(I) Two stable isotopesoflithiumandhave respective abundances of 7.5%and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass oflithium. (II) Boron has twostableisotopes,and. Their respective masses are 10.01294u and11.00931u,andtheatomicmassofboronis10.811u.Findtheabundancesof and.

The three stable isotopesofneon:andhave respective abundances of 90.51%,0.27%and9.22%.Theatomicmassesofthethreeisotopesare19.99u,20.99 u and 21.99 u, respectively. Obtain the average atomic mass ofneon.

Obtain the binding energy (in MeV) of anitrogennucleus,given =14.00307 u

Obtain the binding energy ofthenucleiandin units of MeV from thefollowing data: =55.934939u= 208.980388u

A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of atoms (of mass 62.92960 u). (vii) Electron capture of

A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?

The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactivepresent with the stablecarbonisotope. When the organism isdead, itsinteractionwiththeatmosphere(whichmaintainstheaboveequilibriumactivity) ceasesanditsactivitybeginstodrop.Fromtheknownhalf-life(5730years)of, and themeasuredactivity,theageofthespecimencanbeapproximatelyestimated.Thisis the principle of dating used in archaeology. Suppose a specimen from Mohenjodaro givesanactivityof9decaysperminutepergramofcarbon.Estimatetheapproximate age of the Indus-Valleycivilisation.

Obtain theamountofnecessary to provide a radioactive source of 8.0mCi strength. Thehalf-lifeofis 5.3years.

The half-life of is 28 years. What is the disintegration rate of 15 mg of this isotope?

Obtainapproximatelytheratioofthenuclearradiiofthegoldisotopeand the silverisotope.

FindtheQ-valueandthekineticenergyoftheemitteda-particleinthea-decayof(a) and(b). Given=226.02540u,= 222.01750u, =220.01137u,= 216.00189u.

The radionuclide ¹¹C decays according to The maximum energy of the emitted positron is 0.960 MeV. Given the mass values: calculate Q and compare it with the maximum energy of the positron emitted

Thenucleusdecaysbyemission. Writedownthedecay equationand determinethemaximumkineticenergyoftheelectronsemitted.Giventhat: = 22.994466 u = 22.989770 u.

The Q value of a nuclear reaction A + b ? C + d is defined by Q = [ m_A+ m_b- m_C- m_d]c² where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) (ii) Atomic masses are given to be

Suppose, we think of fissionofanucleus into twoequalfragments,. Is the fission energetically possible? Argue by working out Q of the process.Given and.

The fissionpropertiesofare very similar tothose of. The average energy released per fission is 180 MeV. How much energy, in MeV, is released if all the atoms in 1 kg of pure undergo fission?

A1000MWfissionreactorconsumeshalfofitsfuelin5.00y.Howmuchdid it containinitially?Assumethatthereactoroperates80%ofthetime,thatalltheenergy generated arises from thefissionofand that this nuclide is consumed only bythe fissionprocess.

How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

Calculate the height of the potential barrier for a head on collision of two deuterons. (Hint: The height of the potential barrier is given by the Coulomb repulsion between the two deuterons when they just touch each other. Assume that they can be taken as hard spheres of radius 2.0 fm.)

From the relation R = R0A1/3, where R0 is a constant and A is the mass number of a nucleus, show that the nuclear matter density is nearly constant (i.e. independent of A).

Forthe(positron) emission from a nucleus, there is another competing process knownaselectroncapture(electronfromaninnerorbit,say,theK-shell,iscapturedby the nucleus and a neutrino isemitted). Showthatifemissionisenergeticallyallowed,electroncaptureisnecessarilyallowed but notvice-versa.

In a periodic table the average atomic mass of magnesium is given as 24.312 u. The average value is based on their relative natural abundance on earth. The three isotopes and theirmassesare(23.98504u),(24.98584u)and(25.98259u).The naturalabundanceofis78.99%bymass.Calculatetheabundancesofothertwo isotopes.

Theneutronseparationenergyisdefinedastheenergyrequiredtoremoveaneutron from the nucleus. Obtain the neutron separation energies ofthenucleiand from the following data: = 39.962591 u ) = 40.962278 u = 25.986895 u ) = 26.981541 u

A source contains two phosphorousradionuclides(T_1/2=14.3d)and(T_1/2= 25.3d). Initially, 10% of the decayscomefrom. How long one must wait until90% doso?

Under certain circumstances, a nucleus can decay by emitting a particle more massive than an a-particle. Consider the following decay processes: Calculate the Q-values for these decays and determine that both are energetically allowed.

Consider thefissionofby fast neutrons. In one fission event, no neutrons are emittedandthefinalendproducts,afterthebetadecayoftheprimaryfragments,are and.CalculateQforthisfissionprocess.Therelevantatomicandparticle massesare m=238.05079u m=139.90543u m= 98.90594u

Consider the D-T reaction (deuterium-tritium fusion) (I) Calculate the energy released in MeV in this reaction from thedata: = 2.014102u = 3.016049u (II) Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What isthekineticenergyneededtoovercomethecoulombrepulsionbetweenthetwonuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interactingparticles=2(3kT/2);k=Boltzman’sconstant,T=absolutetemperature.)

Obtain the maximum kinetic energy of ß-particles, and the radiation frequencies of ? decays in the decay scheme shown in Fig. 13.6. You are given that m (¹⁹⁸Au) = 197.968233 u m (¹⁹⁸Hg) =197.966760 u

Calculate and compare the energy released by a) fusion of 1.0 kg of hydrogen deep within Sun and b) the fission of 1.0 kg of ²³⁵U in a fission reactor.

Suppose India had a target of producing by 2020 AD, 200,000 MW of electric power, ten percent of which was to be obtained from nuclear power plants. Suppose we are given that, on an average, the efficiency of utilization (i.e. conversion to electric energy) of thermal energy produced in a reactor was 25%. How much amount of fissionable uranium would our country need per year by 2020? Take the heat energy per fission of 235U to be about 200MeV.