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Standard X

Physics

Nuclear Fusion

Calculate the...

Question

Calculate the energy which can be obtained from $1$ kg of $H_{2} O$ through the fusion reaction
$_{1}^{2} H$ + $_{1}^{2} H$ $\to$ $_{1}^{3} H$ + $p$ .
Assume $1.5 \times 10^{2}$ of the water contains deuterium. The whole deuterium is consumed in the fusion reaction

2820

J

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2820 \times 10^{4}

J

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2820 \times 10^{6}

J

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2820 \times 10^{- 4}

J

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Solution

The correct option is D $2820 \times 10^{6}$ $J$
$D_{2} O$ = $1 \times 1.5 \times 10^{- 4}$ $k g$ = $0.15$ $g$
Number of $_{1}^{2} H$ = $\frac{0.15 \times 6.023 \times 10^{23}}{20}$ = $4.5 \times 10^{21}$

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Similar questions

Q. Calculate the energy that can be obtained from 1 kg of water through the fusion reaction
²H + ²H → ³H + p.
Assume that 1.5 × 10⁻²% of natural water is heavy water D₂O (by number of molecules) and all the deuterium is used for fusion.

How long can an electric lamp of 100W be kept glowing by fusion of 2.0 kg of deuterium? Take the fusion reaction as

Q. In fusion reaction

_{1}^{2} H +_{1}^{2} H \to_{2}^{3} H e +_{0}^{1} n,

the masses of deuteron, helium and neutron expressed in

amu

are

2.015, 3.017

and

1.009

respectively. If

1 kg

of deuterium undergoes complete fusion, find the amount of total energy released

(1 amu c^{2} = 931.5 MeV)

Calculate the Q-values of the following fusion reactions:

(a) $_{1}^{2} H +_{1}^{2} H \to_{1}^{3} H +_{1}^{1} H$

(b) $_{1}^{2} H +_{1}^{2} H \to_{3}^{2} H e + n$

Atomic masses are $m (_{1}^{2} H e) = 2.014102 u, m (_{1}^{3} H e) = 3.016049 u, m (_{2}^{3} H e) = 3.016029 u, m (_{2}^{4} H e) = 4.002603 u$ .

Consider the D−T reaction (deuterium−tritium fusion)

(a) Calculate the energy released in MeV in this reaction from the data:

= 2.014102 u

= 3.016049 u

(b)Consider the radius of both deuterium and tritium to be approximately 2.0 fm. What is the kinetic energy needed to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interacting particles = 2(3kT/2); k = Boltzman’s constant, T = absolute temperature.)

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Calculate the energy which can be obtained from 1 kg of H2O through the fusion reaction 21H +21H → 31H + p. Assume 1.5×102 of the water contains deuterium. The whole deuterium is consumed in the fusion reaction

The correct option is D 2820×106 JD2O = 1×1.5×10−4 kg = 0.15 gNumber of 21H = 0.15×6.023×102320 = 4.5×1021

Calculate the energy which can be obtained from $1$ kg of $H_{2} O$ through the fusion reaction
$_{1}^{2} H$ + $_{1}^{2} H$ $\to$ $_{1}^{3} H$ + $p$ .
Assume $1.5 \times 10^{2}$ of the water contains deuterium. The whole deuterium is consumed in the fusion reaction

The correct option is D $2820 \times 10^{6}$ $J$
$D_{2} O$ = $1 \times 1.5 \times 10^{- 4}$ $k g$ = $0.15$ $g$
Number of $_{1}^{2} H$ = $\frac{0.15 \times 6.023 \times 10^{23}}{20}$ = $4.5 \times 10^{21}$