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Lecture notes of 3 pages for the course 1740 at Ebor (homeowrk answers)
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Winter HW2 Description: Fusion in the SunIntroduction: When the nuclei in the center of a star collide at high velocity then they can fuse
together to form a single larger nucleus and release energy. Fusion is the energy behind starlight.
To understand this reaction, you need to know about the small particles that make up our
everyday atomic matter: protons, electrons and neutrons.
In the sun: a new helium nucleus is formed by fusing together four hydrogen nuclei in several
stages. In this homework you will work out
the different pathways by which this can
happen.
Shown in the figure: four important
isotopes to nuclear fusion in the Sun. Each
isotope is described by a letter, a small
number giving the number of protons or
neutrons and one or more plus signs. Each
plus sign indicates one unit of positive
electric charge.
Fusion Reactions: Two hydrogen nuclei can collide to produce a deuterium nucleus and by-
products like an anti-electron and a neutrino. It is not likely this happens with every collision, but
if it occurs the reaction is written as: 1.𝐻+ + 1.𝐻+ → 2.𝐷 + + 𝑒 + + 𝑛𝑒𝑢𝑡𝑟𝑖𝑛𝑜
The number of positive charges is the same on each side of the arrow
(net electric charge is conserved), and if you add up the small numbers on
each side of the arrow they are equal. Shown on the figure is a
representation of the reaction we just wrote. Each circle represents one
nucleus. The arrows indicate that two 1.𝐻+ nuclei collide and form one
2 +
.𝐷 nucleus. By-products are written on blank lines: in this case an anti-
electron and a neutrino.
In this homework you will work out the three different ways that four hydrogens can combine
into a helium atom (via the p-p chain!) and create fusion energy in the Sun. Make sure to use the
‘chances’ listed for the reactions to gauge how often they will occur and answer all the questions
to get full points.
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