Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

In certain stars the carbon cycle is more effective than the proton–proton cycle in generating energy.This carbon cycle is
${}^{12}C + {}^{1}H \to^{13} N + γ, Q_{1} = 1.95 MeV, {}^{13}N \to^{13} C + e^{+} + v, Q_{2} = 1.19, {}^{13}C + {}^{1}H \to^{14} N + γ, Q_{3} = 7.55, {}^{14}C + {}^{1}H \to^{15} O + γ, Q_{4} = 7.30,^{15} O \to^{15} N + e^{+} + v, Q_{5} = 1.73, {}^{15}C + {}^{1}H \to^{12} C +^{4} He, Q_{6} = 4.97$
(a) Show that this cycle is exactly equivalent in its overall effects to the proton–proton cycle of Fig. 43-11. (b) Verify that the two cycles, as expected, have the same Q value.

(a) The carbon cycle is exactly equivalent to proton-proton cycle.

(b) It is verified that the two cycles have the same Q value.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the expression for energy

The expression for energy is given by,

$Q = - ∆ m c^{2}$

Here, is the energy release in a reaction, $∆ m$ is the mass difference between the parent nuclei and the daughter nuclei, and c is the velocity of light.

Step 2: Show that carbon-carbon cycle is exactly equivalent to the proton–proton cycle(a)

If can be carefully observed thatin the carbon-carbon cycle, the products are two positrons $(2 e^{+})$ , two neutrinos $(2 v)$ , and one helium nucleus $({}^{4}H e)$ .

The same products are also obtained in the proton-proton cycle.

Therefore, the carbon cycle is exactly equivalent to proton-proton cycle.

Step 3: Verify that the two cycles have the same Q value(b)

The value of the energy is the sum of the Q values of the carbon cycle.

$Q_{c} = \sum_{n = 1}^{6} Q_{n} = Q_{1} + Q_{2} + Q_{3} + Q_{4} + Q_{5} + Q_{6} = 1.95 M e v + 1.19 M e v + 7.55 M e v + 7.30 M e v + 1 / 73 M e v + 4.97 M e v = 24.7 M e v$

The Q value is same for both cycles.

Therefore, it is verified that the two cycles have the same Q value.

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Describe the expression for energy

Step 2: Show that carbon-carbon cycle is exactly equivalent to the proton–proton cycle(a)

Step 3: Verify that the two cycles have the same Q value(b)

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Describe the expression for energy

Step 2: Show that carbon-carbon cycle is exactly equivalent to the proton–proton cycle(a)

Step 3: Verify that the two cycles have the same Q value(b)

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