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प्रश्न
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 :
`""_1^2H+_1^3H->_2^4He+n`
Using the data :
m(`""_1^2H`) = 2.014102 u
m(`""_1^3H`) = 3.016049 u
m(`""_2^4He`) = 4.002603 u
mn = 1.008665 u
1u = 931.5 MeV/c2
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उत्तर
Nuclear fission: It is the phenomenon of splitting of a heavy nucleus (usually A > 230) into two or more lighter nuclei.
`""_92U^235+_0n^1->_56Ba^141+_36Kr^92+3_0n^1+Q`
Here, the energy released per fission of `""_92U^235` is 200.4 MeV.
Nuclear fusion: It is the phenomenon of fusion of two or more lighter nuclei to form a single heavy nucleus.
The mass of the product nucleus is slightly less than the sum of the masses of the lighter nuclei fusing together. This difference in masses results in the release of tremendous amount of energy.
Example:
`""_1H^1+_1H^1->_1H^2+e^++v+0.42 MeV`
`""_1H^2+_1H^2->_2He^3+n+3.27MeV`
`""_1H^2+_1H^2->_1H^3+_1H^1+4.03MeV`
`""_1^2H+_1^3H->_2^4He+n`
∴ Δm = (2.014102 + 3.016049) − (4.002603 + 1.008665 )
=0.018883 u
Energy released, Q = 0.018883 × 931.5 `MeV"/"_(c^2`
= 17.589 MeV
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संबंधित प्रश्न
Calculate the energy in fusion reaction:
`""_1^2H+_1^2H->_2^3He+n`, where BE of `""_1^2H`23He=7.73MeV" data-mce-style="position: relative;">=2.2323He=7.73MeV MeV and of `""_2^3He=7.73 MeV`
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.)
Write notes on Nuclear fission
In a nuclear reaction
`"_2^3He + _2^3He -> _2^4He +_1^1H +_1^1H + 12.86 Me V` though the number of nucleons is conserved on both sides of the reaction, yet the energy is released. How? Explain.
Show that the minimum energy needed to separate a proton from a nucleus with Zprotons and N neutrons is `ΔE = (M_(Z-1,N) + M_B - M_(Z,N))c^2`
where MZ,N = mass of an atom with Z protons and N neutrons in the nucleus and MB = mass of a hydrogen atom. This energy is known as proton-separation energy.
Calculate the Q-values of the following fusion reactions :-
(a) `""_1^2H + ""_1^2H → ""_1^3H + ""_1^1H`
(b) `""_1^2H + ""_1^2H → ""_2^3H + n`
(c) `""_1^2H + ""_1^3H → _2^4H + n`.
Atomic masses are `m(""_1^2H) = 2.014102 "u", m(""_1^3H) = 3.016049 "u", m(""_2^3He) = 3.016029 "u", m(""_2^4He) = 4.002603 "u".`
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
Write one balanced reaction representing nuclear fusion.
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A slab of stone of area 0.36 m2 and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. The thermal conductivity of the slab is:
(Given latent heat of fusion of ice = 3.36 × 105 J kg−1)
How long can an electric lamp of 1000 W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as:
\[{}_{1}^{2}\mathrm{H}+{}_{1}^{2}\mathrm{H}\rightarrow{}_{2}^{3}\mathrm{He}+\mathrm{n}+3.27\mathrm{MeV}\]
