NUCLEAR FUSION IN THE SUN KEY
I. N UCLEAR F USION
How many fusion reactions take place in the Sun every second? Let’s find out! Be sure to
show all your work.
1. What is nuclear fission?
Nuclear fission is either a nuclear reaction or a radioactive decay process in
which the nucleus of an atom splits into smaller parts (lighter nuclei). The
fission process often produces free neutrons and photons (in the form of gamma
rays), and releases a very large amount of energy even by the energetic
standards of radioactive decay.
2. What is nuclear fusion?
Nuclear fusion is a nuclear reaction in which two or more atomic nuclei come
very close and then collide at a very high speed and join to form a new nucleus.
During this process, matter is not conserved because some of the matter of the
fusing nuclei is converted to photons (energy).
3. What fusion reaction is happening inside the Sun?
4 Hydrogen atoms are fusing into 1 helium
4. What is a nucleon?
A nucleon is one of the particles that makes up the atomic nucleus. There are
two known kinds of nucleon: the neutron and the proton.
5. Look at the diagrams of hydrogen and helium below. How many nucleons (protons
and neutrons) are present in each atom?
Hydrogen: 1
Helium: 4 |
6. It takes four hydrogen atoms to make one helium atom. The atomic weight of
hydrogen is 1.007825, and the atomic weight of helium is 4.002602.
a. What is the atomic weight of four hydrogen atoms? Is this more or less than
the atomic weight of one helium atom?
4 (1.007825) = 4.0313
More than the weight of one helium atom
7. Mass cannot be created nor destroyed. So where does this extra mass go during
fusion?
It gets turned into energy
8. Let’s calculate the energy released when four hydrogen atoms are fused into helium.
a. What does the c represent and what is its value?
The speed of light = 3.00 x 108 m/s
b. m will represent the difference in mass between four hydrogen atoms and
one helium atom. The answer you got in question 6 gave the difference in
atomic weight (defined as the mass of 1 nucleon = 1.66 x 10-27 kg) Convert
your answer into KILOGRAMS:
(𝟒 ∙ 𝟏. 𝟎𝟎𝟕𝟖𝟐𝟓) – 𝟒. 𝟎𝟎𝟐𝟔𝟎𝟐 = 𝟎. 𝟎𝟐𝟖𝟔𝟗𝟖
𝟎. 𝟎𝟐𝟖𝟔𝟗𝟖 ∙ (𝟏. 𝟔𝟔 × 𝟏𝟎−𝟐𝟕 𝐤𝐠) = 𝟒. 𝟖 × 𝟏𝟎−𝟐𝟗 𝐤𝐠
c. Use Einstein’s famous equation, E = mc2: How much energy is released in one
fusion reaction? (Units are Joules)
𝑬 = 𝒎𝒄𝟐 = (𝟒. 𝟖 × 𝟏𝟎−𝟐𝟗 𝐤𝐠) ∙ (𝟑. 𝟎𝟎 × 𝟏𝟎𝟖 𝐦⁄𝐬)𝟐
𝑬 = 𝟒. 𝟑 × 𝟏𝟎−𝟏𝟐 𝐉
II. U NDERSTANDING O UR R ESULT
At first, this doesn’t seem like a whole lot of energy. But let’s estimate how many reactions
must be happening inside the Sun to produce the luminosity that we observe.
9. The Sun’s luminosity is 4 x 1026 Joules per second (J/s). Using your answer from 8c,
how many reactions must be happening every second?
𝟒 × 𝟏𝟎𝟐𝟔 𝐉/𝐬
≈ 𝟏𝟎𝟑𝟖 𝐫𝐞𝐚𝐜𝐭𝐢𝐨𝐧𝐬 𝐞𝐚𝐜𝐡 𝐬𝐞𝐜𝐨𝐧𝐝!
𝟒. 𝟒 × 𝟏𝟎−𝟏𝟐 𝐉
10. A household 100-Watt light bulb puts out 100 Joules per second. How many light
bulbs would you need to match the Sun’s energy output?
𝟒 × 𝟏𝟎𝟐𝟔 𝐉/𝐬
= 𝟒 × 𝟏𝟎𝟐𝟒 𝐥𝐢𝐠𝐡𝐭 𝐛𝐮𝐥𝐛𝐬
𝟏𝟎𝟎 𝐉/𝐬
11. If the Sun burns hydrogen for a total of 1010 years, how much energy will it put out
over its entire lifetime?
𝟏 𝐲𝐞𝐚𝐫 = 𝟑. 𝟏𝟓 × 𝟏𝟎𝟕 𝐬𝐞𝐜𝐨𝐧𝐝𝐬
𝟏𝟎𝟏𝟎 𝐲𝐞𝐚𝐫𝐬 = 𝟑. 𝟏𝟓 × 𝟏𝟎𝟏𝟕 𝐬𝐞𝐜𝐨𝐧𝐝𝐬
(𝟒 × 𝟏𝟎𝟐𝟔 𝐉/𝐬) ∙ (𝟑. 𝟏𝟓 × 𝟏𝟎𝟏𝟕 𝐬𝐞𝐜𝐨𝐧𝐝𝐬) = 𝟏. 𝟑 × 𝟏𝟎𝟒𝟒 𝐉