**The law of conservation of mass energy:**total amount of mass and energy remains constant in the universe. Different types of transformation among them are possible but creation or destruction of mass energy is not possible.**Nuclear force:**inside the nucleus protons and neutrons are held together tightly due to a tremendous force of attraction between them. This force is called nuclear force.**Unified atomic mass unit:**Mass of \frac1{12} part of one carbon 12 atom is called one unified atomic mass unit (u).**Nuclear mass:**Substracting the mass of electrons present in an atom from the mass of the atom , the nuclear mass of that atom can be obtained .**Mass number:**The nearest whole number of the mass of an atom in the unified atomic mass unit is called mass number of that atom. The sum of the number of protons and neutrons present in the nucleus of an atom is equal to its mass number.**Isotopes:**The atoms of the same element having different mass numbers are called isotopes of that element .**Isobars:**The atoms of different elements having equal mass number are called isobars.**Isotones:**The atoms of different elements having equal number of neutrons and then are called Isotones.**Atomic number:**The number of protons present inside the nucleus of an atom of an element is called atomic number of that element.- The 98 out of nuclear density is nearly 2\times10^{14}g.cm^{-3} .
- Radioactivity is a nuclear phenomena of an element. Due to radioactivity one element is converted into another element.
- From radioactive element \alpha ,\beta ,\gamma -rays are emitted.
- No radioactive isotope can emit \alpha ,\beta ,\gamma -rays simultaneously.
**Half life:**the time after which radioactive atoms present in a radioactive sample becomes half of its initial amount due to disintegration is called half life.**Average life:**The time required for the number of atoms of a radioactive sample to falls to \frac1e of its initial number of atoms is called the average life of the radioactive element.**Artificial radioactivity:**when a natural stable element is transformed into eight unstable isotopes by artificial means and the radioactive disintegration of that isotopes in natural where is possible then this phenomenon is known as artificial radioactivity.**Nuclear fission:**The phenomenon of splitting a heavy nucleus into two relatively light and nuclei of comparable masses is known as nuclear fission.**Nuclear fusion:**The Phenomenon of combination of two or more lighter nuclei to form a heavy nucleus is called nuclear fusion.

## Useful Relations for Solving Numerical Problems

(i) E = mc^2

(ii) 1eV = 1.6\times {10}^{-12}erg = 1.6\times {10}^{-19}J

(iii) 1u = 1.66\times {10}^{-24}g = 931.2 MeV

(iv) {}_<em>ZX^A \rightarrow {}</em>_{Z-2}Y^{A-4}+{}_2He^4

{}<em>ZX^A\rightarrow{}</em>{Z-2}Y^4+{}_{-1}e^0(v) N=N_0e^{-\lambda t}[ N=N_0] number of radioactive atoms at t=0, N=number of radioactive atoms after time t, \lambda = disintegration constant.

(vi) T=\frac{0.693}{\lambda} [T = half life]

(vii) N=\frac{N_0}{2^\frac tT}

(viii) \tau=\frac1\lambda=1.443T \tau = average life

(ix) N = \frac{N_0}{e^{\frac tT}}

### MULTIPLE CHOICE QUESTIONS

#### Properties of a Nucleus

- The approximate value of the density of uranium nucleus (m_p = 1.67\times {10}^{-27}kg) is
- {10}^{20}kg.m^{-3}
- {10}^{17}kg.m^{-3}
- {10}^{14}kg.m^{-3}
- {10}^{11}kg.m^{-3}

- Which of the following is correct?
- the rest mass of a stable nucleus is less than the sum of the rest masses of the isolated nucleons
- the rest mass of a stable nucleus is more than the sum of the rest masses of the isolated nucleons
- in nuclear fusion, energy is emitted due to combination of two nuclei of comparable masses (100u approx)
- in nuclear fission, no energy is released due to fragmentation of a very heavy nucleus

#### Radioactive Phenomena

- During emission of a negative \beta particle
- an electron from the atom is emitted
- an electron already present inside the nucleus is emitted
- an electron is emitted due to disintegration of a neutron inside the nucleus
- a part of nuclear binding energy is converted into an electron.

