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Problem 105 Easy Difficulty

Fission, the process that supplies energy in nuclear power plants, occurs when a heavy nucleus is
split into two medium-sized nuclei. One such reaction occurs when a neutron colliding witha $^{235} \mathrm{U}$ (uranium) nucleus splits that nucleus into a $^{141} \mathrm{Ba}$ (barium) nucleus and a $^{92} \mathrm{Kr}$ (krypton) nucleus. In this reaction, two neutrons also are split off from the original $^{235} \mathrm{U}$ Before the collision, the arrangement is as shown in Fig. 8.49 $\mathrm{a}$ . After the collision, the $^{141} \mathrm{Ba}$ nucleus is moving in the $+z$ -direction and the $^{92} \mathrm{Kr}$ nucleus in the $-z$ -direction. The three neutrons are moving in the $x y$ -plane, as shown in Fig. 8.49 $\mathrm{b}$ . If the incoming neutron has an initial velocity of magnitude $3.0 \times 10^{3} \mathrm{m} / \mathrm{s}$ and a final velocity of magnitude $20 \times 10^{3} \mathrm{m} / \mathrm{s}$ in the directions shown, what are the speeds of the other two neutrons, and what can you say about the speeds of the 141 $\mathrm{Ba}$ and $^{92} \mathrm{Kr}$ nuclei? (The mass of the 14 $\mathrm{Ba}$ nucleus is approximately $23 \times 10^{-25} \mathrm{kg},$ and the mass of $^{92} \mathrm{Kr}$ is about $1.5 \times 10^{-25} \mathrm{kg} . )$

Answer

$=1.5 v_{\mathrm{Be}}$

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Video Transcript

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