To determine which reactions are examples of fission reactions, we need to understand the characteristics of fission. A fission reaction involves a large nucleus splitting into smaller nuclei, often accompanied by the release of neutrons and energy. Let's analyze each given reaction to see which fit this definition.
1. Reaction 1:
[tex]\[ {}_1^3 \text{H} + {}_1^3 \text{H} \rightarrow {}_2^4 \text{He} + 2 \cdot {}_0^1 \text{n} \][/tex]
In this reaction, two tritium (hydrogen-3, [tex]\({}_1^3 \text{H}\)[/tex]) nuclei fuse together to form a helium-4 ( [tex]\({}_2^4 \text{He}\)[/tex]) nucleus and two neutrons. This is a fusion reaction, not a fission reaction, as it involves smaller nuclei combining to form a larger nucleus.
2. Reaction 2:
[tex]\[ {}_{94}^{239} \text{Pu} + {}_0^1 \text{n} \rightarrow {}_{58}^{144} \text{Ce} + {}_{36}^{94} \text{Kr} + 2 \cdot {}_0^1 \text{n} \][/tex]
In this reaction, plutonium-239 ( [tex]\({}_{94}^{239}\text{Pu}\)[/tex]) absorbs a neutron and then splits into two smaller nuclei, cerium-144 [tex]\(({}_{58}^{144}\text{Ce})\)[/tex] and krypton-94 ([tex]\({}_{36}^{94}\text{Kr})\)[/tex], along with the release of two neutrons. This is a classic example of a fission reaction.
3. Reaction 3:
[tex]\[ {}_{95}^{241} \text{Am} + {}_0^1 \text{n} \rightarrow {}_{54}^{144} \text{La} + {}_{38}^{95} \text{Sr} + 3 \cdot {}_0^1 \text{n} \][/tex]
Here, americium-241 ( [tex]\({}_{95}^{241}\text{Am}\)[/tex]) captures a neutron and splits into two smaller nuclei, lanthanum-144 ( [tex]\({}_{54}^{144}\text{La})\)[/tex] and strontium-95 ([tex]\({}_{38}^{95}\text{Sr})\)[/tex], and releases three neutrons. This reaction is also an example of fission.
4. Reaction 4:
[tex]\[ {}_6^{13} \text{C} + {}_1^1 \text{H} \rightarrow {}_7^{14} \text{N} \][/tex]
In this reaction, a carbon-13 ( [tex]\({}_6^{13}\text{C})\)[/tex] nucleus and a proton ( [tex]\({}_1^1 \text{H})\)[/tex] combine to form a nitrogen-14 ( [tex]\({}_7^{14}\text{N})\)[/tex] nucleus. This is a fusion reaction, as it involves the merging of two smaller nuclei to form a larger one.
After examining all the reactions, we can see that only the second and third reactions are examples of fission. Therefore, the checked reactions are:
[tex]\[
\checkmark \quad {}_{94}^{239} \text{Pu} + {}_0^1 \text{n} \rightarrow {}_{58}^{144} \text{Ce} + {}_{36}^{94} \text{Kr} + 2 \cdot {}_0^1 \text{n}
\][/tex]
[tex]\[
\checkmark \quad {}_{95}^{241} \text{Am} + {}_0^1 \text{n} \rightarrow {}_{54}^{144} \text{La} + {}_{38}^{95} \text{Sr} + 3 \cdot {}_0^1 \text{n}
\][/tex]
Thus, the correct fission reactions are the second and third reactions:
[tex]\[ [2, 3] \][/tex]