- Which of the following statements is correct?
- \beta-rays and cathode rays are of identical nature.
- \gamma-rays are a stream of high energetic neutrons
- \alpha-particles are singly charged helium atoms
- The mass of a proton and that of a neutron are exactly equal

#### Laws of Radioactivity

- An excited Ne^{22} nucleus is disintegrated into an unknown nucleus and two \alpha-particles. This unknown nucleus is
- A nitrogen
- carbon
- boron
- oxygen

- The half-life of radioiodine I^{131} is 8 d. If a sample of I^{131} is taken at time
*t*= 0 then it can be said that-- no nuclear disintegration will occur before
*t*= 4 d - no nuclear disintegration will occur before
*t*= 8 d - all nuclei will be disintegrated in
*t*= 16 d - a definite nucleus may be disintegrated at any time after
*t*= 0

- no nuclear disintegration will occur before
- In a freshly prepared radioactive sample the rate of radiation is 64 times greater than the safe limit. If its half-life be 2 h then using this sample experiments can be performed with safety after
- 6 h
- 24h
- 12h
- 128 h

- The mean life of a radioactive element is 13 days. Initially a sample contains 1 g of this element. The mass of the element will be 0.5 g after a time of
- 13 days
- 18.75 days
- 9 days
- 6.5 days

- The half-life of At^{215} is 100 \mus. The time taken for the radioactivity of a sample of the element to decay \frac {1}{16}th of its initial value is
- 400 mus
- 6.3 mus
- 40 mus
- 300 mus

#### Artificial Transmutation of Atoms

- Of the following equations which one is the probable nuclear fusion reaction?
- {}_5C^{13}+{}_1H^1\rightarrow {}_6C^{14}+4.3 MeV
- {}_6C^{122}+{}_1H^1\rightarrow {}_7N^{13}+2 MeV
- {}_7N^{14}+{}_1H^1\rightarrow {}_8O^{15}
- {}_{92}U^{235}+{}_0n^1\rightarrow {}_{34}{Xe}^{140}+{}_{38}{Sr}^{94}+{}_0n^1+\gamma+ 200 MeV

#### Nuclear Fission and Fusion

- Fast moving neutrons are retarded
- by using lead obstacle
- by passing through water
- after colliding elastically with heavy nuclei
- by strong electric fields

- In nuclear fusion,
- a heavy nucleus breaks into two intermediate nuclei and a few high particles
- a light nucleus breaks due to collision with a thermal neutron
- a heavy nucleus breaks due to collision with a thermal neutron
- two or more light nuclei combine into a heavier nucleus and a few light particles

- {}_1H^1\rightarrow {}_2{He}^4+2e^++26 MeV : this is an equation of
- \beta-decay
- fusion
- \gamma-decay fission
- fission

### VERY SHORT ANSWER TYPE QUESTIONS

#### Properties of a Nucleus

- What is the relation between unified atomic mass unit (
*u*) and electron volt? [**1 u = 931.2 MeV**] - The mass of a proton or a neutron is nearly 1.67\times{10}^{-24} g. What is its equivalent energy in Mel? [
**939.4****MeV**] - What is the order of magnitude of the density of nuclear matter? [ {10}^{17}kg.m^{-3} ]
- What is the difference in the structures of {Cl}^{35} and {Cl}^{37} nuclei? [ {Cl}^{37}
**has 2 extra****neutrons**] - What is the relation between the atomic number (Z) and the mass number (A) of two isobars? [
**Z is different, but A is the same**]

#### Radioactive Phenomena

- What is the difference in the properties of the two carbon isotopes C^{12} and C^{14}, in the context of radioactivity? [ C^{14}
**is radioactive, but**C^{12}**is not**] - What is the approximate ratio of the penetrating power of a\alpha,\beta and \gamma-rays? [1:{10}^2: {10}^4 ]

### Laws of Radioactivity

- What is the relation between half-life and decay constant of a radioactive isotope? [ \lambda=\frac{ln\left(2\right)}{T} ]
- When \alpha-particle is emitted from the radioactive isotope {}_{15}P^{32}, it is converted into {}_{16}S^{32}. Write down the required transformation equation. [ {}_{15}P^{32}+{}_{16}S^{32}+{}_{-1}{\beta}^0 ]
- When an \alpha-particle is emitted from a uranium nucleus (atomic no. 92, mass number 238), a new nucleus is formed. From this nucleus a \beta-particle is also emitted. What will be the atomic number and mass number of the final nucleus? [
**91, 234**] - What are the. atomic number and the mass number of the plutonium isotope produced due to two successive \beta-decays of the isotope {}_{92}U^{239} of uranium? [
**94, 239**]

#### Artificial Transmutation of Atoms

- Which fundamental particle was first discovered from artificial transmutation? [
**neutron**]

- {}_1H^1+{}_1H^3\rightarrow {}_2H^4+ ________ .[Fill in the blank] [ {}_0n^1 ]
- Write down the decay scheme of a free neutron. [ n\rightarrow p+e ]

#### Nuclear Fission and Fusion

- {}_1H^1+{}_1H^1+{}_1H^1+{}_1H^1\rightarrow {}_1H^4+2 ________. [Fill in the blank ] [ {}_{+1}{\beta}^0 ]
- What are thermal neutrons? Why are neutrons considered as ideal particles for nuclear fission?

