Current Affairs JEE Main & Advanced

Soddy, Fajans and Russell (1911-1913) observed that when an a-particle is lost, a new element with atomic number less by 2 and mass number less by 4 is formed. Similarly, when b-particle is lost, new element with atomic number greater by 1 is obtained. The element emitting then a or b-particle is called parent element and the new element formed is called daughter element. The above results have been summarized as, (1) When an a-particle is emitted, the new element formed is displaced two positions to the left in the periodic table than that of the parent element (because the atomic number decreases by 2). (2) When a b-particle is emitted, the new element formed is displaced one position to the right in the periodic table than that of the parent element (because atomic number increased by 1). (3) When a positron is emitted, the daughter element occupies its position one group to the left of the parent element in periodic table. Group displacement law should be applied with great care especially in the case of elements of lanthanide series (57 to 71), actinide series (89 to 103), VIII group (26 to 28; 44 to 46; 76 to 78), IA and IIA groups. To determine the number of a- and b- particles emitted during the nuclear transformation. It can be done in following manner, \[_{c}^{a}X\to \,_{d}^{b}Y+x\,_{2}^{4}He+y{{\,}_{-1}}{{e}^{0}}\] \[a=b+4x\] or \[\text{ }x=\frac{a-b}{4}\]                                    .....(i) \[c=d+2x-y\]                                                                                .....(ii) where x = no. of a-emitted, y = no. of b-emitted substituting the value of x from eq. (i) in eq. (ii) we get \[c=d+\left( \frac{a-b}{4} \right)\,2-y\]; \[y=d+\left[ \frac{a-b}{2} \right]-c\]

(1) Nuclear fission : The  splitting of a heavier atom like that of uranium – 235 into a number of fragments of much smaller mass, by suitable bombardment with sub-atomic particles with liberation of huge amount of energy is called Nuclear fission. Hahn and Startsman discovered that when uranium-235 is bombarded with neutrons, it splits up into two relatively lighter elements. \[_{92}{{U}^{235}}{{+}_{0}}{{n}^{1}}\to {{\,}_{56}}B{{a}^{140}}{{+}_{36}}K{{r}^{93}}+3{{\,}_{0}}{{n}^{1}}\]+ Huge amount of energy Spallation reactions are similar to nuclear fission. However, they differ by the fact that they are brought by high energy bombarding particles or photons. Elements capable of undergoing nuclear fission and their fission products. Among elements capable of undergoing nuclear fission, uranium is the most common. The natural uranium consists of three isotopes, namely \[{{U}^{234}}(0.006%)\], \[{{U}^{235}}(0.7%)\] and \[{{U}^{238}}(99.3%)\]. Of the three isomers of uranium, nuclear fission of \[{{U}^{235}}\] and \[{{U}^{238}}\] are more important. Uranium-238 undergoes fission by fast moving neutrons while \[{{U}^{235}}\] undergoes fission by slow moving neutrons; of these two, \[{{U}^{235}}\] fission is of much significance. Other examples are \[P{{u}^{239}}\] and \[{{U}^{233}}\]. Uranium-238, the most abundant (99.3%) isotope of uranium, although itself does not undergo nuclear fission, is converted into plutonium-239. \[_{92}{{U}^{238}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{92}}{{U}^{239}}\] ; \[_{92}{{U}^{239}}\to {{\,}_{92}}N{{P}^{239}}+{{\,}_{-1}}{{e}^{0}}\]  \[_{93}N{{p}^{238}}\to {{\,}_{94}}P{{u}^{239}}+{{\,}_{-1}}{{e}^{0}}\] Which when bombarded with neutrons, undergo fission to emit three neutrons per plutonium nucleus. Such material like U-238 which themselves are non-fissible but can be converted into fissible material (Pu-239) are known as fertile materials. Nuclear chain reaction : With a small lump of \[{{U}^{235}}\], most of the neutrons emitted during fission escape but if the amount of \[{{U}^{235}}\] exceeds a few kilograms (critical mass), neutrons emitted during fission are absorbed by adjacent nuclei causing further fission and so producing more neutrons. Now since each fission releases a considerable amount of energy, vast quantities of energy will be released during the chain reaction caused by \[{{U}^{235}}\] fission. Atomic bomb : An atomic bomb is based upon the process of that nuclear fission in which no secondary neutron escapes the lump of a fissile material for which the size of the fissile material should not be less than a minimum size called the critical size. There is accordingly a sudden release of a tremendous amount of energy, which represents an explosive force much greater than that of the most powerful TNT bomb. In the world war II in 1945 two atom bombs were used against the Japanese cities of Hiroshima and Nagasaki, the former contained U-235 and the latter contained Pu-239. Atomic pile or Nuclear reactor : It is a device to obtain the nuclear energy in a controlled way to be used for peaceful purposes. The most common reactor consists of a large assembly of graphite (an allotropic form of carbon) blocks having rods of uranium metal (fuel). Many of the neutrons formed by the fission of nuclei of \[_{92}{{U}^{235}}\] escape into the graphite, where they are very much slow down (from a speed of about 6000 or more miles/sec to a more...

