Class 10TH Physics Notes Chapter 18 Nuclear Physics

Class 10TH Physics Notes Chapter 18 Nuclear Physics

Class 10TH Physics Notes Chapter 18 Nuclear Physics. Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons. Class 10TH Physics Notes Chapter 18 Nuclear Physics.

Class 10TH Physics Notes Chapter 18 Nuclear Physics
Class 10TH Physics Notes Chapter 18 Nuclear Physics

Discoveries in nuclear physics have led to applications in many fields. This includes nuclear energy, nuclear weapons, nuclear medicine and magnetic resonance imaging, industrial and agricultural isotopes, ion implantation in materials engineering, and radiocarbon dating in geology and archeology. Such applications are studied in the field of nuclear engineering. Class 10TH Physics Notes Chapter 18 Nuclear Physics .

Class 10TH Physics Notes Chapter 18 Nuclear Physics
Class 10TH Physics Notes Chapter 18 Nuclear Physics

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Chapter No.18

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Major Concepts

• Atom and nucleus

• Natural radioactivity

• Background radiations

• Nuclear transmutations

• Nature and properties of radiations

• Half-life and its measurement

• Uses of radioisotopes

• Nuclear fission

• Nuclear fusion

• Hazards of radiation and safety measure

• Solution of problems

Comprehensive Questions

Q1: What is nucleus? How a nuclide is represented symbolically.

Ans. Atom and Atomic nucleus:

All matter is composed of atoms that are in turn composed of a heavier, central, positively charged core called ‘nucleus’ surrounded by a less massive negatively charged cloud of ‘electrons’ the nucleus lies zi the center of the atom, occupying only 10-15 of its volume since the electrical force comes from both the electron and the nucleus as shown in figure. The nucleus is about 10,000 times smaller than atom. The size difference is like a ping pong ball in the center of a 2km circle.

Volume occupied by negatively charged electrons approximately 10 m Aciamit—iateiy ID r.

All nuclei are composed of two types of particles; protons and neutrons (called nucleons). The only exception is the. Ordinary hydrogen nucleus, which is a single proton. In describing the atomic nucleus, we must use the following quantities:

The atomic number Z; sometimes caned the charge number), which equals the number of protons in the nucleus. The nucleon (or mass) number A, which equals the number of nucleons (neutrons plus pro-.ons) .n tne nucleus. The neutron number N, which equals the number of neutrons in, nuciebz; N=A-Z) A

In representing nuclei, it is convenient to have a system of symbol to show many protons and neutrons are present. The symbol used is “zie where -x” Number cf Protons represents the chemical symbol for the element, Z represents tne number of proton and ‘A” represent the number of nucleus (i-e number of proton anc neutron)

For example 26FE56 (iron) nes a nucleon number of 5 and an atomic number of 56; It therefore contain 26 proton and (56 — 26) 30 neutrons. The subscript Z is thus some time dropped .for example of nitrogen 7N15 we already known that Z=7 form nitrogen is simply write N15, call it as nitrogen fifteen (or may write as nitrogen-15). The nuclei of all atom of a particular element contain same number of proton (and consequently electrons in a neutral atom) but often contain different number of neutrons. The nuclei of atom which have the same number of proton and neutron are termed as nuclides. Within the nucleus Z positive charge s. to keep these charges from flying apart, the nuclear force must supply an attraction that overcomes their electrical repulsion.

Q2. What is radioactivity? What are ex, Thy rays. Describe their properties.

Ans. History:

In 1896 a French scientist Henry Becquerel discovered the process of radioactivity while performing experiment on the compound of uranium.


The disintegration of the nuclei of certain atoms with the emission of alpha, beta and gamma rays is called radioactivity. OR

The phenomena of emission of radioactivity rays (alpha, beta and gamma rays) from the nuclei of certain atoms is called radioactivity.


There are two type of radioactivity.

i. Natural radioactivity

ii. Artificial radioactivity

i. Natural radioactivity:

The spontaneous and uncontrollable disintegration of the nuclei of certain heavy atom having atomic number greater than 82 with the emission of radioactive rays is called natural radioactivity.

ii. Artificial radioactivity:

The radioactivity produce by bombarding subatomic particles in to same element is called artificial radioactivity. OR

The radioactivity produced as a result of bombardment of nucleus of an element by subatomic particle is called artificial radioactivity.


Becquerel (Bq) is the SI unit of radioactivity. One Becquerel is defined as the activity of quantity of radioactive material in which one nucleus decays per second. A common unit of activity curie (C,) which is 3.70 x 1010 decay per second i.e. C, = 3.70x 1010 Bq.


