   Chapter 10, Problem 64P ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185

#### Solutions ### University Physics Volume 3

17th Edition
William Moebs + 1 other
ISBN: 9781938168185
Textbook Problem

# Another set of reactions that fuses hydrogen into helium in the Sun and especially in hotter stars is called die CNO cycle:   12 C + 1 H → 13 N + γ    13 N → 13 C + e + + v e    13 C + 1 H → 14 N + γ    14 N + 1 H → 15 O + γ    15 O → 15 N + e + + v e    15 N + 1 H → 12 C + 4 H e This process is a “cycle” because 12 C appears at the beginning and end of these reactions. Write down the overall effect of this cycle (as done for die proton-proton chain in 2 e − + 4 1 H → 4 H e + 2 v e + 6 γ . Assume that the positrons annihilate elections to form more γ rays.

To determine

The overall effect of the carbon cycle.

Explanation

Introduction:

During the reaction process when a particle is colliding with respective anti particle and produce another particle then this type of reactions called annihilation reaction. Energies and momentums are conserved in these types of reactions.

Set of reactions are:

12C + 1H13N + γ        13N13C + e++ νe13C + 1H14N + γ14N + 1H15O + γ         15O15N + e++ νe15N + 1H12C + 4He

Now, write the overall reaction. Take the sum of first two reactions. Eliminate the elements which are present on both sides. So,

12C + 1H13N + γ         13N13C + e++ νe12C + 1H13C + e++ νe+ γ

Similarly, add third reaction to this reaction and eliminate common variable.

12C + 1H13C + e++ νe+ γ13C + 1H14N + γ12C + 21H14N + e++ νe+ 2γ

Add fourth reaction to this reaction and eliminate common variable.

12C + 21H14N + e++ νe+ 2γ 14N + 1H15O + γ12C + 31H15O + e++ νe+ 3γ

Add fifth reaction to this reaction and eliminate common variable

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