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In a fusion reactor the reaction occurs in two stages : (i) Tw

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In a fusion reactor the reaction occurs in two stages :
(i) Two deuterium $(_{1}^{2} D)$ nuclei fuse to form a tritium $(_{1}^{3} T)$ nucleus with a proton as product. The reaction may be represented as $D$ $(D, p) T$ .
(ii) A tritium nucleus fuses with another deuterium nucleus to form a helium $(_{2}^{4} He)$ nucleus with neutron as another product. The reaction is represented as $T (D, n) α$ . Find :
(a) The energy release in each stage.
(b) The energy release in the combined reaction per deuterium
Given : $(_{1}^{2} D) = 2.014102 amu; (_{1}^{3} T) = 3.016049 amu; (_{2}^{4} He) =$ $4.002603 amu; (l_{1}^{P} P) = 1.00785 amu; (_{0}^{1} n) = 1.008665 amu$

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Physics Galaxy Optics and Modern Physics Vol 4 (Ashish Arora)

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In a fusion reactor the reaction occurs in two stages :
(i) Two deuterium

(_{1}^{2} D)

nuclei fuse to form a tritium

(_{1}^{3} T)

nucleus with a proton as product. The reaction may be represented as

D

(D, p) T

.
(ii) A tritium nucleus fuses with another deuterium nucleus to form a helium

(_{2}^{4} He)

nucleus with neutron as another product. The reaction is represented as

T (D, n) α

. Find :
(a) The energy release in each stage.
(b) The energy release in the combined reaction per deuterium
Given :

(_{1}^{2} D) = 2.014102 amu; (_{1}^{3} T) = 3.016049 amu; (_{2}^{4} He) =

4.002603 amu; (l_{1}^{P} P) = 1.00785 amu; (_{0}^{1} n) = 1.008665 amu

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Text solutionVerified

(a) (i) The reaction is

_{1} D^{2} +_{1} D^{2} \to_{1} T^{3} +_{1} P^{1} E_{1} Δ m = [2 (2.014102) - 3.016049 - 1.007825] = 0.00433

∴

Energy released,

E_{1} = 0.00433 \times 931 MeV

= 4.031 MeV

(ii)

_{1} T^{3} +_{1} D^{2} \to_{2} He^{4} +_{0} n^{1} + E_{2}

Δ m = [(3.016049 + 2.014102) - (4.002603 + 1.008665)] = 0.0188 a \cdot m \cdot u

∴

Energy released

E_{2} = 0.01888 \times 931 MeV = 17.580 MeV

Total energy released in both processes

= 17.580 + 4.031 = 21.611 MeV

(b) Energy released per

_{1} D^{2} = \frac{21.611}{3} = 7.206 MeV

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Question Text	In a fusion reactor the reaction occurs in two stages : (i) Two deuterium $(_{1}^{2} D)$ nuclei fuse to form a tritium $(_{1}^{3} T)$ nucleus with a proton as product. The reaction may be represented as $D$ $(D, p) T$ . (ii) A tritium nucleus fuses with another deuterium nucleus to form a helium $(_{2}^{4} He)$ nucleus with neutron as another product. The reaction is represented as $T (D, n) α$ . Find : (a) The energy release in each stage. (b) The energy release in the combined reaction per deuterium Given : $(_{1}^{2} D) = 2.014102 amu; (_{1}^{3} T) = 3.016049 amu; (_{2}^{4} He) =$ $4.002603 amu; (l_{1}^{P} P) = 1.00785 amu; (_{0}^{1} n) = 1.008665 amu$
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1
Upvotes	72

Text solutionVerified

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