Advertisements
Advertisements
Question
How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as
\[\ce{^2_1H + ^2_1H -> ^3_1He + n + 3.27 MeV}\]
Advertisements
Solution
The given fusion reaction is:
\[\ce{^2_1H + ^2_1H -> ^3_1He + n + 3.27 MeV}\]
Amount of deuterium, m = 2 kg
1 mole, i.e., 2 g of deuterium contains 6.023 × 1023 atoms.
∴2.0 kg of deuterium contains = `(6.023 xx 10^23)/2 xx 2000 = 6.023 xx 10^26` atoms
It can be inferred from the given reaction that when two atoms of deuterium fuse, 3.27 MeV energy is released.
∴ Total energy per nucleus released in the fusion reaction:
`"E" = 3.27/2 xx 6.023 xx 10^26 "MeV"`
`= 3.27/2 xx 6.023 xx 10^26 xx 1.6 xx 10^(-19) xx 10^6`
`= 1.576 xx 10^14 " J"`
Power of the electric lamp, P = 100 W = 100 J/s
Hence, the energy consumed by the lamp per second = 100 J
The total time for which the electric lamp will glow is calculated as:
`(1.576 xx 10^14)/100`s
`(1.576 xx 10^14)/(100 xx 60 xx 60 xx 24 xx 365) ~~ 4.9 xx 10^4` year
RELATED QUESTIONS
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
In a photon-electron collision ______.
(A) only total energy is conserved.
(B) only total momentum is conserved.
(C) both total energy and total momentum are conserved.
(D) both total momentum and total energy are not conserved
Write notes on Nuclear fission
Write one balanced equation to show Nuclear fission
Write one balanced equation to show Nuclear fusion
Free 238U nuclei kept in a train emit alpha particles. When the train is stationary and a uranium nucleus decays, a passenger measures that the separation between the alpha particle and the recoiling nucleus becomes x in time t after the decay. If a decay takes place when the train is moving at a uniform speed v, the distance between the alpha particle and the recoiling nucleus at a time t after the decay, as measured by the passenger will be
Consider the fusion in helium plasma. Find the temperature at which the average thermal energy 1.5 kT equals the Coulomb potential energy at 2 fm.
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.)
Why nuclear fusion reaction is also called thermo-nuclear reaction?
In our Nature, where is the nuclear fusion reaction taking place continuously?
Explain in detail the four fundamental forces in nature.
For a nuclear fusion process, the suitable nuclei are:
Solar energy is mainly caused due to:
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:
\[{}_{1}^{2}\mathrm{H}+{}_{1}^{2}\mathrm{H}\rightarrow{}_{2}^{3}\mathrm{He}+\mathrm{n}+3.27\mathrm{MeV}\]
Nuclear fusion reaction that powers the sun involves:
