Particle and Radioactivity Assignment Help

Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, radioactive decay happens due to a proceses confined to the nucleus of the unstable atom, but occasonally (as with the different proceses of electron capture and internal conversion) an inner electron of the radioactive atom is also necessary to the process.


Introduction to radioactive decay physics

The scientist Fredric Soddy and Ernest Rutherford explained the radioactive decay physics. Fredric Soddy received the Nobel Prize in 1921 fro the radioactive decay and for the formulation of theory of isotopes. Radioactive decay is the result of an atom trying to achieve the stable configuration. In the radioactive decay process always can participate in the reaction and hence the reaction is nuclear.

Laws for Radioactive Decay Physics

The laws for the radioactive decay physics given by the famous scientists Rutherford and Fredrick Soddy. They both studied the radioactive decay experimentally. The laws for the radioactive decay are as follows:

(i) Radioactive decay phenomenon is a spontaneous process. Radioactive decay process does not depend on the external factors like temperature, pressure etc. It is impossible to guess that which on the particular atom will decay in the particular interval of time.

(ii) In the process of radioactive decay of an atom, either an alpha particle or a beta particle is emitted.No any two particles emitted simultaneously . Even no two alpha or beta particles simultaneously. At one time only one particle is emitted.
(iii) The emission of an alpha particle from an atom causes the decrement of two in atomic number and of four in mass number in the parent atom.

ZXA        `->`                   Z–2 Y A – 4 + 2 He 4 (alpha particle)


(iv) The emission of a beta particle from an atom causes the increment in atomic number by one and the mass number remains same.

ZXA        `->`                  Z+1 Y A + -1e 0 (beta particle)

(v) The number of atoms decayed per second at any instant is directly proportional to the number of  atoms present in the sample at that instant. This law is also known as radioactive decay law.

Thus, if in the sample the number of atoms is more, then the rate of decay is more and vice versa.

Expression for Radioactive Decay Law in Physics:

Let N0 be the total number of atoms present originally in the sample at the time t = 0.

N be the number of atoms left undecayed in the sample at time t = t.

dN be the small number of atoms which are decayed in the small time interval dt.

Rate of disintegration of atoms = - dN / dt

‘-’ sign indicates that number of atoms left undecayed decreases with time.

Now according to the law of radioactive decay, we get

- dN / dt N

- dN / dt  = img N

So, R = - dN / dt  = img N

Where, img is the decay constant or disintegration constant.


Introduction to Types  Of  Radioactivity

Radioactivity refers to the particles which are emitted from nuclei as a result of nuclear instability.There are different types of radioactivity.

  All substance are made of atoms.These have electrons (e) around the outside,and a nucleus in the middle.
The nucleus consists of protons (p) and neutrons (n), and is extremely small.The different types of radioactivity is due to the difference in the particles or the properties of the rays emitted during radioactive emissions.  Many radioactive substances emit  particles as well as  rays.

Types of Radioactive Emissions

Alpha radiations:

  The alpha particle is the nucleus of the helium atoimg  and is the nucleus of highest stability.Alpha-decay occurs in very heavy elements, for example, Uranium and Radium.These heavy elements have too many protons to be stable. They can become more stable by emitting an alpha particle. When an alpha particle is emitted:

*The atomic mass decreases by 4                                                                                                              

*The atomic number decreases by 2

Beta radiations:

These are high energy  electrons which have greater range of penetration than alpha particles, but still much less than gamma rays. Beta decay can be seen as the decay of one of the neutrons to a proton via the weak interaction
 when a nucleus emits a  Beta particle:    * the atomic mass is unchanged
                                                                      * the atomic number increases by 1.

Gamma radiations:

Gamma rays are waves, not particles.This means that they have no mass and no Gamma decay:-
    * atomic number unchanged
    * atomic mass unchanged

Types of Radioactive Reactions.

Electron Capture:

 A parent nucleus may capture one of its own electrons and emit a neutrino

Positron or positive beta decay:

Positron emission is called beta decay because the characteristics of electron or positron decay are similar. They both show a characteristic energy spectrum because of the emission of a neutrino or antineutrino.

Internal conversion:

Internal conversion is the use of electromagnetic energy from the nucleus to expel an orbital electron from the atom.

These are some of the types of  radioactivity. The different types of radioactivity has diffferent effects on our living and non -living surroundings.The following data table shall clearly show the features and gradation in properties of the alpha, beta and gamma rays.


Laws of Radioactivity

1. The displacement law. Rutherford and Soddy were the first to give a simple explanation of the spontaneous production of radioactive matter observed experimentally. They aruged that the atoms of the radioactive elements must undergo disintegration when they emit an a-particle. In the process, the original atoms disappear giving rise to new atoms. These are also radioactive and hence spontaneously break up, in their turn, thereby leading to a long chain of different radioactive atoms, in the form of a series till an inactive element is reached.

Soddy and Fajans discovered, in 1913, a simple law known as displacement law which govern these radioactive transformations. It can be stated as follows :

'In all known radioactive transformations, either an a- or a p-particle (i.e., never both or more than one of each) is ejected by the atom. When an a-particle is given out, a new atom, is formed whose atomic weight is less by four units and atomic number, less by two units than those of the' original atom. When a p-particle is expelled, the new atom formed has the same atomic weight as the original atom but the atomic number is increased by one unit. The emission ofy-ray does not change either the mass number (atomic weight) or the atomic number."

