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# Xam Idea Class 12 Physics Chapter 13 Solutions: Nuclei

Xam Idea Class 12 Physics Solutions for Chapter 13 ‘Nuclei’ provides a clear picture of the composition of a nucleus. You will learn about atomic mass, size of the nucleus, and nuclear density here. This chapter also teaches what is radioactivity and its laws, what is meant by radioactive decay and half-life of radioactive elements. Alpha, Beta, and gamma rays properties, mass-energy relation, nuclear fission, and fusion are all parts of this chapter. Our Xam Idea solutions for Chapter 13 Nuclei include well-explained concepts with diagrams for your understanding. All the formulas are explained with derivations to clarify all these concepts at the root level.

Xam Idea Class 12 Physics Solutions for Nuclei have a total of 102 questions separated into 8 segments. These questions help in testing your preparedness for CBSE Class 12 board exams by ensuring that you work on the difficult parts of the chapter. There are questions that require short and long answers; some multiple-choice questions and some are classified as HOTS which involve high order thinking. Practising these varied questions will give you a grip on the topic and also increase your chances of qualifying in many competitive exams like IIT-JEE and NEET.

Having a good foundation in Physics is very beneficial for a good career in engineering or pursuing advanced courses in Physics. Our Instasolv team will help you achieve your dreams by giving you tailor-made Xam Idea Class 12 solutions for every question on a given topic. These solutions are meant to not just help with basic concepts but also stimulate analytical thinking in you. You should be able to solve different kinds of sums on Physics after going through our solutions.

## Important Topics for Xam Idea Class 12 Physics Solutions Chapter 13: Nuclei

Nucleus – In an atom, all its positive charge and almost the entire mass (more than 99.9 %) is densely concentrated at its centre which is its nucleus. It is made up of protons and neutrons.

Atomic mass – The mass of an atom or nucleus is expressed in atomic mass unit u.

1 u = 1.660565×10–27 kg

Mass of proton mp = 1.007276 u

Mass of electron me = 0.000549 u

Mass of a neutron mn = 1.008665 u

Mass of C-12 is taken as a standard for measuring this and

1 u = Mass of C-12 atom/12

Composition of the Nucleus – Following terms explain the composition of a nucleus:

Atomic number Z – This is the number of protons in the nucleus = number of neutrons in the nucleus

Mass number A – This is the total of protons and neutrons inside the nucleus

A = number of protons + number of neutrons = number of electrons + number of neutrons = Z + N

Nucleus Size – For a nucleus of radius R and mass number A, it was observed experimentally that:

R = R0A1/3

Here R is the range of nuclear size also called the nuclear unit radius = 1.2×10–15 m = 1.2 FM

Nucleus Density – The ratio of nucleus mass and its volume define nucleus density. It does not depend on A (mass number)

= 3m/4πR03

Radioactivity – It was observed by Becquerel that some elements like radium which have heavy nuclei (A > 180) are unstable and disintegrate spontaneously into other elements by emitting radiations like α, β, or ϓ rays. This phenomenon is called radioactivity.

Radioactivity is a natural and spontaneous activity that is not changed by any physical or chemical conditions.

The radioactive rays α, β, and ϓ originate from nuclei of an atom and form new radioactive substances.

The rate of decay of a radioactive substance is proportional to the number of un-decayed radioactive atoms in that substance. So if a radioactive substance has N undecayed atoms at any time t and dN atoms disintegrate in dT time then:

DN/DT = -λN, here  is the constant of proportionality called decay constant

N = N0e; Here N0 is the original amount of un-decayed radioactive atoms.

The Half-Life of Radioactive Substances – The time in which a radioactive substance loses half of its initial amount of radioactive atoms is called its half-life and expressed as:

T(half-life) = 0.6931/λ

N = N0 (1/2)n

Here n = number of half-lives = Total time(t)/half-life period

Mean or Average Life of Radioactive Substances – This is obtained by calculating the total time of all the atoms of the substance divided by the original amount of atoms present in the sample:

t = 1/ λ = 1.44 T1/2

Isotopes, Isobars, and Isotones –

Nuclides with the same atomic number Z but different mass number A are called isotopes.

Nuclides with the same mass number A but different atomic number Z are called isobars.

Nuclides with the same number of neutrons (A-Z) are called isotones.

The activity of Radioactive Substances – The rate of decay of a radioactive substance is referred to as its activity. It is the number of disintegrations per second.

A = |dN/dT| = |d(N0eλI)/dT| = λN

If A0 is the activity at t = 0 then

A/A0 = N/N0 = eλI

Mass Defect – Mass defect is described as the difference in the mass of the nucleus and mass of its constituent nucleons i.e. protons and neutrons. The mass of the nucleus is always lesser. Mass defect is given by:

Mass Defect – Mass defect is described as the difference in the mass of the nucleus and mass of its constituent nucleons i.e. protons and neutrons. The mass of the nucleus is always lesser. Mass defect is given by:

Dm = Mass of nucleons – Mass of the nucleus

= Zmp + (A-Z) mn – Mnucleus

Here Z – atomic number

A – mass number

mp – a mass of a proton

mn– a mass of a neutron

Becquerel – This is the unit of radioactivity in the SI system and 1 Becquerel = 1 disintegration/second

Curie – This gives the activity of a radioactive substance and 1 Curie (Ci) = 3.7 × 1010 decays per seconds

Rutherford – This gives the activity of a radioactive substance and 1 Rutherford (Rd) = 106 decays per seconds

### Discussion of Exercises of Xam Idea Class 12 Physics Solutions Chapter 13: Nuclei

• There are 15 selected NCERT in the 1st set. Some of the topics covered in these questions are:
1. Isotopes
2. nuclear reactions
3. the activity of a radioactive substance
4. the half-life of a radioactive substance
5. Nuclear fission
• In the 2nd set, there are 20 multiple choice questions which touch upon half-life, nucleus size, radioactive rays, nuclear fusion, and decay rate.
• The 3rd set has 1 assertion-reason type question in which you have to evaluate 10 statements with assertions and reasons. The topics cover density of the nucleus, basics of nuclear fission, and fusion.
• The 4th set has 17 questions that require very short answers. Some highlights of the questions are:
1. Relationship between the size of a nucleus and its mass number
2. Mean life and half-life relations
3. Nuclei densities
4. Nuclear fusion
• In the 5th set, there are 15 questions where you have to give short answers. You have to apply your knowledge of the activity of radioactive substances, nuclear reactions, half-life, and symbolic representation of radioactive decay of a few elements.
• There are 14 questions in the 6th set which need long answers from you. There are problems where definitions of activity of a radioactive substance and its SI units have to be given, basic nuclear processing of β rays is to be explained, the concept of isotopes are to be applied.
• In the 7th section, there are 7 questions which are again long answer types. Some important questions are taken from previous CBSE papers in which a graphical representation of binding energy per nucleon of a large number of nuclei is to be shown. You also need to give explanations about the nature of the graph. One question needs derivation of the law of radioactive decay and definitions of half-life and decays constantly is to be given.
• The last section is a self-assessment section with 13 questions in which all topics are discussed and the question types are also varied. There are MCQs, assertion-reasons, short and long answer types questions in this set.

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