In this experiment a small quantity of radioactive element (uranium) was so placed in the cavity in a lead block that the radiation from uranium come out of the mouth of the cavity .a photographic plate is placed at some distance above the lead block so that the radiation from the uranium fall upon it. The apparatus is placed in vacuum tight chamber, which is evacuated by a power pull pump. This chamber is then placed between the poles of a strong magnet so that the magnetic field is perpendicular to the plane of the paper and is directed inward. Under the action of magnetic field three separate images are formed on the photographic plate. This show that the radiation coming from uranium are of three types as shown in figure.

The radiation which here deflected toward right are known as /3 —rays. The radiation which here defected toward left are known as a-rays, while the radiation which were passes unelected are known as y – ray.

Properties of radioactive rays:

a) Alpha rays(a-rays):

i) a-rays are deflected by electric and magnetic field,

ii) a-rays are double positive.

iii) The a-ray effect the photographic plate.

iv) a-rays have high ionization power.

v) The speed range of —rays in between 1.4x m/sec to

1.8x 107m/sec.

vi) a-rays have low penetrating power.

vii) a -rays produce artificial radioactivity in certain substances.

viii) a -rays produce burns and sores on human body.

b) Beta rays (f3-rays):

i) /3-rays affect the photographic plate.

h) /3-rays are negatively charged particles.

iii)/3-rays produce fluorescence in certain substance

iv)p-Rays the speed of /3-rays is in between 2.7x 107m/sec to 9 x 1 Or/sec

v) The ionization power of (3-rays is very small.

vi) The penetrating power of /3-rays is very high

vii) /3-rays are deflected by electric and magnetic field. ) Genie Ray (y ray):

It y —rays are neutral particles.

Y —rays move with the speed of light.

Ill) the penetrating power or y —rays Is very large compared to P- rays and a -rays

iv) The ionization power of y —rays Is very low as compared to. a -rays and a Rays. v) v — rays produce feeble fluorescence In Barium platinocynide, v’; v ray$ erect the photographic ptate

vii) y —rays are electromagnetic waves.

Q3. Discuss the half- life of radioactive elements in detail?

Ans. Half-life of radioactive element:


“Tne time interval in which half of the atoms io any given sample decay in to c:aur;hter element is known as the halPic2 of that element”. OP

‘The half-life of an element is that time during which the number. of atoms of the radioactive element reduced to one half.”

Parent Element:

The original radioactive element which continuously emits radiations is called parent element.

Daughter element: The element which. is formed as a result of continuous emission of radiations from an element is called daughter element.

Half-life range:

The amount of radioactive isotope in the sample decreases with time as shown in the half-life curve shown in figure. The number of nuclei present at time t=Os is N=No, and the number present at t= T112 is N=Nd2. The number present at t=2-1112 is N=No/4, and so on. The value of the half life depends on the nature of the radioactive nucleus. For example, radium has a half—life of 1600 years. Because it takes this amount of time for one-half of a given quantity of this isotope to disintegrate.

Nonce In another 1600 years, one —h alf of the remaining radium atoms will have disintegrated. Leaving only one fourth of the original number intact. Omaha’ sample remaining after any end the original amount in the sample Let N represent oz. he given time interval; GT and N3 repress given in the same unit as After 1 half-life

After 2 half-life

After 3 half-life N = 1 N

2 °

N =1 X • N = 1 N

2 °

N =1 X • 2

1 1

N= — x –

2 2 No = (1)2 No


X No = (i) Generally

There, the number n, of half-lives is i “• n

X N (1) N

2 ° °

Equal to the interval (fit) divided by the time for one half-life T


N =

TABLE. For half-lives of some common radioisotopes

Decay Half Life

Beryllium-8 a 2.0)1O-1°s

Po osier a 1.64×104s

Iodine-‘3 /3 8.04 d

Cobalt-60 /3 5.3 y

Radium-226 a 1.62×10-3 y

Carbon-14 /3 5.73×10-3 y

Uranium-235 a 7.04×10-9 y

Uranium-238 a 4.45×10-9 y

Different materials have different half-lives which ranges from 1010 years to a fraction of second. Half-lives of some common radioisotopes are shown in table,

Q4. What are nuclear transmutations? What changes in the composition of nucleus is observed when cx, fl and y particles are emitted? Explain by symbolic equation.

