Question

In the following nuclear reaction X is
\(_{2}^{4}\text{He} + _{7}^{14}\text{N} \rightarrow _{8}^{17}\text{O} + \text{X}\)

• A. Proton
• B. Neutron
• C. Electron
• D. Deuteron

Hint:

Familiarize yourself with the notations for common particles in nuclear physics: \begin{itemize} \item Proton: \(_{1}^{1}\text{p}\) or \(_{1}^{1}\text{H}\) \item Neutron: \(_{0}^{1}\text{n}\) \item Electron (Beta-minus particle): \(_{-1}^{0}\text{e}\) or \(_{-1}^{0}\beta\) \item Positron (Beta-plus particle): \(_{+1}^{0}\text{e}\) or \(_{+1}^{0}\beta\) \item Alpha particle (Helium nucleus): \(_{2}^{4}\text{He}\) or \(_{2}^{4}\alpha\) \item Deuteron (Deuterium nucleus): \(_{1}^{2}\text{H}\) or \(_{1}^{2}\text{D}\) \end{itemize}

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In any nuclear reaction, two fundamental quantities must be conserved: the total mass number (A), which is the superscript, and the total atomic number (Z), which is the subscript.
The mass number (A) represents the total number of protons and neutrons in the nucleus.
The atomic number (Z) represents the number of protons.

Step 2: Key Formula or Approach:
Let the unknown particle X be represented as \(_{Z}^{A}\text{X}\). The conservation laws can be written as two separate equations:
1. Conservation of Mass Number (A): \(\sum A_{\text{reactants}} = \sum A_{\text{products}}\)
2. Conservation of Atomic Number (Z): \(\sum Z_{\text{reactants}} = \sum Z_{\text{products}}\)

Step 3: Detailed Explanation:
The given nuclear reaction is: \[ _{2}^{4}\text{He} + _{7}^{14}\text{N} \rightarrow _{8}^{17}\text{O} + _{Z}^{A}\text{X} \] Applying Conservation of Mass Number (A):
The sum of mass numbers on the left side (reactants) is \(4 + 14 = 18\).
The sum of mass numbers on the right side (products) is \(17 + A\).
Equating them: \(18 = 17 + A \implies A = 1\).
Applying Conservation of Atomic Number (Z):
The sum of atomic numbers on the left side (reactants) is \(2 + 7 = 9\).
The sum of atomic numbers on the right side (products) is \(8 + Z\).
Equating them: \(9 = 8 + Z \implies Z = 1\).
The unknown particle X has a mass number \(A=1\) and an atomic number \(Z=1\). A particle with one proton and a mass number of 1 is a proton (\(_{1}^{1}\text{p}\) or \(_{1}^{1}\text{H}\)).

Step 4: Final Answer:
The particle X is a proton. Therefore, option (A) is correct.