a) Deduce the expression, N = N0 e−λt, for the law of radioactive decay.
(b) (i) Write symbolically the process expressing the β+ decay of  . Also write the basic nuclear process underlying this decay.
(ii) Is the nucleus formed in the decay of the nucleus  , an isotope or isobar?As per the law of radioactive decay, we have
where,
NÂ = Number of nuclei in the sample
ΔN = Amount of nuclei undergoing decay
Δt = Time taken for decayÂ
So, where λ is Decay constant or disintegration constant.(b)
(i) The β+ decay for  is given below:
A proton is converted into neutron if, the unstable nucleus has excess protons than required for stability.
In the process, a positron e+ (or a β+) and a neutrino ν are created and emitted from the nucleus.
p → n + β+ + ν
This process is called beta plus decay.
(ii) The nucleus so formed is an isobar of  because the mass number is same, whereas the atomic numbers are different.
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction:Â
Nuclear Fission |
Nuclear Fusion |
The process of breaking a heavy nucleus into two or more lighter nuclei. |
The phenomenon of combining or fusing two or more lighter nuclei to form a single nucleus. |
 |  |
The given equation is,Â
Mass of the reactant,Â
                 = (2.014102 + 3.016049) u
                 = 5.030151u Â
Mass of the product,Â
                 = (4.002603 + 1.008665) u
                 = 5.011268 uÂ
Difference in energy,Â
                  = (5.030151 – 5.011268) u
                  = 0.018883uÂ
Therefore, Energy released, E =Â
                   = 0.018883 × 931.5 MeVÂ
                   = 17.589514 MeVÂ
For the radioactive nuclei that undergo either α or β decay, which one of the following cannot occur ?
Isobar of original nucleus is produced
Isotope of the original nucleus is produced
Nuclei with higher atomic number than that of the original nucleus is produced
Nuclei with lower atomic number than that of the original nucleus is produced
B.
Isotope of the original nucleus is produced
Isotope of the original nucleus is produced.
Define the activity of a given radioactive substance. Write its S.I. unit. Â Â Â Â Â
The rate of decay of a radioactive substance is called activity of that substance. Activity is the negative of the rate of decay of the radioactive substance.Â
SI unit is Becquerel (Bq.)
(i) What characteristic property of nuclear force explains the constancy of binding energy per nucleon (BE/A) in the range of mass number ‘A’ lying 30 < A < 170?
(ii) Show that the density of nucleus over a wide range of nuclei is constant- independent of mass number A.i) The characteristic property of nuclear force that explains the constancy of binding energy per nucleon is the saturation or short range nature of nuclear forces.
In heavy nuclei, nuclear size > range of nuclear force.
ii) Using the formula for radius of the nucleon, we have
Let, m be the mass of nucleon.
Therefore,
Density, Â
Thus, we can see that density is independent of mass number A.