### SHORT ANSWER TYPE QUESTIONS-I

- What are the basic differences between natural and artificial radioactivity?
- {}_1H^2+{}_1H^2\rightarrow {}_2{He}^4+Q. In this reaction the masses of deuterium and helium atoms are 2.0141
*u*and 4.0024*u*respectively. What is this proces called, and what is the energy released Q , in Mev . - What are the similarities and dissimilarities of the nuclei of two isobars C^{14} and N^{14}?
- An artificial radio-isotope {}_{15}P^{30} can be prepared by disintegrating {}_{13}{Al}^{27} nucleus by \alpha-particle. Later o n it emits a positron and is converted into {}_{14}{Si}^{30} nucleus. Write down the transition equations.
- From the nucleus of a Polonium atom {}_{84}{Po}^{218}, an \alpha-particle and two \beta-particles are emitted successively due to radioactive disintegration. What will be the nuclei produced in these steps?
- In a radioactive disintegration a nucleus emits an \alpha-particle first and then two \beta-particles. Show that the final nucleus thus formed is the isotope of the first.
- Mass of a proton or a neutron is approximately 939 MeV, but unified atomic mass unit is approximately 931 MeV. What is the reason of this difference?
- 'half-life of radium is 1622 years'-what do you mean by this statement?
- Positively charged protons and neutral neutrons are packed inside the atomic nucleus. But protons, though similarly charged, do not repel each other. How do you account for this phenomenon?
- Complete the nuclear reaction and explain the result thus obtained: {}_7N^{14}+{}_2{He}^4
- Explain why nuclear fission should precede nuclear fusion?
- A piece of radioactive material is placed at the bottom of a long groove in a lead block. A photographic plate is placed above the lead block at some distance. The whole system is evacuated and a strong magnetic field is applied at right angles to the length of the groove. What do you expect to s e e in the photographic plate? Interpret the result with the help of a diagram.
- Nuclear force is charge independent-what do you mean by this statement?
- Atomic nuclei do not contain any electrons, yet electrons come out of them in \beta-decay. Explain how it is possible.
- 'Nuclear fission, as a source of energy, can be used for the benefit of mankind' - discuss in short.
- 1 unified atomic mass unit is equivalent to 93102 MeVof energy. What is the meaning of this equivalence?
- What is the basic difference in the use of 'radio-carbon clock' and 'uranium clock'?

### SHORT ANSWER TYPE QUESTIONS-II

- Complete the following equations:

- {}_{88}{Ra}^{226}\rightarrow {}_{86}{Rn}^{222}+...
- {}_{90}{Th}^{234}\rightarrow {}_{91}{Rn}^{234}+...
- {}_7N^{14} +{}_2{He}^4\rightarrow ... +{}_1H^1
- {}_{13}{Al}^{27}+{}_2{He}^4\rightarrow {}_{15}P^{30}+...
- Complete the following nuclear reactions:
- {}_{15}P^{30}\rightarrow {}_{14}{Si}^{30}+...
- {}_{11}{N}^{23}+...\rightarrow {}_{11}{Na}^{24}+{}_1H^1
- {}_4{Be}^9 +{}_2{He}^4\rightarrow ...+{}_0n^1
- {}_7N^{14}+{}_0n^1\rightarrow ...+{}_1H^1
- Complete the following nuclear reactions:

- {}_6C^{14}\rightarrow ... +{}_{-1}{\beta}^0
- {}_{13}{Al}^{27}+...\rightarrow {}_{14}{Si}^{28}+{}_{-1}{\beta}^0
- {}_{92}U^{235}+{}_0n^1\rightarrow {}_{56}{Ba}^{141}+{}_{36}{Kr}^{92}+...{}_0n^1
- {}_1H^2+{}_1H^2\rightarrow ...+{}_0n^1
- A radioactive nucleus
*X*decays as follows:

A\xrightarrow{{\beta}^+}A_1 \xrightarrow{\alpha}A_2

If the mass number and atomic number of A_1 and A_2 are 176 and 71 respectively, what are the mass numbers and the atomic numbers of A_1 and A_2 ? Which of these three elements are isobars ?