Ans. Nuclear Transmutations:


“The process through which an unstable nucleus (parent nucleus) transform (or changes) in to a more stable nuclide (daughter nucleus) is called nuclear transmutation (Nuclear decay).” In these nuclear transmutations, the original element is called parent and new formed element is termed as daughter.

Alpha decay: In alpha decay. The angina: parent’ nuclide is converted to a ‘daughter’ by the emission of an x particles. Balancing the reaction shows that the daughter nuclide has a nucleon number reduced by four and a charge reduced by two, mathematically.

Z…”X7A-4, +aq

C -e: easec t’-e process. Nuclide ‘x’ changes into nuclide with the emission of alpha ‘x’ particle and the release of energy ‘Q’. Ri-2SV, IfRf44HeT+0

LB o8 u _., 21h 4 He



238, k= 234 Th

92 90’

+ He 4 (a) +Q the emission of an alpha particle by uranium -238 results in the formation of thorium -234

Beta decay:

Unlike 0:- decay. 13 (or electron) decay of nuclei does not change the number of nucleons. In essence-decay changes a neutron into a proton.

: X= ‘;’. Y+ +Q

Where Q is the energy released in the process. Nuclide ‘X’ changes in to nuclide ‘Y’ with the emission of beta “f3” particle and released of energy ‘Q’.Example

N+Ir+Q the emission of a Beta particle by thorium -234 results in the formation of protactinium -234

Gamma decay:

!in most cases the or g remission from the nuclei leaves it in excited state such nuclei achieve further stability by emitting gamma rays.

For example; X=: x +;

, CCO= C0+”:

Q5. What are radio isotopes? Explain their uses for various applications?

Ans. Definition:

“The isotopes that are unstable and emit radiations are called radioactive isotopes or simply radioisotopes”.


Isotopes of elements that occur naturally are somewhat stable. But the isotopes, manufactured in nuclear laboratories by bombarding o subatomic particles, usually have a short life span, mostly due to their unstable nature and radioactivity. Among about 3000known nuclides, only 257 are stable. The time scale of these decay processes ranges from a small fraction of a microsecond to billions of years. The element carbon (figure) as we find it in nature consists 98 89% of ’20 atoms and only about 1.11%13C atoms. Where ‘4C isotopes of carbon is in trace amounts, with a half- life of 5,700 years. Carbon as a whole hasl5known isotopes from8C to 220. of which the most stable artificial radioisotopes have half- lives under 20 seconds, most less than 200 milliseconds.

Most elements have between two and six stable isotopes (as opposed to unstable or radioactive ones). Twenty elements, including fluorine, sodium, aluminum, phosphorus, and gold consist of only one stable isotope each. Tin, however, has ten-more than any other element.

Uses of radioisotopes:

Radioactive isotope behaves in just the same way as the normal isotope chemically, which make it useful in wide variety of applications. Over 2,000 radioisotopes- radioactive isotopes- either exist in nature or have been made artificially by bombarding stable isotopes in particle accelerators. They are useful in so many applications that the word isotope is commonly used to mean radioisotope, as if stable isotopes did not exist. Few of the use of radioisotopes are discussed below.

I. Food preservation:

Food irradiation is a method of treating food in order to make it safer to eat and have a longer shelf life. Even after it has been packaged, gamma rays can penetrate the packing and be used to kill bacteria, mould and insect in food as shown in figure (a). This process prolongs the shelf —life of the food. But sometime changes the taste.


Gamma rays are also used to sterilize hospital equipment by radiation, especially the plastic syringes that would be damaged if heated as shown in figure (b). iii. Agriculture:

If a plant is given fertilizer tagged with radioactive carbon then the plant is releases “beta radiation” and thus by measuring radioactive in different part of the plant, the uptake of the fertilizer by plant can be determined.

This technique can help in elaborating the complex process of photosynthesis as well. Higher yield varieties of seed have also been developed after mutation through radiation. iv. Medicaid uses.

Radio pharmaceutical – drugs that contain radioactive material -are imported in diagnosis and treatment of many disease. They can be injected into the body, inhaled, or taken orally as medicines or to enable imaging of internal organ and bodily processes. Ionizing radiation has two very different uses in medicine – for the diagnosis and therapy.

a. Medical dlacanostic:

Every organ in our body acts differently from a chemical point of view. Doctors and chemist have identified a number of chemical which are absorbed by specific organs. The thyroid, for example, takes of iodine; the brain consumes quantities of glucose, and so on. With this knowledge, radio-pharmacists are able to attract various radioisotopes to biologically active substances. Image are then obtained via gamma camera or a PET scan in nuclear diagnostic which enable to accurately detect disease progression and staging in vital organs.

