To predict the missing component in the nuclear equation:
[tex]\[ \,_{20}^{45} \text{Ca} \rightarrow \,_{21}^{45} \text{Sc} + X \][/tex]
we need to ensure both the mass number and atomic number are balanced on both sides of the equation.
1. Mass Number (Superscript):
- On the left side of the equation, the mass number of calcium (Ca) is 45.
- On the right side of the equation, scandium (Sc) has a mass number of 45.
- To balance the mass number:
[tex]\[
45_{(\text{Ca})} = 45_{(\text{Sc})} + \text{Mass number of } X
\][/tex]
Solving for the mass number of [tex]\( X \)[/tex]:
[tex]\[
45 = 45 + \text{Mass number of } X
\][/tex]
[tex]\[
\text{Mass number of } X = 0
\][/tex]
2. Atomic Number (Subscript):
- On the left side of the equation, the atomic number of calcium (Ca) is 20.
- On the right side of the equation, scandium (Sc) has an atomic number of 21.
- To balance the atomic number:
[tex]\[
20_{(\text{Ca})} = 21_{(\text{Sc})} + \text{Atomic number of } X
\][/tex]
Solving for the atomic number of [tex]\( X \)[/tex]:
[tex]\[
20 = 21 + \text{Atomic number of } X
\][/tex]
[tex]\[
\text{Atomic number of } X = -1
\][/tex]
Based on these balances:
- The mass number of [tex]\( X \)[/tex] is 0.
- The atomic number of [tex]\( X \)[/tex] is -1.
These values correspond to an electron or beta particle, typically represented as [tex]\(_{-1}^{0}e\)[/tex] or [tex]\(\beta^{-}\)[/tex].
Therefore, the missing component [tex]\( X \)[/tex] in the nuclear equation is:
[tex]\[ \,_{-1}^{0} e \][/tex]
