The missing species is \(^{13}_{7}N\), and the balanced equation is:
\[ ^{10}_{5}B + ^{4}_{2}He \rightarrow ^{13}_{7}N + ^{1}_{0}n \]
To balance the nuclear equation \(^{10}_{5}B + ^{4}_{2}He \rightarrow \_\_ + ^{1}_{0}n\), let's identify the missing species.
The sum of the mass numbers and atomic numbers must be equal on both sides of the equation.
On the left side:
- Mass number: \(10 + 4 = 14\)
- Atomic number: \(5 + 2 = 7\)
Now, consider the neutron on the right side (\(^{1}_{0}n\)):
- Mass number: 1
- Atomic number: 0
To balance the equation:
- The missing species must have a mass number of \(14 - 1 = 13\) and an atomic number of \(7 - 0 = 7\).
So, the missing species is \(^{13}_{7}N\), and the balanced equation is:
\[ ^{10}_{5}B + ^{4}_{2}He \rightarrow ^{13}_{7}N + ^{1}_{0}n \]