# In the CNO cycle, how does Nitrogen-15 become Carbon-12 and Helium-4?

• AAAA
In summary, the CNO cycle involves the emission of positrons, and it is a process which occurs after the various nuclei fuse with a proton.
AAAA

## Homework Statement

I understand the rest of the cycle, the way my textbook has it, which is:
12C→13N→13C→14N→15O→15N→12C+4He

The portion in bold is what I don't understand.

## The Attempt at a Solution

I do understand that when the mass number increases (like from Carbon-13 to Nitrogen-14), that a hydrogen nucleus is fused(?) together with the Carbon-12 nucleus, and the Nitrogen-14 nucleus and energy (in the form of gamma rays?) are emitted. What I don't understand is how Nitrogen-15 can decay(?) into Carbon-12 and a Helium-4 nucleus.

I was thinking that this was a form of alpha decay, the emitting of the Helium nucleus. However, if that is the case, I don't see how Carbon-12 is also formed.

Any help is appreciated, thanks :)

Sorry if what I wrote down is hard to follow.

AAAA said:

## Homework Statement

I understand the rest of the cycle, the way my textbook has it, which is:
12C→13N→13C→14N→15O→15N→12C+4He

The portion in bold is what I don't understand.

## The Attempt at a Solution

I do understand that when the mass number increases (like from Carbon-13 to Nitrogen-14), that a hydrogen nucleus is fused(?) together with the Carbon-12 nucleus, and the Nitrogen-14 nucleus and energy (in the form of gamma rays?) are emitted. What I don't understand is how Nitrogen-15 can decay(?) into Carbon-12 and a Helium-4 nucleus.

I was thinking that this was a form of alpha decay, the emitting of the Helium nucleus. However, if that is the case, I don't see how Carbon-12 is also formed.

Any help is appreciated, thanks :)

Sorry if what I wrote down is hard to follow.

There are several different CNO cycles which occur in stars of different masses. The various products in the CNO reaction chain occur at different times due to the fusion of a proton with a C or N nucleus, which then decays radioactively in one of several different ways. For more details on the various CNO cycles, see this article:

http://en.wikipedia.org/wiki/CNO_cycle

It is not a decay. It is a process involving an extra proton which is not visible since you did not write out the additional protons needed in any of the reactions.

Orodruin said:
It is not a decay. It is a process involving an extra proton which is not visible since you did not write out the additional protons needed in any of the reactions.

I think if you review the attached article in Post #2, you will see that some of the steps in the CNO cycles occur due to the spontaneous emission of positrons from unstable nuclei produced after fusion with a proton. This process occurs over a period of time (i.e., there is a measurable half-life associated with it), and it fits with the definition of radioactive decay as it is understood in non-stellar processes:

I believe I clearly stated that this process is initiated after the various nuclei fuse with a proton, but in the interest of brevity, I chose not to reproduce the details of all of the reactions and instead referred the OP to the attached article in Post #2 for the details.

In the CNO cycle, Nitrogen-15 (15N) can become Carbon-12 (12C) and Helium-4 (4He) through a process called beta decay. This occurs when a neutron in the 15N nucleus decays into a proton, releasing an electron and an antineutrino. This results in the formation of a 12C nucleus, with 6 protons and 6 neutrons, and an ejected electron and antineutrino. The remaining 4 neutrons in the 15N nucleus then combine with 4 protons to form a 4He nucleus, also known as an alpha particle. This process of beta decay and alpha particle formation is what allows for the conversion of 15N into 12C and 4He in the CNO cycle.

## 1. How does Nitrogen-15 become Carbon-12 and Helium-4 in the CNO cycle?

In the CNO cycle, Nitrogen-15 is converted into Carbon-12 and Helium-4 through a series of nuclear reactions. First, Nitrogen-15 captures a proton to form Oxygen-16. Then, Oxygen-16 captures another proton to form Neon-20. Neon-20 then undergoes beta-plus decay, releasing a positron and forming Fluorine-20. Fluorine-20 captures a proton to form Neon-21, which then undergoes beta-plus decay to form Oxygen-18. Finally, Oxygen-18 captures another proton to form Carbon-12 and Helium-4.

## 2. Why is the CNO cycle important in stellar nucleosynthesis?

The CNO cycle is important in stellar nucleosynthesis because it is the primary way in which stars with masses greater than the Sun convert hydrogen into helium. This process releases large amounts of energy, which is what sustains the star's luminosity and allows it to continue burning for millions to billions of years.

## 3. What conditions are necessary for the CNO cycle to occur?

The CNO cycle requires high temperatures (around 15 million Kelvin) and high densities (around 100 times denser than the Earth's atmosphere) in the core of a star. These conditions are typically found in stars with masses greater than the Sun.

## 4. How does the CNO cycle differ from the proton-proton chain?

Both the CNO cycle and the proton-proton chain are processes by which hydrogen is converted into helium in stars. However, the CNO cycle is more efficient in stars with masses greater than the Sun, while the proton-proton chain dominates in smaller, cooler stars. Additionally, the CNO cycle involves the use of carbon, nitrogen, and oxygen as catalysts, while the proton-proton chain only involves protons.

## 5. Can the CNO cycle occur in all stars?

The CNO cycle can only occur in stars with masses greater than the Sun, as it requires high temperatures and densities that are not present in smaller stars. However, the CNO cycle is the dominant process for hydrogen fusion in stars with masses between 1.3 and 3 times that of the Sun.

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