Nuclides can be grouped on the basis of nuclear stability,  i.e. stable and unstable nucleus. The most acceptable theory about the atomic nuclear stability is based upon the fact that the observed atomic mass of all known isotopes (except hydrogen) is always less from the sum of the weights of protons and neutrons present in it. Electron (b- particle) from a radioactive nucleus may be regarded as derived from a neutron in the following way, \[Neutron\to Proton+Electron\] Similarly, photons are produced from internal stresses within the nucleus. The stability of nucleus may be discussed in terms of any one of the following, (1) Nuclear Binding Energy and Mass defect : It is observed that atomic mass of all nuclei (except hydrogen) is different from the sum of masses of protons and neutrons. The difference is termed mass defect. Mass defect = Total mass of nucleons – obs. atomic mass The mass defect is converted into energy. This energy is called the binding energy. This is the energy required to break the nucleus into is constituents (p and n). Binding energy = Mass defect \[\times 931MeV\] The stability of the nucleus is explained on the value of binding energy per nucleon and not on the basis of total binding energy . Binding energy per nucleon is maximum (8.7 MeV) in the case of iron (56). The value of binding energy per nucleon can be increased either by fusion of lighter nuclei or fission of heavier nuclei. Value of binding energy predicts the relative stability of the different isotopes of an element. If the value of binding energy is negative, the product nucleus or nuclei will be less stable than the reactant nucleus. Thus the relative stability of the different isotopes of an element can be predicted by the values of binding energy for each successive addition of one neutron to the nucleus. \[_{2}H{{e}^{3}}+{{\,}_{0}}{{n}^{1}}{{\xrightarrow{{}}}_{2\,}}H{{e}^{4}}+20.5MeV\]  \[_{2}H{{e}^{4}}+{{\,}_{0}}{{n}^{1}}\xrightarrow{{}}{{\,}_{2}}H{{e}^{5}}-0.8MeV\] Therefore, \[_{2}H{{e}^{4}}\] is more stable than \[_{2}H{{e}^{3}}\] and \[_{2}H{{e}^{5}}\]. (2) Packing fraction : The difference of actual isotopic mass and the mass number in terms of packing fraction is defined as, \[\text{Packing fraction}=\frac{\text{Actual isotopicmass}-\text{Mass number}}{\text{Mass number}}\times {{10}^{4}}\] The value of packing fraction depends upon the manner of packing of the nucleons with in the nucleus. Its value can be negative, positive or even zero. A negative packing fraction generally indicates stability of the nucleus. In general, lower the packing fraction, greater is the binding energy per nucleon and hence greater is the stability. The relatively low packing fraction of He, C and O implies their exceptional stability, packing fraction is least for Fe  (negative) and highest for H  (+78).  (3) Magic number : Nucleus of atom, like extra-nuclear electrons, also has definite energy levels (shells). Nuclei with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons have been found to be particularly stable with a large number of isotopes. These numbers, commonly known as Magic numbers are defined as the number of nucleons required for completion of the energy levels of the nucleus. Nucleons are more...

