- Identify the reaction reactants: two deuterium atoms denoted by \({ }_1^2 \text{H}\).
- Determine the mass number \(A\) for these atoms: The notation \({ }_1^2 \text{H}\) indicates \(A=2\).
- Evaluate the statements: The reactant side contains two atoms each with a mass number of \(2\).
- Final Answer: \(\boxed{\text{There are two atoms with mass numbers of 2.}}\)
Explanation
- Analysis of the Nuclear Reaction Equation
In the nuclear reaction equation \({ }_1^2 \text{H} + { }_1^2 \text{H} \rightarrow { }_2^4 \text{He} + \text{energy}\), we use the standard nuclear notation \({ }_Z^A \text{X}\), where \(A\) represents the mass number and \(Z\) represents the atomic number. Examining the reactants, we have two atoms of deuterium, which are represented by \({ }_1^2 \text{H}\). For these atoms, the mass number \(A\) is \(2\). Since the equation shows two \({ }_1^2 \text{H}\) atoms as reactants, there are indeed two atoms with a mass number of \(2\).
- Evaluating the Options
Comparing our analysis to the provided options:
- "There are two atoms with mass numbers of 2": This accurately describes the two deuterium reactants \({ }_1^2 \text{H}\), both of which have a mass number of \(2\).
- "There is one atom with a mass number of 1": This is incorrect, as there are no atoms with a mass number of \(1\).
- "There are two atoms with mass numbers of 1": This is incorrect, as the reactants have mass numbers of \(2\).
- "There is one atom with a mass number of 2": This is incorrect, as there are two reactant atoms with a mass number of \(2\).
Thus, the correct statement is the first one.
- Conclusion
The correct description of the mass numbers of the atoms in the reaction is that there are two atoms with mass numbers of \(2\), corresponding to the two deuterium (\({ }_1^2 \text{H}\)) reactant atoms. Therefore, the answer is the first option. \(\boxed{\text{There are two atoms with mass numbers of 2.}}\)
Examples
In nuclear physics, understanding mass numbers is critical for balancing reaction equations. For instance, in the fusion of deuterium to helium, tracking mass numbers helps scientists predict the energy output and the stability of the resulting isotopes, which is a foundational concept in developing sustainable energy through fusion reactors.