For example when Radium of atomic weight 226 and atomic number 88 (ggRa226) ejects an a-particle, the resulting nucleus has 86 protons and 136 neutrons i.e., atomic weight 222. Hence it gives rise to Radon (gfiRn222) which is known as radium emanation. This transformation can be represented by a simple nuclear reaction as

a - particle

—r "Rn222

Similarly when g^c227 ejects a p-particle, the resulting nucleus has 90 protons and has atomic weight 227. Thus a new radioactive substance ^Thm is formed.

89Ac227 p - particle ^Th227

This law is readily understood since a-particle, identified with the helium nucleus, has a mass four times the mass unit and a charge twice the unit charge. P-particle is produced by the conversion of a neutron into a proton. The emission of a P-particle brings about practically no change in the atomic weight of the atom, but atomic number increases by one unit.

With the help of the displacement law, one can determine easily the mass and atomic number of the different elements formed in the successive radioactive changes.

2. Law governing radioactive disintegration. Rutherford and Soddy formulated the law to explain the spontaneous disintegration of radioactive elements. The law states that

"The number of atoms that break up at any instant is proportional to the number present at that instant. In other words, the rate of disintegration is entirely dependent upon the law of chance."

If there are TV number of radioactive atoms of any substance and a number dN breaks in a time dt, then according to this law

dN Al ---- N


or -4L-XN


or ' IN ' -(0


where X, the constant of proportionality, is known as the disintegration or decay constant, characteristic of the element that disintegrates, but entirely independent of all external conditions, such as temperature, pressure etc.

Disintegration constant may be defined as the ratio of the number of atoms of the substance which disintegrates in a unit lime to the number of the atoms of the substance present.

The above relation (0 can be written as

*l = -Xdt N

Integrating both sides


logeN = -\t + C (where C is integration constant)

Applying initial conditions, if N is the number of radioactive atoms initially present i.e.,

at t = 0\N = N  O

then log N = C • O

logc N=-Xt + \0gN0 or log — = - Xt




This means that the number of radioactive atoms remaining unchanged decreases rapidly at first, then more and more slowly as time goes on.

According to expression (//), an infinite time is required, theoretically speaking for the radioactivity to disappear completely, and in this respect all radioelements are the same. Hence in order to differentiate one radioactive substance from another, a quantity known as the half life or half period (7) is often used.

Half life is defined as the time in which the radioactive atoms are reduced to half their initial number.

In the relation (it), replacing t by the period 7", we get

N _ 1 _ -at

N0 2 or eXT=2 or XT = loge2

T _ log. 2 _ 0,693 XX

T is, therefore, inversely proportional to X and hence is a characteristic constant also like X e.g., T for radium is 1590 years, while for radon it is only 3.8 days.


Suppose for example, that we have 100 million 55 Cs nuclei in a box. If we could go away and return 30 years later, and again count the number of cesium nuclei present, we would find that we had only 50 million left The other 50 million would have spontaneously transformed themselves into barium nuclei by the following beta-decay

137 . nO 137 „

jj Cs > -lP + 56Ba If this is the case, we say that the half-life of 55Cs137 is 30 years. The half-life of 92C/238 is 4.5 x 10® years, whereas for nUas it is 0.17 x 10® years. This explains why 92U235 occurs in such a small proportion in the natural uranium. The half-life of radioactive atoms varies considerably—ranging from billions of years to a fraction of a second. For example, 6C14 which is a P-emitter and transforms to has a half-life of 5730 years and that of uNa2i is about 15 hours. The half-life of 21Sc' is 0.6 s.


The half-life is a measure'of the stability of a particular nuclear species. In one half-life the amount of the radioactive substance is cut to half ; in two half-lives it is reduced by a factor of 4 ; in three half-lives by a factor of 8, and so on as shown in Fig. 13.19 for the decay of 55Cs137. At the end of three half-lives (i.e., about 90 years in this case) seven out of every eight Cs nuclei have been changed into Ba, on the average. This kind of decay is plotted in Fig. 13.20, where the symbol Tm denotes half-life. The average life of any nucleus is 1.44 times its half-life.

In Sf units decay rate — or activity of a radioactive source is dt

measured in terms of a unit called the curie (Ci) in honour of Madame Curie. It is defined as ,

, ' Ci (curie) = 3.70 x 1010 disintegrations per second by a.radioactive substance.

1 mCi (millicurie) = 3.70 x 107 disintegrations per second 1 /JCi (micro-curie) = 3-70 x 104 disintegrations per second

Dosage of electromagnetic radiation is measured in roentgen units and confined to y-rays or X-rays. The roentgen (r) is the quantity ofy-radiation giving rise to 1.6 x 1012 pairs of ions in Ig of air. One thousandth of this roentgen is the mill-roentgen (mr). Another unit has, therefore, being proposed based on an energy definition, the red (radiation absorbed dose which is a unit of energy given by any ionizing radiation to unit mass of any material. The rad is then formally defined as 100 ergs absorbed per g (10~3 joules/^) and applies to both particle and electromagnetic radiations.

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