Advertisements
Advertisements
Question
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.
Advertisements
Solution
Given:-
Average thermal energy, E = 1.5 kT
Point of coulomb potential energy = 2 fm
Potential energy is given by
`U = (Kq_1q_2)/r ......(1)`
Here , `K = 1/(4pi∈_0) = 9 xx 10^9`
Charge , `q_1 = q_2 = 2 xx 1.6 xx 10^-19 C`
Average kinetic energy (E) is given by
`E = 3/2 kT ....(2)`
Here, k = Boltzman constant
T = Temperature
Equating equation (1) and (2) , we get
`(kq_1q_2)/r = 3/2kT`
`⇒ T = (2Kq_1q_2)/(3kr)`
`= (2 xx 9 xx 10^9 xx 4 xx (1.6 xx 10^-19)^2)/(3 xx 1.38 xx 10^-23 xx 2 xx 10^-15)`
`= 2.23 xx 10^10 "K"`
APPEARS IN
RELATED QUESTIONS
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
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 fusion
Write one balanced equation to show Nuclear fusion
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.
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.
In a nuclear reactor, what is the function of a moderator?
In our Nature, where is the nuclear fusion reaction taking place continuously?
Explain in detail the four fundamental forces in nature.
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)
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:
\[{}_{1}^{2}\mathrm{H}+{}_{1}^{2}\mathrm{H}\rightarrow{}_{2}^{3}\mathrm{He}+\mathrm{n}+3.27\mathrm{MeV}\]
In the context of fusion, what causes the Coulomb barrier?
Why is energy released when light nuclei combine in a fusion reaction?
In the fusion reaction \[^{2}_{1}H + ^{2}_{1}H \rightarrow ^{3}_{2}He + n\] which products are formed and how much energy is released?
Why can thermonuclear fusion in stars occur even when the average thermal energy of particles is lower than required?
How do the temperature requirements of nuclear fusion and nuclear fission compare?
