Balance this nuclear reaction by supplying the missing nucleus
249 ? ? ——> 260 Db + 4 1 n
98 Cf + ? 105 0
The correct answer and explanation is :
To balance the nuclear reaction, let’s first analyze the equation:
249 ? ? → 260 Db + 4 ¹n
Here, we have a nuclear reaction where a certain nucleus undergoes fission, resulting in the creation of 260 of the element Dubnium (Db) and 4 neutrons (¹n). The unknown is the nucleus that undergoes fission to produce these products.
Step 1: Analyze the given nuclear products
- 260 Db: Dubnium (Db) has an atomic number of 105, so its symbol is ₁₀₅Db, with mass number 260.
- 4 ¹n: Each neutron has a mass number of 1 and an atomic number of 0.
Step 2: Set up the equation for the balance of mass and atomic numbers
The law of conservation of mass and atomic number must apply here, so we balance both the mass number (A) and the atomic number (Z) on both sides of the equation.
On the right-hand side:
- The mass number of 260 Db is 260.
- The mass number of 4 neutrons is 4 × 1 = 4.
- Total mass number on the right side: 260 + 4 = 264.
- The atomic number of Db (₁₀₅Db) is 105.
- The atomic number of each neutron is 0, so the total atomic number on the right side is 105.
Now, on the left-hand side (before the reaction):
- The mass number of the unknown nucleus, let’s call it X, must add up to 264 (to match the total mass number on the right side).
- The atomic number of the unknown nucleus must add up to 105 (to match the atomic number on the right side).
Step 3: Identify the missing nucleus
To get the total mass number of 264 and the atomic number of 105, we must consider the reactant nucleus. This suggests the unknown nucleus has a mass number of 264 and an atomic number of 100, which corresponds to Fermium (Fm).
Thus, the missing nucleus is ₁₀₀Fm.
Step 4: Final balanced equation
The balanced nuclear reaction is:
₁₀₀Fm → ₁₀₅Db + 4 ¹n
Explanation
- The nuclear reaction represents fission, where the Fermium-264 (₁₀₀Fm) nucleus splits into Dubnium-260 (₁₀₅Db) and 4 neutrons (¹n). The balance of mass and atomic numbers on both sides of the equation ensures the conservation of both quantities. By identifying the required mass and atomic numbers, we determined that the missing nucleus is Fermium-264.