To identify the nuclide symbol [tex]\(X\)[/tex] in the nuclear equation [tex]\({ }_{92}^{235} U \longrightarrow X + { }_2^4 He\)[/tex], we must apply the principles of conservation of mass and atomic numbers.
1. Conservation of Mass Number:
The mass number of [tex]\(^{235}_{92}U\)[/tex] is 235. The mass number of the alpha particle [tex]\(^{4}_{2}He\)[/tex] is 4.
According to the conservation of mass number:
[tex]\[
235 = A(X) + 4
\][/tex]
Solving for [tex]\(A(X)\)[/tex] (the mass number of [tex]\(X\)[/tex]):
[tex]\[
A(X) = 235 - 4 = 231
\][/tex]
2. Conservation of Atomic Number:
The atomic number of [tex]\(^{235}_{92}U\)[/tex] is 92. The atomic number of the alpha particle [tex]\(^{4}_{2}He\)[/tex] is 2.
According to the conservation of atomic number:
[tex]\[
92 = Z(X) + 2
\][/tex]
Solving for [tex]\(Z(X)\)[/tex] (the atomic number of [tex]\(X\)[/tex]):
[tex]\[
Z(X) = 92 - 2 = 90
\][/tex]
3. Determine the Nuclide Symbol:
Using the calculated values, the nuclide [tex]\(X\)[/tex] has a mass number of 231 and an atomic number of 90. The element with atomic number 90 is Thorium (Th).
Therefore, the nuclide symbol for [tex]\(X\)[/tex] is:
[tex]\[
{ }_{90}^{231}Th
\][/tex]
Among the given options, the correct nuclide symbol for [tex]\(X\)[/tex] is:
[tex]\[
{ }_{90}^{231} Th
\][/tex]
Thus, the answer is:
[tex]\[
{ }_{90}^{231} Th
\][/tex]