“According to the law of radioactive decay, the quantity of a radio-element which disappears in unit time (rate of disintegration) is directly proportional to the amount present.” The law of radioactive decay may also be expressed mathematically. Suppose N0 be the number of atoms of the radioactive element present at the commencement of observation, \[t=0\] and after time t, the number of atoms remaining unchanged is \[{{N}_{t}}\].  The rate of disintegration \[\left( -\frac{d{{N}_{t}}}{dt} \right)\]at any time t is directly proportional to N.  Then,\[-\frac{d{{N}_{t}}}{dt}\]= lN where l is a radioactive constant or decay constant. Various forms of equation for radioactive decay are, \[{{N}_{t}}={{N}_{0}}{{e}^{-\lambda t}}\]; \[\log {{N}_{0}}-\log {{N}_{t}}=0.4343\,\lambda t\] \[\log \frac{{{N}_{0}}}{{{N}_{t}}}=\frac{\lambda t}{2.303}\];  \[\lambda =\frac{2.303}{t}\log \frac{{{N}_{0}}}{{{N}_{t}}}\] This equation is similar to that of first order reaction, hence we can say that radioactive disintegration are examples of first order reactions. However, unlike first order rate constant (K), the decay constant (l) is independent of temperature. Rate of decay of nuclide is independent of temperature, so its energy of activation is zero. (1) Half-life period (T1/2 or t1/2) : The half-life period of a radioelement is defined, as the time required by a given amount of the element to decay to one-half of its initial value. \[{{t}_{1/2}}=\frac{0.693}{\lambda }\] Now since l is a constant, we can conclude that half-life period of a particular radioelement is independent of the amount of the radioelement. In other words, whatever might be the amount of the radioactive element present at a time, it will always decompose to its half at the end of one half-life period. Let the initial amount of a radioactive substance be \[{{N}_{0}}\] Amount of radioactive substance left after n half-life periods \[N={{\left( \frac{1}{2} \right)}^{n}}{{N}_{0}}\] Total time T \[=n\times {{t}_{1/2}}\] where n is a whole number. (2) Average-life period (T) : Since total decay period of any element is infinity, it is meaningless to use the term total decay period (total life period) for radioelements. Thus the term average life is used. Average life (T)\[=\frac{\text{Sum of lives of the nuclei}}{\text{Total number of nuclei}}\] Average life (T) of an element is the inverse of its decay constant, i.e., \[T=\frac{1}{\lambda }\], Substituting the value of l in the above equation, \[T=\frac{{{t}_{1/2}}}{0.693}=1.44\,{{t}_{1/2}}\] Thus, Average life (T) \[=1.44\times \text{Half life}({{T}_{1/2}})=\sqrt{2}\times {{t}_{1/2}}\] Thus, the average life period of a radioisotope is approximately under-root two times of its half life period. (3) Activity of population or specific activity : It is the measure of radioactivity of a radioactive substance. It is defined as ' the number of radioactive nuclei, which decay per second per gram of radioactive isotope.' Mathematically, if 'm' is the mass of radioactive isotope, then \[\text{Specific activity}=\frac{\text{Rate of decay}}{m}=\frac{\lambda N}{m}=\lambda \times \frac{\text{Avogadro number}}{\text{Atomic mass in }g}\] where N is the number of radioactive nuclei which undergoes disintegration. (4) Radioactive equilibrium : Suppose a radioactive element A disintegrates to form another radioactive element B which in turn disintegrates to still another element C. \[A\xrightarrow{{}}B\xrightarrow{{}}C\] B is said to be in radioactive equilibrium with A if its rate of formation from more...

The conversion of one element into another by artificial means, i.e., by means of bombarding with some fundamental particles, is known as artificial transmutation. The phenomenon was first applied on nitrogen whose nucleus was bombarded with a-particles to produce oxygen. \[\underset{\text{Nitrogen isotope}}{\mathop{_{7}{{N}^{14}}}}\,+\,\underset{\text{Alpha particle}}{\mathop{_{2}H{{e}^{4}}}}\,\to \,\underset{\text{Oxygen isotope}}{\mathop{_{8}{{O}^{17}}}}\,+\,\underset{\text{Proton}}{\mathop{_{1}{{H}^{1}}}}\,\] The element, which is produced, shows radioactivity, the phenomenon is known as Induced radioactivity. The fundamental particles which have been used in the bombardment of different elements are, a-particle : \[_{2}H{{e}^{4}}\] ; Proton : \[_{1}{{H}^{1}}\] Deutron : \[_{1}{{H}^{2}}\] or \[_{1}{{D}^{2}}\] ; Neutron : \[_{0}{{n}^{1}}\] Since a-particles, protons and deutrons carry positive