A radioisotopes used for diagnostic must emit gamma rays of sufficient energy to escape from tit? Body and it must have a half -life short enough for it to decay away soon after imaging is completed.

b. Radiation therapy:

High energy radiation can be used to destroy selected tissues, such as cancerous tumor. Cobalt 60 which emits bête particle and high energy gamma rays can be used to treat various cancers. Some radioisotopes are made absorb by selected organ and radiation is concentrated on the infected tissue. For example cancerous thyroid can be treated with iodine-131.

Q6. How is carbon -14 used to determine the age of wood, bones and other artifacts?

Ans. Radioactive dating:

Archeologist and geologist use radioactive dating to estimate the age of ancient objects. One common used procedure carbon-14 which has a half -life of 5730 years as long as the creature is alive, it will continue to absorb and collectcorbon-14. Once the creature dies, no further carbon -14 will be ingested, and the proportion of corbon-14 is very small. Nevertheless the amount is the measurable .the measurement of the activity present can therefore be used to estimate the age of the specimen. Corbon-14 dating can be used for biological tissue as old as 50 or 60 thousand year, but is most accurate for younger samples, since the abundance 140 nuclei in them are greater. Very old biological material contains no 140 at all. Material with relatively longer half-life can be used to determine the age of geological formation, Uranium -238, for example, with a half-life of 4.53 x 1010 year can be used to date even the oldest deposits on earth.

Q7. Discuss nuclear fission and fusion in detail?

Ans. Nuclear fission:


The splitting of the heavy nucleus in the fragment with the emission of energy when bombarded by a slow neutron is called nuclear fission. OR

The process of splitting of nuclei into intermediate size nuclei is called nuclear fission. The fission processes often produce free neutron and gamma rays, and release a large amount of energy.


Nuclear fission was discovered in December 17, 1938 by Otto Hahn and his assistant fritz Stress man, and explains theoretically in January 1939 by Lise Meitner and her nephew Otto Robert Frisch.

They found that a uranium nucleus, after absorbing a low energy neuron (thermal neutron). Splits into two fragment of intermediate size .the splitting of a massive nucleus into two less fragments were termed a nuclear fission. It can be represented by the following nuclear reaction.ion+2392U-2392lf—X + Y + neutrons Where. U236m is an intermediate excited state that last for only about 1012 s before splitting in to X and Y. the resulting nuclei X and Y are called fission fragments. Many combination of X and Y are possible in the above nuclear reaction.

Figure show that the actual mass distribution of fragment in the fission of U235. The process results in then production cf several neutrons, typically two or three. On the average. About 2.5 net, trons are released per event. A typically reaction of this type is,

O n+232U—TLI— ig6E3a+126Kr+3 in

Where O is the nuclear reaction energy RI, the uranium nucleus the nucleons are bound with an average energy of about 7.6 me per nucleon. In the fission product nuclei, the medium binding energy per nucleon amount to approx. 8.5 Me. This difference in binding energy of .0.9 Vey per nucleon is released it “‘e nuclear fission, since the uranium nucleus has 235 nucleons, F. quantity of about 210 Mev is released per fission. It is made up of thetilowing pita; amounts.K.E of fission products 175 Mev.K.E of fission neutrons 5 Mev.

C. Energy of y- radiation occurring during the fission 7 Mev.K.E. Energy of V” and “y” radiation during the decay of the radioactive fission products 13 Mev.

C. Energy of the neutrinos 10 Mev.

It is found that 1kg of uranium delivers as much energy as 3000tons of coal.

Fission Chain reaction:

When one nuclear reaction causes an average of one or more nuclear reactions, thus a self—propagating series of these reactions is achieved and is called chain reaction.

The fact that fission reactions of uranium-235 give oft more than one neutron on average has significant implications. As the fission of uranium -235 is initiated by the absorption of a neutron. So the neutrons given off by one fission reaction may cause additional fission reactions in other nuclei. If each of the neutrons. Followed by more fission, and so forth. A long as the average number of neutrons available to produce new fission, is greater than 1 per reactions, the number of fissions grows with time as shown in figure. If we have such an event in uncontrolled way, it may produce huge amount Of energy is veiy short time. In explosion of atomic bomb we produce such an uncontrolled fission chain reaction. The nuclear reactors on the other hand release the energy from nuclear fission in a controlled manner.