### PROBLEM SET-

#### Properties of a Nucleus

- The mass of a proton is 1.00816 u and that of a neutron is 1.00902 u. If the mass of a deuterium nucleus ( ) is 2.01479 u, then what will be the binding energy of this nucleus? (1 u =931.2 MeV) [ 2.226 MeV ]

- At a given time, 25% of the nuclei present in a sample is radioactive. After 10 s that amount reduces to 12.5%. After what time from the beginning, why 0.78% of the nuclei present in the sample would be radioactive? [
**50 s**] - The masses of a proton and a neutron are 1.0073 u and 1.0087 u, respectively. If the mass of an nucleus is 15.990525 u, then find out its binding energy per nuclear. [
**8.001 MeV/A**] - If 1 u = 1.66\times{10}^{-27} kg and average radius of a nuclear is 1.2 \times {10}^{-15} m, then determine the radius and density of a {Ra}^{226} nucleus. [ 7.3\times{10}^{-15} m, 2.29\times{10}^{17} kg.m^{-3} ]

#### Laws of Radioactivity

- The rate of disintegration of a radioactive element at any instant is {10}^3 dps.If the half-life ofthat element is 1second then what is its rate of disintegration after 1 second and after 3 second? [
**500, 125**] - The half-life of a radioactive element is 8 d. Ift he initial mass of the element be 1g then what amount of it will be disintegrated in 24 d ? [
**0.875 g**] - The half-life of a radioactive element is 1600 y. What part of the element will remain after 6400 y? [ \frac {1}{16} ]

- The half-life of a radioactive element is 3 min. If the initial mass of the element be 1 g then after what time 0.0625 g of the element remains intact? [ 12 min ]
- The half-life of a radioactive element is 1600 y. After what time 10% of that element present in any radioactive sample will disintegrate? [
**243.2****y**] - One-fourth part of a radioactive element is disintegrated in 664 y. Determine the half-life of the element. [
**1600 y**] - Initial mass of a radioactive element is 1 g. If 0.25 g of the element remains intact after 6 min then determine the half-life of the element. [
**3****min**] - The half-life of U^{238} is 4.5\times {10}^9 y. In any radioactive sample if 1g of that element remains present then determine the activity of the sample in curie unit. (Avogadro's number = 6.023\times {10}^{23} ) [ 3.34\times {10}^7 ]
- The activity of 1 g of a sample of {Po}^{210} is 4442 Ci. Determine the half-life of the element. (Avogadro's number = 6.023\times {10}^{23} [
**140 d**] - The half-life of an isotope of carbon is 6000 y. In how many years the amount this isotope in a sample will be \frac 18th part of its initial amount? [
**18000 y**] - The half-life of a radioactive element is 2 h. If its initial mass be 5g then determine the residual mass of the element after 10 h . [
**0.156 g**] - The half-life of radon is 3.8 d. After how many days \frac 1{20} part of some amount of radon will remain intact? [
**16.41 d**] - If a radioactive substance disintegrates by 20% in 5 d, then what part of the initial mass of the substance will remain intact after 15 d? [
**51.2%**]

- Radioactive isotope {Th}^{232} (Z = 90) emits six \alpha-particles and four \beta-particles successively. What will be the mass number and atomic number of the isotope thus produced? Identify the element. [
**208 , 82 ; lead**] - One-fourth of the amount of a radioactive element decays in 2490 years. Find out the half-life of this element. [
**6000 years**] - The half-life of radium-226 is 1600 years. What will be the activity of a sample containing 1 mg of this element. Given, Avogadro number = 6.023\times {10}^{23}. [ 3.66\times{10}^7 dps ]
- The half-life of a radio-isotope is 3 min. What fraction of the number of these isotopes in a sample would remain intact after 15 min? [ \frac 1{32} ]
- The activity of 1 g of {Pb}^{210} is 77.4 curie. Find its half-life. Given, Avogadro number =6.023\times {10}^{23}, and 1 curie = 3.7\times{10}^{10} decay per second. [
**22 years**] - A radioactive isotope has a half-life of
*T*years. How long will it take for the activity to reduce to 3.125% of its original value? [**5 T**] - The nuclei
*P*and*Q*have equal number atoms at*t*= 0. Their half-lives are 3 hour and 9 hour respectively. Compare their rates of disintegration after 8 hour from the start. [**3 : 16**] - The half-life of a undergoing -decay is year. What is the activity of 1 g sample of ? [
**12358 dps**]

### Nuclear Fission and Fusion

- The binding energies of deuterium ( {}_1H^2 ) and helium ( {}_2{He}^4 ) per nucleon are 1.1 MeV and 7.0 MeV respectively. When a helium nucleus ( {}_2{He}^4 ) is formed by fusion of two deuterium nuclei then how much energy will be evolved? [
**236 MeV**]