# DC Pandey Modern Physics-2 Solutions

DC Pandey Optics and Modern Physics Solutions Chapter 30 ‘Modern Physics 2’ will help you revise the concepts of this chapter effortlessly for JEE Mains and JEE Advanced along with CBSE Class 12 board exams. DC Pandey Solutions include all the important concepts of the chapter like nuclear stability and radioactivity, radioactive decay law, successive disintegration, the equivalence of mass and energy, binding energy and nuclear stability are covered in this chapter in detail. Other topics of this chapter include nuclear fission and nuclear fusion and the Q-value of a nuclear reaction.

DC Pandey Optics and Modern Physics Chapter – ‘Modern Physics 2’ includes more than 100 questions. There are separate exercises for JEE preparation given in the chapter. All the questions are arranged systematically in order of the increasing difficulty levels. These questions are based on topics such as radioactivity, x-ray photons, binding energy, nuclear reaction, chain reactions and nuclear stability. We have designed easy to understand solutions for all the questions of the chapter.

Relying on Instasolv as your source of reference for DC Pandey Optics and Modern Physics solutions book is a smart choice because we provide you with a one-stop solution to all the queries. The answers at Instasolv are prepared after a procedure of extensive research by experienced facilities to make sure all questions are addressed with the same conceptual depth.

## Important Topics in DC Optics and Modern Physics Solutions Chapter 30: Modern Physics 2

**Nuclear Stability and Radioactive Decay**

Most known nuclides decay by emitting the electromagnetic radiations α, β and γ ray to form other nuclides. A nucleus is most stable when the number of protons, Z, and neutrons N are nearly equal in case of elements with lighter nuclei while for heavier nuclei, there should be more neutrons than protons for stability.

Atoms become radioactive if they have unstable nuclei and they emit α, β and γ radiations. Radioactivity can be exhibited by a nucleus either naturally or artificially. The radioactive nucleus is termed as a parent nucleus while the resulting nuclei are the daughter nucleus.

**Alpha Decay**

Alpha decay is given by:

In alpha decay, a helium atom is emitted, such that ‘A’ in the above equation gives the mass number, and ‘Z’ gives the proton number.

**Beta Decay**

In beta decay, a nucleus is converted into a proton, electron, and neutrino.

**Gamma Decay**

Whenever an exciting nucleus after an alpha or beta decay goes to a lower energy level, it emits gamma radiation.

**Radioactive Decay Law**

According to the radioactive decay law, the rate of decay of nuclei is directly proportional to the number of nuclei, N which are considered in a given sample. Mathematically,

Where λ is the decay constant.

We can integrate it from parent number of nuclei, N_{0} to get the number of surviving Nuclei after time t as,

Half-life is the time period required for the number of parent nuclei to fall to half of its original value. It is given as . The reciprocal of the decay constant is known as mean life.

**Successive Disintegration**

Consider a radioactive nucleus A decaying into nucleus B with decay constants a and b respectively. Then,

- Number of atoms in B, N
_{b}at time t=0 and t=∞ is 0 - Nb increases to a maximum value while Na decreases and then begin to decrease.
- λ
_{a}>λ_{b}

**Equivalence of Mass and Energy**

According to Einstein, E=mc^{2}

Such that E is the energy change in a body, m is the change in mass of a body and c is the speed of light.

Since 1 unit of mass has energy 931.5 MeV

**Binding Energy and Nuclear Stability**

The energy needed to completely disintegrate a nucleus into the nucleons is termed as the Binding Energy denoted by E_{b}.

Where m_{p} gives the mass of the proton, m_{N} gives the mass of neutron and m_{x} gives the mass of the nucleus.

**Nuclear Fission and Nuclear Fusion**

In nuclear fission, the mass of the two new daughter nuclei is less than the mass of the parent nucleus. This is termed as the mass defect. In an atomic bomb, an uncontrolled chain reaction is triggered by bringing two Uranium-235 pieces together to form a mass that is larger than the critical size.

The binding energy in two lighter nuclei is lower than that of the heavier nucleus formed after the fusion of the two nuclei. Hydrogen Bomb works on this principle.

**Q-Value of a Nuclear Reaction**

If we assume a parent nucleus X which is bombarded with particle a to form daughter nucleus Y and particle b, then the energy in the reaction is given as the total energy released in the reaction and is given as Q. Mathematically,

### Exercise Discussion for DC Pandey Optics and Modern Physics Solutions Chapter 30: Modern Physics 2

- There are two introductory exercises in this chapter. Introductory Exercise 30.1 comprises 5 questions in which you will be required to calculate the fringe width, maxima and minima of the intensities, etc. in certain situations of interference of light waves.
- Exercise 30.2 consists of questions in which you will be required to complete the reactions, evaluate the change in mass, and the number of fission, etc.
- The next set of exercises is for JEE and it comprises of 2 levels of subjective questions and objective questions each. The topics covered in the questions of each section include radioactivity and the formulae based on the same.

### Why Use DC Pandey Optics and Modern Physics Solutions Chapter 30: Modern Physics 2 by Instasolv?

- DC Pandey Modern Physics 2 solutions are created to guide for CBSE Class 12 board exams as well as JEE Mains and NEET entrance exams.
- We adhere to the latest Physics syllabus for these exams and include all tips and tricks in the solutions that will guide you.
- These DC Pandey Optics and Modern Physics Solutions are arranged in such a manner that they are ideal for self-study.
- Instasolv intends to minimise your time in struggling with doubts which makes us your reliable source of reference.