charge, they are repelled by the positively charged nucleus and hence these are not good projectiles. On the other hand, neutrons, which carry no charge at all, are the best projectiles. Cyclotron is the most commonly used instrument for accelerating these particles. The particles leave the instrument with a velocity of about 25,000 miles per second. A more recent accelerating instrument is called the synchrotron or bevatron. It is important to note that this instrument cannot accelerate the neutrons, being neutral. When a target element is bombarded with neutrons, product depends upon the speed of neutrons. Slow neutrons penetrate the nucleus while a high-speed neutron passes through the nucleus. \[_{92}{{U}^{238}}+\,\underset{\text{slow speed}}{\mathop{_{0}{{n}^{1}}}}\,\to {{\,}_{92}}{{U}^{239}};{{\ }_{92}}{{U}^{238}}+\,\underset{\text{high speed}}{\mathop{_{0}{{n}^{1}}}}\,\to {{\,}_{92}}{{U}^{237}}+\,{{2}_{0}}{{n}^{1}}\] Thus slow neutrons, also called thermal neutrons are more effective in producing nuclear reactions than high-speed neutrons. Alchemy : The process of transforming one element into other is known as alchemy and the person involved in such experiments is called alchemist. Although, gold can be prepared from lead by alchemy, the gold obtained is radioactive and costs very high than natural gold. (i) Transmutation by a-particles (a)                a, n type \[_{4}B{{e}^{9}}(\alpha ,\,n){{\,}_{6}}{{C}^{12}}\] i.e. \[_{4}B{{e}^{9}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{6}}{{C}^{12}}+{{\,}_{0}}{{n}^{1}}\] \[_{94}P{{u}^{239}}\,(\alpha ,\,n){{\,}_{96}}C{{m}^{242}}\]i.e. \[_{94}P{{u}^{239}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{94}}C{{m}^{242}}+{{\,}_{0}}{{n}^{1}}\] (b) a, p type \[_{9}{{F}^{19}}\,(\alpha ,\,p){{\,}_{10}}N{{e}^{22}}\] ie.\[_{9}{{F}^{19}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{10}}N{{e}^{22}}+{{\,}_{1}}{{H}^{1}}\] \[_{7}{{N}^{14}}\,(\alpha ,\,p){{\,}_{8}}{{O}^{17}}\] i.e.,  \[_{7}{{N}^{14}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{8}}{{O}^{17}}+{{\,}_{1}}{{H}^{1}}\] (c) a, b type \[_{26}F{{e}^{59}}\,(\alpha ,\,\beta ){{\,}_{29}}C{{u}^{63}}\] i.e., \[_{26}F{{e}^{59}}+{{\,}_{2}}H{{e}^{4}}\to {{\,}_{29}}C{{u}^{63}}+{{\,}_{-1}}{{e}^{0}}\] (ii) Transmutation by protons (a) p, n type \[_{15}{{P}^{31}}\,(p,\,n){{\,}_{16}}{{S}^{31}}\]  i.e., \[_{15}{{P}^{31}}+{{\,}_{1}}{{H}^{1}}\to {{\,}_{16}}{{S}^{31}}+{{\,}_{0}}{{n}^{1}}\] (b) p, g type \[_{6}{{C}^{12}}\,(p,\,\gamma ){{\,}_{7}}{{N}^{13}}\] i.e., \[_{6}{{C}^{12}}+{{\,}_{1}}{{H}^{1}}\to \,{{N}^{13}}+\,\gamma \] (c) p, d type \[_{4}B{{e}^{9}}\,(p,\,d){{\,}_{4}}B{{e}^{8}}\]  i.e., \[_{4}B{{e}^{9}}+{{\,}_{1}}{{H}^{1}}\to {{\,}_{4}}B{{e}^{8}}+{{\,}_{1}}{{H}^{2}}\] (d) p, a type \[_{8}{{O}^{16}}\,(p,\,\alpha ){{\,}_{7}}{{N}^{31}}\]  i.e., \[_{8}{{O}^{16}}+{{\,}_{1}}{{H}^{1}}\to {{\,}_{7}}{{N}^{13}}+{{\,}_{2}}H{{e}^{4}}\] (iii) Transmutation by neutrons (a) n,p type \[_{13}A{{l}^{27}}\,(n,\,p){{\,}_{12}}M{{g}^{27}}\] i.e., \[_{13}A{{l}^{27}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{12}}M{{g}^{27}}+{{\,}_{1}}{{H}^{1}}\] (b) n,a type \[_{8}{{O}^{16}}\,(n,\,\alpha ){{\,}_{12}}M{{g}^{27}}\] i.e., \[_{8}{{O}^{16}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{6}}{{C}^{13}}+{{\,}_{2}}H{{e}^{4}}\] (c) n, g  type \[_{92}{{U}^{238}}\,(n,\,\lambda ){{\,}_{92}}{{U}^{239}}\] i.e., \[_{92}{{U}^{238}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{92}}{{U}^{238}}+\,\lambda \] (d) n,b type \[{{\,}_{8}}{{O}^{18}}\,(n,\,\beta ){{\,}_{9}}{{F}^{19}}\] i.e., \[{{\,}_{8}}{{O}^{18}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{9}}{{F}^{19}}+{{\,}_{-1}}{{e}^{0}}\] (iv) Transmutation by deutrons (a)                d,p type \[_{3}L{{i}^{6}}\,(d,\,p){{\,}_{3}}L{{i}^{7}}\]i.e.,\[_{3}L{{i}^{6}}+{{\,}_{1}}{{H}^{2}}\to {{\,}_{3}}L{{i}^{7}}+{{\,}_{1}}{{H}^{1}}\] \[_{32}A{{s}^{75}}\,(d,\,p){{\,}_{32}}A{{s}^{76}}\] i.e., \[_{32}A{{s}^{75}}+{{\,}_{1}}{{H}^{2}}\to {{\,}_{32}}A{{s}^{76}}+{{\,}_{1}}{{H}^{1}}\] (v) Transmutation by g-radiations (a) g, n type \[_{4}B{{e}^{9}}\,(\lambda ,\,n){{\,}_{4}}B{{e}^{8}}\] i.e., \[_{4}B{{e}^{9}}+\gamma \to {{\,}_{4}}B{{e}^{8}}+{{\,}_{0}}{{n}^{1}}\] Synthetic elements : Elements with atomic number greater than 92 i.e. the elements beyond uranium in the periodic table are not found in nature like other elements. All these elements are prepared by artificial transmutation technique and are therefore known as transuranic elements or synthetic elements.  

