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प्रश्न
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.)
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उत्तर
When two deuterons collide head-on, the distance between their centres, d is given as:
Radius of 1st deuteron + Radius of 2nd deuteron
Radius of a deuteron nucleus = 2 fm = 2 × 10−15 m
∴ d = 2 × 10−15 + 2 × 10−15 = 4 × 10−15 m
Charge on a deuteron nucleus = Charge on an electron = e = 1.6 × 10−19 C
Potential energy of the two-deuteron system:
`"V" = "e"^2/(4pi in_0 "d")`
Where,
`in_0` = Permittivity of free space
`1/(4piin_0) = 9 xx 10^9 "N" "m"^2"C"^(-2)`
`therefore "V" = (9 xx 10^9 xx (1.6 xx 10^(-19))^2)/(4 xx 10^(-15)) "J"`
`= (9 xx 10^9 xx (1.6 xx 10^(-19))^2)/(4 xx 10^(-15) xx (1.6 xx 10^(-19)) " eV"`
= 360 keV
Hence, the height of the potential barrier of the two-deuteron system is 360 keV.
संबंधित 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
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
How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as
\[\ce{^2_1H + ^2_1H -> ^3_1He + n + 3.27 MeV}\]
Write one balanced equation to show Nuclear fission
During a nuclear fission reaction,
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.
In a nuclear reactor, what is the function of a moderator?
For a nuclear fusion process, the suitable nuclei are:
Solar energy is mainly caused due to:
Nuclear fusion reaction that powers the sun involves:
What is thermonuclear fusion?
In the first step of the proton–proton cycle, what is formed when two protons combine, and what is released?
What does the production of carbon from helium fusion in stellar cores demonstrate?
What is expected to happen to the Sun after the hydrogen in its core is exhausted?
How do the temperature requirements of nuclear fusion and nuclear fission compare?
