To solve the problem, we need to balance the nuclear reaction equation. Here are the detailed steps to complete the equation:
1. Determine the total atomic number and mass number before and after the reaction.
Before the reaction:
- Curium-245 (Cm-245) has an atomic number of 96 and a mass number of 245.
- A neutron has an atomic number of 0 and a mass number of 1.
So, the total atomic number before is [tex]\( 96 + 0 = 96 \)[/tex].
The total mass number before is [tex]\( 245 + 1 = 246 \)[/tex].
After the reaction:
- Molybdenum-103 (Mo-103) has an atomic number of 42 and a mass number of 103.
- Three neutrons each have an atomic number of 0 and a mass number of 1.
So, the total atomic number after is [tex]\( 42 + 3 \times 0 = 42 \)[/tex].
The total mass number after is [tex]\( 103 + 3 \times 1 = 106 \)[/tex].
2. Find the difference between the atomic number and mass number before and after to identify the missing particle.
- Difference in atomic number: [tex]\( 96 - 42 = 54 \)[/tex]
- Difference in mass number: [tex]\( 246 - 106 = 140 \)[/tex]
This means the missing element must have an atomic number of 54 and a mass number of 140.
3. Identify the missing element based on the atomic number. An atomic number of 54 corresponds to the element Xenon (symbol: Xe).
Therefore, the complete equation is:
[tex]\[
{}_{96}^{245} Cm + {}_0^1 n \longrightarrow {}_{42}^{103} Mo + {}_{54}^{140} Xe + 3 {}_0^1 n
\][/tex]
So the tiles should be placed as follows:
[tex]\[
{}_{96}^{245} Cm + {}_0^1 n \longrightarrow {}_{42}^{103} Mo + {}_{54}^{140} Xe + 3 {}_0^1 n
\][/tex]