Nuclear fusion:

“The process in which small nuclei diffuse to form a heavy nucleus is called nuclear fusion.” OR

“The nuclear process in which two light nuclei (A< 30) fuse together to form a heavy nucleus is called nuclear fusion. “OR

“When two light nuclei combine to form a heavy nucleus, the process is called nuclear fusion.


In 1920, Mark Edington gave the idea about the energy released from the sun and other stars. He told that in sun and other stars, the protons are converted into Helium nucleus. This idea was confirmed.


When two nuclei form a large nucleus, the mass of larger nucleus is less than the mass of nuclei that formed it. This loss in mass appears in the form of energy. A self-sustaining fusion reaction is also possible but the energy required is possible only in the environments of stars including sun. One such, cycle is;

A. proton — proton cycle:

In this process the direct collision of protons results it formation

of heavier nuclei whose collision in turn produces helium nuclei as shown in figure 18.15. The initial reaction in proton- proton cycle is,

+ 111 tlf + /I+

A deuteron produced in the above reaction may combine with other proton as,

TH + if/ –0 11 e + y

Finally two such reactions can combine to form helium-4 with the release of two protons as,

ZHe+ —> life +1H + 1H + y

The total energy released in this process is 24.7 Mev which is the difference between the masses of 4-Protons and mass of alpha particle plus two positrons.

Q8. What are back ground radiations? What are of major sources?

Ans. Background radiation:


All living creatures, from the beginning of time, have been and are still being exposed to radiation. When a radiation detector is used it will record these radiations called natural back ground radiation. It comes from three sources:

Major sources of background radiations:

The earth and all living things on it are constantly bombarded by radiations from space. The dose from cosmic radiation varies in different parts of the world due to differences in elevation and to the effects of the earth’s magnetic field.

Terrestrial radiation;

Radioactive material is also found throughout nature. It is in the soil, water and vegetation. Low levels of uranium, thorium, and their decay products are found everywhere. The dose from terrestrial sources also varies in different parts of the world.

Internal radiation:

All people also have radioactive potassium -40, carbon-14, lead -210, and other isotopes inside their bodies from birth.

Q9. What are radiation hazards? How can we safeguard missives from radiation?

Ans. Hazard Radiation:

Nuclear radiation is potentially harmful to human because the ionization it produces can significantly alter the structure of molecules within a living cell. The alteration significantly can lead to the death of the cell and even of the organism itself. The amount of biological! Damage produced by ionizing radiation is different for different kind of radiation.

Everyone is continually exposed to hack ground radiation from natural sources, such as cosmic rays (high-energy particles that come from outside the solar system), radioactive material in the environment, radioactive nuclei (primarily carbon and potassium) within our bodies, and radon.

The effect of radiation on human can be grouped it o two categories. according to the time span between initial exposure and the appearance of physiological symptom:

(1) short -term or acute effect that appear wi9th in a matter of minute , days or week and (2) long term or latent effect that appear year , decades, or even generation later.

The radiation from the material can damage the cells of the person directly. This is damage by irradiation. Some of the radioactive material can be swallowed or breathed in .while inside the body; the radiation it emits can produce damage. This is damage by contamination.

Radiation Sickness:

Radiation sickness is the general term applied to the acute effect of radiation. Depending on the severity of the dose, a person with radiation sickness can exhibit nausea, vomiting, fever, diarrhea and loss of hair. Ultimately, death can occur. The severity of radiation sickness’s related to the dose received, and in the flowing discussion, the i

Equivalent doses quoted are whole -body single doses.

Long – term or latent effect of radiation may appear as a result of high-level, brief exposure or low level exposure over a long period of time. Some long-level effects are hair loss, eye cataract, and various kind of cancer In addition; genetic defect cause by mutated genes may be passed on from one generation to the next.

Safety measure:

There are general three guidelines for contrcil’ng expcsoce to ionizing radiation:, minimizing exposure time, maximizing distance from the radiation source and shielding yourself from the radiation source.

While working in the radiation, Lab coat, Shoes and safety glasses must be warn in the laboratory. Material/equipment which is not required must not be brought in the laboratory or stored insides. An inventory of radioactive sources used in the laboratory must be maintain and updated.

Important symbol:

International symbol ;trefoil) of radiation this sign must be posted where radioactive material are handled or where radiation producing equipment is used .sign is used as a warning to protect people from being exposed to radioactivity

International atomic energy agency (IAEA) in 2007 has launched a new symbol for ‘ionizing radiation warning — supplement symbol’ new symbol is intended to supplement the existing, well recognized, radiation trefoil symbol. The new symbol has been designed to convey the message “danger-stay away” to anyone who sees it, regardless of their age, education or cultural back ground.

