Nuclei Class 12 Notes CBSE Physics Chapter 13 (Free PDF Download)

Section-A (1 Mark Questions)

1. What will be the ratio of the radii of two nuclei of mass numbers $A_{1}$ and $A_{2}$ ?  

Ans. The strong attractive nuclear force holds the nucleons together inside a nucleus which even overcomes the electrostatic repulsion between the protons. 

2. What holds nucleons together in a nucleus? 

Ans. The strong attractive nuclear force holds the nucleons together inside a nucleus which even overcomes the electrostatic repulsion between the protons. 

3. Define mass defect of a nucleus. How is it related to the binding energy of the nucleus? 

Ans. The difference between the sum of the rest masses of the nucleons constituting a nucleus and the rest mass of the nucleus is called mass defect. The binding energy of a nucleus is a measure of the energy equivalent to its mass defect $B\cdot E=\Delta m\times c^{2}$ 

4. In the nuclear decay reaction $_{1}^{1}\textrm{H}\rightarrow _{0}^{1}n+_{Q}^{P}\textrm{X}$ find P, Q and hence identify X. 

Ans. By conservation of mass, P=1-1=0.

By conservation of charge, 

Q=1-0=1

$\therefore X=_{1}^{0}\textrm{e}$

i.e., X is a positron.

5. What is the difference between an electron and a $\beta -$ particle? 

Ans. An electron and a $\beta -$ particle are essentially the same. An electron of nuclear origin is called a $\beta -$ particle. 

6. Why do lighter nuclei tend to fuse together? 

Ans. When lighter nuclei fuse together, they from heavier nuclei having greater binding energy per nucleon and they tend to attain a stable structure. 

7. State the reason, why heavy water is generally used as a moderator in a nuclear reactor. 

Ans. The basic principle of mechanics is that momentum transfer is maximum when the mass of colliding particle and target particle are equal. Heavy water has negligible absorption cross-section for neutrons and its mass is small; so heavy water molecules do not absorb fast neutrons; but simply slow them.

8. The sun is constantly losing mass due to thermonuclear fusion. Comment.

Ans. In each fusion reaction, a small mass of the sun changes into thermal energy. So, sun is constantly losing mass due to thermonuclear fusion.

9. Why is nuclear fusion not possible in a laboratory? 

Ans. Nuclear fusion requires extremely high temperature of $10^{6}-10^{7}K$ . This temperature is attained by causing explosion due to the fission process. Moreover, no solid container can withstand such a high temperature.

10. Two nuclei have mass number in the ratio 1:3. What is the ratio of their nuclear densities?

Ans. Since nuclear density is independent of the mass number, the ratio of nuclear densities will be 1:1.

Section-B (2 Marks Questions)

11. Write any two characteristic properties of nuclear force.

Ans. Characteristic properties of nuclear forces are: 

1. Nuclear force are strongest forces in nature: magnitude of nuclear forces is 100 times that of electrostatic force and $10^{38}$ times the gravitational forces.

2. Nuclear forces are charge independent: Nuclear forces between a pair of protons, a pair of neutrons or a pair of neutron and proton act with same strength.

12. Calculate the energy released in MeV in the following nuclear reaction:

$_{92}^{238}\textrm{U}\rightarrow _{90}^{234}Th+_{2}^{4}He+Q\left [ Mass\;of\;_{92}^{238}\textrm{U}=238\cdot 05079u \right ]$

$Mass\;of\;_{92}^{238}\textrm{U}=238\cdot 05079u$

$Mass\;of\;_{2}^{4}\textrm{th}=234\cdot 043630u$

$Mass\;of\;_{2}^{4}\textrm{He}=4\cdot 002600u$

$1u=931\cdot 5MeV/c^{2}$

Ans. Given nuclear reaction is $_{92}^{238}\textrm{U}\rightarrow _{90}^{234}Th+_{2}^{4}He+Q$

Mass defect $=M_{u}-M_{Th}-M_{He}=238\cdot 05079-234\cdot 043630-4\cdot 002600=0.00456u$

Energy released $=(0\cdot 00456u)\times (931\cdot 5MeV/C^{2})=4\cdot 25MeV$

13. Two nuclei have mass numbers in the ratio 1: 8 what is the ratio of their nuclear radii?

Ans. $A_{1}:A_{2}=1:8$

Since, 

$\Rightarrow \dfrac{A_{1}}{A_{2}}=\dfrac{1}{8}$

$R=R_{0}A^{1/3}$

$\therefore \dfrac{R_{1}}{R_{2}}=\left ( \dfrac{A_{1}}{A_{2}} \right )^{1/3}=\left ( \dfrac{1}{8} \right )^{1/3}=\dfrac{1}{2}$

14. Give one similarity and one dissimilarity between nuclear fission and nuclear fusion.

Ans. Similarity. Both nuclear fission and fusion are the source of enormous amount of energy. Dissimilarity. In nuclear fission, a heavy nucleus splits into two smaller nuclei. In nuclear fusion, two smaller nuclei fuse together to form a heavier nucleus.

15. If both the number of protons and neutrons in a nuclear reaction is conserved, in what way is mass converted into energy (or vice versa)? Explain giving one example.

