaction.

→ Multiplication factor K: It is defined as the ratio of the number Of neutrons in the present generation to the number of neutrons in the previous generation.

→ Sustained chain reaction : To sustain the chain reaction the mass of Uranium should be equal to or more than a particular amount of mass called critical mass.

→ MODERATOR: The average energy of neutrons released in fission process is 2 MeV. They are used to slow down the velocity of neutrons. Heavy water or graphite are used as moderating materials in reactor.

→ CONTROL RODS : These are used to control the fission rate in reactor by absorbing the neutrons. Cadmium and Boron are used as controlling the neutrons, in the form of rods.

→ SHIELDING : During fission reaction, beta and gamma rays are emitted in addition to neutrons. Suitable shielding such as steel, lead, concrete etc., are provided around the reactor to absorb and reduce the intensity of radiations.

→ COOLANT : The heat generated in fuel elements is removed by using a suitable coolant to flow around them: The coolants used are water at high pressures, molten sodium etc.

→ Power reactor : In the nuclear reactor, large amount of heat will be generated in the core. These reactors have elaborate cooling systems that use water. This water absorbs the heat and produces steam. This steam in turn is used to run the steam turbines which ultimately generate electric power. Such reactors are called power reactors.

→ The power generated by a nuclear reactor is power, P = $$\left(\frac{\mathrm{n}}{\mathrm{t}}\right)$$ × energy released per fission. If  is used as fuel.
P = $$\left(\frac{\mathrm{n}}{\mathrm{t}}\right)$$ 200 MeV = $$\left(\frac{\mathrm{n}}{\mathrm{t}}\right)$$ 200 × 106 × 1.6 × 10-19 J

→ Source of energy in the sun: Sun and stars have been radiating huge amount of energy for several bilions of years. This energy of the sun and the brightest stars is produced by nuclear fusion in the core of sun or of the stars, where the temperature is of the order of 107 K or more.

Formulae

→ 1 u = 1.660539 × 10-27 kg

→ Nuclear Radius R = R0A1/3 where R0 = 1. 2 × 10-15 m

→ Mass defect ∆M = [Zmp + (A – Z mn – M]

→ B.E. ∆E = ∆M × 931.5 (in MeV)

→ Binding energy per nucleon Ebn = $$\frac{B . E}{A}$$

→ Packing fraction = $$\frac{\Delta M}{A}$$

→ Redioactive decay law is $$\frac{\mathrm{dN}}{\mathrm{dt}}$$ = -λN (or) N = N0e-λt

→ Activity of a radioactive substance R = – $$\frac{\mathrm{dN}}{\mathrm{dt}}$$ (or) R = R0e-λt

→ Half life of radioactive substance is T1/2 = $$\frac{0.693}{\lambda}$$

→ Average life of radioactive substance is τ = $$\frac{1}{\lambda}$$ (or) T = 0.693 τa