Write the complete expressions of conversions of 1 P 15 32 to S due to β - decay and 2 Na 11 22 to Ne due β + decay.

In beta decay, a nucleus spontaneously emits an electron or a positron. In β + decay, a positron is emitted and, a neutrino is generated. In β - decay, an electron is emitted and, an antineutrino is generated. 1 P 15 32 → β - 1 + S 16 32 + ν - 2 N 11 22 a → N 10 22 e + β + + ν

Explain the source of energy with the help of proton proton cycle. What is the role of cadmium rod in nuclear reactor?

Solar energy is created by nuclear fusion that takes place in the sun. Fusion occurs when protons of hydrogen atoms violently collide in the sun's core and fuse to create a helium atom. This process, known as a PP (proton-proton) chain reaction, emits an enormous amount of energy. The reaction involves the following steps: Two protons within the Sun fuse. Most of the time the pair breaks apart again, but sometimes one of the protons transforms into a neutron via the weak nuclear force. Along with the transformation into a neutron, a positron and neutrino are formed. This resulting proton-neutron pair that forms sometimes is known as deuterium. A third proton collides with the formed deuterium. This collision results in the formation of a helium-3 nucleus and a gamma-ray. These gamma rays work their way out from the core of the Sun and are released as sunlight. Two helium-3 nuclei collide, creating a helium-4 nucleus plus two extra protons that escape as two hydrogen. H 1 1 + H 1 1 ⇒ H 1 2 + e + + ν + 0 . 42 MeV .......................................................(1) e + + e - ⇒ γ + γ + 1 . 02 MeV .....................................................................(2) H 1 2 + H 1 1 ⇒ He 2 3 + γ + 5 . 49 keV ...................................................................(3) He 2 3 + He 2 3 ⇒ He 2 4 + H 1 1 + H 1 1 + 12 . 86 MeV .............................................(4) For the fourth reaction to occur, the first three reactions must occur twice, in which case two light He nuclei unite to form an ordinary helium nucleus. If we consider 2 1 + 2 2 + 2 3 + 4 ,The net effect is: 4 H 1 1 + 2 e - ⇒ He 2 4 + 2 ν + 6 γ + 26 . 7 MeV The role of cadmium in nuclear reactor The element Cadmium has a higher neutron absorption cross-sectional area than nuclear fuels like Uranium or Thorium. Therefore, Cadmium rods are inserted into the nuclear reactor chamber which absorbs some high energy neutrons, leaving required neutrons for further reaction.

Give one example each of Alpha, Beta and Gamma decay.

Alpha decay: Alpha decay is a common mode of radioactive decay in which a nucleus emits an alpha particle (a helium-4 nucleus). During alpha decay, the mass number is decreased by 4 and the atomic number by 2 e.g. X Z A ⇒ Y Z - 2 A - 4 + He 2 4 + Q U 92 239 ⇒ Th 90 234 + He 2 4 + Q . The total mass of the decay products ia less than the mass of the original. The difference of mass appears as the disintegration energy Beta decay: Beta decay is a common mode of radioactive decay in which a nucleus emits a high energy electron. The daughter nucleus will have a higher atomic number than the original nucleus. X Z A ⇒ Y Z + 1 A + β - 1 0 + Q . Th 90 234 ⇒ Pa 91 234 + β - 1 0 During gamma decay, the energy of the parent atom is changed by the emission of a photon. The resulting energy of the daughter atom is lower than the parent atom. After alpha or beta decay, the daughter nucleus is often in an excited state and it achieves stability by gamma emission. Co 27 60 ⇒ Ni 28 60 + e - 1 0 + ν → Ni 28 60 ⇒ N 28 60 + 1 . 17 MeV

Briefly describe the working of a nuclear reactor.

NUCLEAR REACTOR A nuclear reactor is a device to produce nuclear energy based on a controlled nuclear chain reaction. The main component of a nuclear reactor are shown in the figure (1) NUCLEAR FUEL It is a fissionable material to be used for the fission process. Commonly used fuel are U 235 , Pu 239 . The fuel as pallets is packed in the fuel rods. When slow neutrons interact with the fuel, the fission starts. (2) MODERATOR Its function is to slow down the fast-moving secondary neutrons during the fission. Proton rich material e.g. Heavy water, paraffin wax which is light and does not absorb neutrons are used as a moderator. (3) CONTROL RODS They have the ability to capture the slow neutrons to control the chain reaction, in the beginning, the rods of boron and cadmium are inserted in the hole of the reactor core up to the desired length so that it can absorb the required number of neutrons. These rods can be adjusted from outside the reactor. (4) COOLANT The substance which is used to remove heat produced and transfer it to surrounding water and liquid sodium are generally used. The heat,thus transfer is used to produce steam to run turbines. (5) SHIELDING T he whole reactor is protected by a covering of concrete walls about 2meter thick, to prevent the radiations to go out of the reactor. Principle: It works on the principle of achieving a controlled chain reaction of Uranium - 235 and as a result generating a huge amount of energy. The controlled chain is made possible by slowing down the fission neutrons to thermal neutrons by using a moderator. Insert rods that can absorb neutrons(control rods) and use them to maintain the reaction rate. The heat generated is used to make steam which in turns fed to turbines which generate electricity.

