Answer:
[tex]_{13}^{27}\text{Al} + \rm _{2}^{4}\text{He} \longrightarrow \, _{15}^{31}\text{P}[/tex]
Explanation:
The unbalanced nuclear equation is
[tex]^{27}\text{Al} + \rm \text{He} \longrightarrow \, ^{31}\text{P}[/tex]
We can insert the subscripts, because these are the atomic numbers of the elements
[tex]_{13}^{27}\text{Al} + \, \rm _{2}\text{He} \longrightarrow \, _{15}^{31}\text{P}[/tex]
That leaves only the superscript of He to be determined,
The main point to remember in balancing nuclear equations is that the sums of the superscripts must be the same on each side of the equation.
Then
27 + x = 31, so x = 31 - 27 = 4
Then, your nuclear equation becomes
[tex]_{13}^{27}\text{Al} + \, \rm _{2}^{4}\text{He} \longrightarrow \, _{15}^{31}\text{P}[/tex]