Ans. Since proton number and neutron number are conserved in a nuclear reaction, the total rest mass of neutrons and protons is the same on either side of the nuclear reaction. But total binding energy of nuclei on the left side need not be the same as that on the right hand side. The difference in binding energy causes a release of energy in the reaction. Examples:

(i) $_{1}^{2}\textrm{H}+_{1}^{2}\textrm{H}\rightarrow _{2}^{3}He+_{0}^{1}n+energy$

(ii) $_{92}^{235}\textrm{U}+_{0}^{1}N\rightarrow _{56}^{144}Ba+_{36}^{89}Kr+3_{0}^{1}n+energy$

16. Calculate the energy in fusion reaction:

$_{1}^{2}\textrm{H}+_{1}^{2}\textrm{H}\rightarrow _{2}^{3}He+n$ , Where B.E, of $_{1}^{2}\textrm{H}=2\cdot 23MeV$ and of $_{1}^{2}\textrm{He}=7\cdot 73MeV$

Ans. Total binding energy of initial system $(E_{i})$

$=_{1}^{2}\textrm{H}+_{1}^{2}\textrm{H}=(2\cdot 23+2\cdot 23)MeV=4\cdot 46MeV$

Binding energy of final system

i.e., $=_{1}^{2}\textrm{He}(E_{f})=7\cdot 73MeV$

Hence, energy released $=E_{f}-E_{i}$

$=7\cdot 73MeV-4\cdot 46MeV$

$=3\cdot 27MeV$

17. Distinguish between nuclear fission and fusion. Explain how the energy is released in both the processes.

Ans. In nuclear fission a heavy nucleus breaks up into smaller nuclei accompanied by release of energy; whereas in nuclear fusion two light nuclei combine to form a heavier nucleus accompanied by release of energy.

In both the cases, some mass (= mass defect) gets converted into energy as per the relation: $E=\Delta mc^{2}$

18. Show that the density of nucleus over a wide range of nuclei is constant- independent of mass number A. 

Ans. Let A be the mass number and R be the radius of a nucleus 

If m is the average mass of a nucleon, then

Mass of nucleus = mA

Volume of nucleus $=\dfrac{4}{3}\pi R^{3}$

$=\dfrac{4}{3}\pi (R_{0}A^{1/3})^{3}=\dfrac{4}{3}\pi R_{0}^{3}A$

∴ nuclear density $=\dfrac{mass\;of\;nucleus}{volume\;of\;nucleus}$

$=\dfrac{mA}{\dfrac{4}{3}\pi R_{0}^{3}A}=\dfrac{3m}{4\pi R_{0}^{3}}$

Clearly, nuclear density is independent of mass number A or the size of the nucleus.

19. Why is the binding energy per nucleon found to be constant for nuclei in the range of mass number (A) lying between 30 and 170? 

Ans. The binding energy is a very short order range force. So, beyond a certain amount of range the force has no influence beyond that. That is why after certain number the binding energy per nucleon do not change even if we add more nucleons.

PDF Summary - Class 12 Physics Nuclei Notes (Chapter 13)

By a factor of about 26,634 (uranium atomic radius is about 156 pm to 60250 (i.e. 156×10−12 m))  (the radius of hydrogen atomic is about 52.92 pm). We have seen and discussed in many of the subjects that there is a smallest unit which is often referred to as the cell and this whole cell was discussed in the biology of junior classes. Now if we see then we can notice that it's the same structure which we are discussing here about the cells is the atoms. The atom was also considered as the smallest unit on the planet until the quarks were discovered.

Forces 

• Nuclei are bound together by the residual strong force, also known as the nuclear force.

• The residual strong force binds quarks together to form protons and neutrons.

• The nuclear force is highly attractive at typical nucleon separation distances, overcoming the electromagnetic repulsion between protons.

• Nuclei exist because the attractive nuclear force overcomes the electromagnetic repulsion.

• The residual strong force has a limited range and decays quickly with distance.

• Only nuclei smaller than a certain size can be completely stable due to the limited range of the residual strong force.

• The largest completely stable nucleus is lead-208, which contains 208 nucleons (126 neutrons and 82 protons).

• Nuclei larger than lead-208 are unstable and tend to have shorter lifetimes.

• Bismuth-209 is stable to beta decay and has the longest half-life to alpha decay among all known isotopes.

• The residual strong force is effective over a very short range, typically only a few femtometers.

• The residual strong force causes an attraction between any pair of nucleons.

Advances and Challenges 

• Ongoing research efforts are focused on nuclei with up to eight nucleons to measure various properties of light.

• The simplest nuclei provide the basis for quantitative comparisons between experimental and theoretical maps of their global and short-range structure.

• Light nuclei are ideal for probing the microscopic aspects of nuclear structure, especially those related to gluons and quarks.

• Light nuclei play important roles in astrophysics, elementary particle physics, and energy production.

• The majority of matter in the visible universe exists in the form of light nuclei.

• Reactions between light nuclei primarily govern the nuclear physics of conventional stars like the Sun and the Big Bang.

• Free neutrons are unstable and undergo radioactive decay.

• Helium-3 (3He) and Deuterium (2H) are useful surrogates for neutron targets in comparative measurements of the internal structure of neutrons to protons.

• A detailed understanding of the structure of these nuclei is necessary for interpreting experimental results.

• Electron scattering is a direct method for probing the structure of nuclei.

• The nucleus, located at the core of an atom, is a quantal many-body system governed by the strong interaction.

• Neutrons and protons, as the most stable hadrons, compose the nucleus, just like gluons and quarks compose hadrons.

• The binding of nucleons together in nuclei through the strong force is a fundamental question related to the existence of the universe.

• Mutual interactions between nucleons shortly after the Big Bang led to the formation of light nuclei.

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