Write down different set of proton-proton cycle of fusion reaction in the sun.

The proton-proton cycle is a chain of thermonuclear reactions that is the chief source of the energy radiated by the Sun and other cool main-sequence star s. It has the following steps: H 1 1 + H 1 1 ⇒ H 1 2 + e + + ν + 0 . 42 MeV .......................................................(1) e + + e - ⇒ γ + γ + 1 . 02 MeV .....................................................................(2) H 1 2 + H 1 1 ⇒ He 2 3 + γ + 5 . 49 keV ...................................................................(3) He 2 3 + He 2 3 ⇒ He 2 4 + H 1 1 + H 1 1 + 12 . 86 MeV .............................................(4) For the fourth reaction to occur, the first three reactions must occur twice, in which case two light He nuclei unite to form an ordinary helium nucleus. If we consider: 2 1 + 2 2 + 2 3 + 4 , The net effect is: 4 H 1 1 + 2 e - ⇒ He 2 4 + 2 ν + 6 γ + 26 . 7 MeV

Derive an expression of mean life of a radio active substance.

Mean life is the average lifetime of all the nuclei of a particular unstable atomic species. This time interval may be thought of as the sum of the lifetimes of all the individual unstable nuclei in a sample, divided by the total number of unstable nuclei present. Let a radioactive element contains N 0 atoms at a time t 0 and after time t . N atoms are left. Let a small number d N disintegrate in time dt . Hence the lifetime of each of these atoms lies between t and t + dt . If d t is taken very small, then the age of each atom can be taken as t ,then the total age of dN atom= dN . t . Therefore, the total lifetime of all the atoms = ∫ 0 N o t d N . By definition, the average lifetime of all atoms of the sample τ = ∫ 0 N 0 t d N N 0 .............(1) But by radi0 active law, we have, dN = - λNdt = - λ N 0 e - λt , hence, we get, τ = ∫ 0 N 0 - λN 0 e - λt dt . t N 0 = λ ∫ 0 ∞ te - λt dt .........................(A) Note that the limit of integration is changed in terms of time. Integrating by parts, we get, τ = - λ t . e - λt - λ 0 ∞ - . e - λt - λ dt = λ 0 + 1 λ ∫ 0 ∞ e - λt dt = ∫ 0 ∞ e - λt dt . Or τ = c - λ t - λ 0 ∞ = 0 - 1 λ = 1 λ o r τ = 1 λ . i.e the average lifetime of a radioactive substance is reciprocal of the decay constant Further as λ = 0 . 6931 T or τ = T 0 . 6931 = 1 . 44 T or average life = 1 . 44 half life.

Some scientists have predicted that global nuclear war on the earth would be followed by a severe "Nuclear Winter". What might be basis of this prediction?

Nuclear winter is a severe and prolonged global climatic cooling effect that is hypothesised to occur after widespread firestorms following a large-scale nuclear war. Nuclear winter is the term for a theory describing the climatic effects of nuclear wa. Smoke from the fires started by nuclear weapons, especially the black sooty smoke from cities and industrial facilities would be heated by the Sun, lofted into upper stratosphere and spread globally, lasting for years. The soot turns out to be a key factor in how bad a nuclear winter would get; three years after the bombs explode, The sun will be masked by the sooty smoke for decades, hence, the global temperatures would have plummeted by more than 10 °C in the first scenario — more than the cooling during the last ice age. Climate change and prolonged cooling of the entire atmosphere will cause global crop failure resulting in millions of deaths.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Nuclei>assam board-2020>Q 8

MEDIUM

12th Assam Board

IMPORTANT

Earn 100

Explain in brief, how do the positively charged proton reside unitedly within the nucleus.

Important Questions on Nuclei

HARD

12th Assam Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Nuclei>assam board-2020>Q 9

What are the types in which radioactive decay takes place? If $N$ is the number of nuclei in the radioactive substance and $△ N$ undergo decay in time $△ t,$ show that,

$N (t) = N_{0} e^{- λt}$

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