To complete the nuclear fission equation where a californium (^282Cf) atom undergoes fission when bombarded by a neutron (^1n), we need to identify the missing products of this reaction. Given the information and the resulting answer, these are the steps to solve the equation:
1. Start with the original nuclear equation:
[tex]$
{ }_{96}^{282} Cf + { }_0^1 n \rightarrow \square \qquad \square + { }_{52}^{130} Te + 3{ }_0^1 n
$[/tex]
2. Determine the missing mass number and atomic number:
The mass number on the left (reactants side) is: 282 (from ^282Cf) + 1 (from ^1n) = 283.
The atomic number on the left (reactants side) is: 96 (from ^282Cf) + 0 (from ^1n) = 96.
3. The equation also shows Tellurium (Te) with mass number 130 and atomic number 52, and 3 neutrons, each with atomic number 0 and mass number 1. So we need to subtract these from the totals to balance the equation.
- Mass number on the products side should be equal to 283. So, for our unknown element:
[tex]$
\text{Mass number of unknown} + 130 + 3 \times 1 = 283
$[/tex]
Simplifying,
[tex]$
\text{Mass number of unknown} = 283 - 130 - 3 = 150
$[/tex]
- Atomic number on the products side should be equal to 96. So, for our unknown element:
[tex]$
\text{Atomic number of unknown} + 52 + 3 \times 0 = 96
$[/tex]
Simplifying,
[tex]$
\text{Atomic number of unknown} = 96 - 52 = 44
$[/tex]
4. Based on the atomic number, the missing element is Palladium (Pd):
So, we can now complete the nuclear fission equation as follows:
[tex]$
{ }_{96}^{282} Cf + { }_0^1 n \rightarrow { }_{44}^{150} Pd \qquad { }_{52}^{130} Te + 3{ }_0^1 n
$[/tex]
Therefore, the correct tiles to place are:
- "150" for the mass number
- "44" for the atomic number
- "Pd" for the element symbol