I Examples I

Example 18.1: An unstable polonium-218 (284Po) atom spontaneously • emits an alpha (a) particle and transmutes into an atom of some other Element. Show the process, including the new element, in standard nuclear-reaction notation. Original sample remaining after any given interval is,

Putting value N = bein No

N = (17)3160 pg

N = – x 160 pg N = 20 pg


The graphical representation confirms that 20 pg of polonium -218 half-life of 3.0 min will be present after 9.0 min.

Example 18.4: Suppose you found frozen dead animal remains in the Himalayas. You took a sample from it and found that carbon-14 (half-life 71,2′ = 5730 years) activity is reduced 1/8 per gram from original value. How old are the dead animals remaining?


Given: Quantity left of carbon -14 ‘N’ = No

Half-life of carbon-14 7112′ = 5730 years


Total elapsed at =?


We know that;

N = (z) n No (1)

Putting value

N = 8N.

N = N,


N = No ———— (2)

Comparing equation 1 and 2 n = 3

Thus in three half-lives the quantity left of carbon 14, will be-8 No and the number of half-lives ‘n’ past is given by relation,




t = NT, i2

Putting value

A t = 3 x 5730 years


A t = 17,190 years Answer



The remain of dead animals are 17,190 years old.

I Assignments I

Assignment 18.1: Find the daughter nucleus when radium -224 undergoes alpha decay.



For CX- decay for any nuclide is given by,

A — A-4

2X Z-2Y +CX Q (1)

Replaced zyA by a 224

R in equation (1), we get,

0,224 88.2y224

881 2 -4″ +a + Q

OR 88Ra224 = 86y220 + cc ÷ Q (2)

Now the element with (Z= 86), and (A = 220) in periodic table is Radon 88Ra220, replace 04220 by 88R _ in equation (2), we get,


88Ra224 = 88Rn22o cx + Q (3)


So when 88Ra224 undergoes cc- emission, it is converted into p6Rn220.

Assignment 18.2: An atom of sodium-24 can transudate into an atom of some other element by emitting a beta particle. Represent this reaction in symbols, and identify the daughter element.



The general equation for (3- decay in given by,

zXA = ziy p


Replaced zXA by 11Na24 in equation (1), we get,

11Na24 = lit, Y24 + 0 +

OR 11Na24 = 12)124 + (2)

Now the element with (Z=12) and (A=24) in periodic table is magnesium


24 24

• Y in So replace i2 by ,2 in equation (2), we get.

24 24 _

Na=Mg+ 13+Q (3)

11 12


• .4

Thus when Na undergoes 13- emission, it is converted into “^P.

Assignment 3: lead 210 has a half-life of 22.3 years. How much of the 80 mg of lead will be left after 66.9 years?


Given data:

Half-life lead=T 1=22.3 years


Total quantity of pure lead =NO =80 mg

Total elapsed = At = 66.Q years


Quantity left =N=?


• We know that.


n = t (1)

Putting the values in equation (1). we EP(

66.9 years

n =

22.3 years

n = 3

Now the remaining sample is given by.

N = (2)”No (2) Putting the values in equation (2). we get.

I No = (1)” N.

A (1)n

8 ‘2

(2 2)3-0-r (3)

Comparing the powers on both sides of equation (3). We get. n=3 Now putting the values of ‘n’ and 11 in equation (1). We get.

At = 3 x 5730 years At = 17190 years

Assignment 4: Suppose the fossil of bone you are examining has ‘A of carbon 14 deposits as compared to bone of the living animal per gram. The half-life of 4C is 5730 years, what is the approximate age of the fossil?


Given data:

Half-life=T – = 5730 years Quantity left of carbon =ts1=-1- No


Total elapsed = at –=-7


We know that,



At NT —2

We also know that;

N = (D2 No (2)

Put N = (-) 2No in equation (2), we get,


4 No = (2) No

1 = (1)n

4 2

1 2 ‘1’ 71

() = (2) (3)

Comparing the power on both sides of equation (3), we get, 2=nn=2 Now putting the values of ‘n’ and T12 in equation (1)

At = 2 x 5730 years

At = 11460 years



Every element has a unique atomic number the periodic table shows the new element to be lead (Pb) with z= 82. The finalized equation can now be written as,

2gPo 241 X + 1He (oc) + Q

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