Answer :
To determine which nuclear equation is balanced, we need to check if both the mass number (top number) and the atomic number (bottom number) are the same on both sides of the equation.
Let's review each option step-by-step:
1. [tex]\({ }_{11}^{23} Na \longrightarrow{ }_{12}^{24} Mg +{ }_1^1 H\)[/tex]
- Reactant: Sodium (Na) with mass number 23 and atomic number 11.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and Hydrogen (H) with mass number 1 and atomic number 1.
Checking mass numbers:
- Reactant side: [tex]\(23\)[/tex]
- Product side: [tex]\(24 + 1 = 25\)[/tex]
The mass numbers do not match.
Checking atomic numbers:
- Reactant side: [tex]\(11\)[/tex]
- Product side: [tex]\(12 + 1 = 13\)[/tex]
The atomic numbers do not match.
This equation is not balanced.
2. [tex]\({ }_{11}^{24} Na \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
- Reactant: Sodium (Na) with mass number 24 and atomic number 11.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and an electron (e) with mass number 0 and atomic number -1.
Checking mass numbers:
- Reactant side: [tex]\(24\)[/tex]
- Product side: [tex]\(24 + 0 = 24\)[/tex]
The mass numbers match.
Checking atomic numbers:
- Reactant side: [tex]\(11\)[/tex]
- Product side: [tex]\(12 + (-1) = 11\)[/tex]
The atomic numbers match.
This equation is balanced.
3. [tex]\({ }_{13}^{24} Al \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
- Reactant: Aluminum (Al) with mass number 24 and atomic number 13.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and an electron (e) with mass number 0 and atomic number -1.
Checking mass numbers:
- Reactant side: [tex]\(24\)[/tex]
- Product side: [tex]\(24 + 0 = 24\)[/tex]
The mass numbers match.
Checking atomic numbers:
- Reactant side: [tex]\(13\)[/tex]
- Product side: [tex]\(12 + (-1) = 11\)[/tex]
The atomic numbers do not match.
This equation is not balanced.
4. [tex]\({ }_{12}^{23} Mg \longrightarrow{ }_{12}^{24} Mg +{ }_{0}^{1} n\)[/tex]
- Reactant: Magnesium (Mg) with mass number 23 and atomic number 12.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and a neutron (n) with mass number 1 and atomic number 0.
Checking mass numbers:
- Reactant side: [tex]\(23\)[/tex]
- Product side: [tex]\(24 + 1 = 25\)[/tex]
The mass numbers do not match.
Checking atomic numbers:
- Reactant side: [tex]\(12\)[/tex]
- Product side: [tex]\(12 + 0 = 12\)[/tex]
The atomic numbers match.
This equation is not balanced.
From the above analysis, the balanced nuclear equation is:
[tex]\({ }_{11}^{24} Na \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
Let's review each option step-by-step:
1. [tex]\({ }_{11}^{23} Na \longrightarrow{ }_{12}^{24} Mg +{ }_1^1 H\)[/tex]
- Reactant: Sodium (Na) with mass number 23 and atomic number 11.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and Hydrogen (H) with mass number 1 and atomic number 1.
Checking mass numbers:
- Reactant side: [tex]\(23\)[/tex]
- Product side: [tex]\(24 + 1 = 25\)[/tex]
The mass numbers do not match.
Checking atomic numbers:
- Reactant side: [tex]\(11\)[/tex]
- Product side: [tex]\(12 + 1 = 13\)[/tex]
The atomic numbers do not match.
This equation is not balanced.
2. [tex]\({ }_{11}^{24} Na \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
- Reactant: Sodium (Na) with mass number 24 and atomic number 11.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and an electron (e) with mass number 0 and atomic number -1.
Checking mass numbers:
- Reactant side: [tex]\(24\)[/tex]
- Product side: [tex]\(24 + 0 = 24\)[/tex]
The mass numbers match.
Checking atomic numbers:
- Reactant side: [tex]\(11\)[/tex]
- Product side: [tex]\(12 + (-1) = 11\)[/tex]
The atomic numbers match.
This equation is balanced.
3. [tex]\({ }_{13}^{24} Al \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
- Reactant: Aluminum (Al) with mass number 24 and atomic number 13.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and an electron (e) with mass number 0 and atomic number -1.
Checking mass numbers:
- Reactant side: [tex]\(24\)[/tex]
- Product side: [tex]\(24 + 0 = 24\)[/tex]
The mass numbers match.
Checking atomic numbers:
- Reactant side: [tex]\(13\)[/tex]
- Product side: [tex]\(12 + (-1) = 11\)[/tex]
The atomic numbers do not match.
This equation is not balanced.
4. [tex]\({ }_{12}^{23} Mg \longrightarrow{ }_{12}^{24} Mg +{ }_{0}^{1} n\)[/tex]
- Reactant: Magnesium (Mg) with mass number 23 and atomic number 12.
- Products: Magnesium (Mg) with mass number 24 and atomic number 12, and a neutron (n) with mass number 1 and atomic number 0.
Checking mass numbers:
- Reactant side: [tex]\(23\)[/tex]
- Product side: [tex]\(24 + 1 = 25\)[/tex]
The mass numbers do not match.
Checking atomic numbers:
- Reactant side: [tex]\(12\)[/tex]
- Product side: [tex]\(12 + 0 = 12\)[/tex]
The atomic numbers match.
This equation is not balanced.
From the above analysis, the balanced nuclear equation is:
[tex]\({ }_{11}^{24} Na \longrightarrow{ }_{12}^{24} Mg +{ }_{-1}^{0} e\)[/tex]