(1) Nuclear fission : The  splitting of a heavier atom like that of uranium – 235 into a number of fragments of much smaller mass, by suitable bombardment with sub-atomic particles with liberation of huge amount of energy is called Nuclear fission. Hahn and Startsman discovered that when uranium-235 is bombarded with neutrons, it splits up into two relatively lighter elements. \[_{92}{{U}^{235}}{{+}_{0}}{{n}^{1}}\to {{\,}_{56}}B{{a}^{140}}{{+}_{36}}K{{r}^{93}}+3{{\,}_{0}}{{n}^{1}}\]+ Huge amount of energy Spallation reactions are similar to nuclear fission. However, they differ by the fact that they are brought by high energy bombarding particles or photons. Elements capable of undergoing nuclear fission and their fission products. Among elements capable of undergoing nuclear fission, uranium is the most common. The natural uranium consists of three isotopes, namely \[{{U}^{234}}(0.006%)\], \[{{U}^{235}}(0.7%)\] and \[{{U}^{238}}(99.3%)\]. Of the three isomers of uranium, nuclear fission of \[{{U}^{235}}\] and \[{{U}^{238}}\] are more important. Uranium-238 undergoes fission by fast moving neutrons while \[{{U}^{235}}\] undergoes fission by slow moving neutrons; of these two, \[{{U}^{235}}\] fission is of much significance. Other examples are \[P{{u}^{239}}\] and \[{{U}^{233}}\]. Uranium-238, the most abundant (99.3%) isotope of uranium, although itself does not undergo nuclear fission, is converted into plutonium-239. \[_{92}{{U}^{238}}+{{\,}_{0}}{{n}^{1}}\to {{\,}_{92}}{{U}^{239}}\] ; \[_{92}{{U}^{239}}\to {{\,}_{92}}N{{P}^{239}}+{{\,}_{-1}}{{e}^{0}}\]  \[_{93}N{{p}^{238}}\to {{\,}_{94}}P{{u}^{239}}+{{\,}_{-1}}{{e}^{0}}\] Which when bombarded with neutrons, undergo fission to emit three neutrons per plutonium nucleus. Such material like U-238 which themselves are non-fissible but can be converted into fissible material (Pu-239) are known as fertile materials. Nuclear chain reaction : With a small lump of \[{{U}^{235}}\], most of the neutrons emitted during fission escape but if the amount of \[{{U}^{235}}\] exceeds a few kilograms (critical mass), neutrons emitted during fission are absorbed by adjacent nuclei causing further fission and so producing more neutrons. Now since each fission releases a considerable amount of energy, vast quantities of energy will be released during the chain reaction caused by \[{{U}^{235}}\] fission.                       Atomic bomb : An atomic bomb is based upon the process of that nuclear fission in which no secondary neutron escapes the lump of a fissile material for which the size of the fissile material should not be less than a minimum size called the critical size. There is accordingly a sudden release of a tremendous amount of energy, which represents an explosive force much greater than that of the most powerful TNT bomb. In the world war II in 1945 two atom bombs were used against the Japanese cities of Hiroshima and Nagasaki, the former contained U-235 and the latter contained Pu-239. Atomic pile or Nuclear reactor : It is a device to obtain the nuclear energy in a controlled way to be used for peaceful purposes. The most common reactor consists of a large assembly of graphite (an allotropic form of carbon) blocks having rods of uranium metal (fuel). Many of the neutrons formed by the fission of nuclei of \[_{92}{{U}^{235}}\] escape into the graphite, where they are very much slow down more...