Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Please sign up to our reward program to support us in return and take advantage of the incredible listed offers.

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY
BUSINESS MANAGER

Advertise your business, and reach millions of students around the world.

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 13.8

One of the processes by which supergiant stars produce heavier masses is the reaction ${ }^{4} He +{ }^{12} C \rightarrow{ }^{16} O +\gamma$. (a) How much energy is expended in this reaction? (b) Explain why such a fusion reaction cannot occur in low-mass stars.

Strategy (a) To find the energy expended we find the Q value from Equation (13.7). (b) We consider the progression of a star’s life to determine what fusion reactions can occur.

$Q=M_{x} c^{2}+M_{X} c^{2}-\left(M_{y} c^{2}+M_{Y} c^{2}\right)=K_{y}+K_{Y}-K_{x}$ (13.7)

## Verified Solution

(a) We look up the masses in Appendix 8 to find the Q value:

\begin{aligned}Q &=\left[M\left({ }^{4} He \right)+M\left({ }^{12} C \right)-M\left({ }^{16} O \right)\right] c^{2} \\Q &=(4.002603 u +12.0 u -15.994915 u ) c^{2} \\&=0.007688 u \cdot c^{2} \\Q &=0.007688 u \cdot c^{2}\left(931.5 \frac{ MeV }{ u \cdot c^{2}}\right)=7.2 MeV\end{aligned}

(b) Stars begin by burning hydrogen to form helium. As the helium is exhausted, the stars contract to higher densities and temperatures, which then allows helium to burn. Because there are no mass-5 and mass-8 stable nuclides, there is a hurdle to get beyond mass-4 nuclides. The hurdle is cleared only if the star is large enough so that as it contracts, helium can burn to create heavier masses. Our sun can produce carbon, but the burning of alpha particles and carbon requires temperatures as high as 300 million K in order to overcome the Coulomb barrier and undergo nuclear fusion. Our sun does not reach this temperature.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 3, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8682120442390442, "perplexity": 2974.09521183788}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104432674.76/warc/CC-MAIN-20220704141714-20220704171714-00017.warc.gz"}