Question

Which represents a balanced nuclear equation?

Answer 1

Answer:

The correct option is 2.

Explanation:

In a nuclear reaction balanced we have that:

1. The sum of the mass number (A) of the reactants (r) is equal to the sum of the mass number of the products (p) $\Sigma A_{r} = \Sigma A_{p}$

2. The sum of the atomic number (Z) of the reactants is also equal to the sum of the atomic number of the products $\Sigma Z_{r} = \Sigma A_{p}$      

So, let's evaluate each option.

1) $^{23}_{11}Na \rightarrow ^{24}_{11}Mg + ^{1}_{1}H$

The mass number of the reactant is:

$A_{r} = 23$

The sum of the mass number of the products is:

$A_{p} = 24 + 1 = 25$

This is not the correct option because it does not meet the first condition ($\Sigma A_{r} = \Sigma A_{p}$).

2) $^{24}_{11}Na \rightarrow ^{24}_{12}Mg + ^{0}_{-1}e$  

The mass number of the reactant and the products is:

$A_{r} = 24$

$A_{p} = 24 + 0 = 24$

Now, the atomic number of the reactants and the products are:

$Z_{r} = 11$

$Z_{p} = 12 + (-1) = 11$      

This nuclear reaction is balanced since it does meet the two conditions for a balanced nuclear equation, ($\Sigma A_{r} = \Sigma A_{p}$ and $\Sigma Z_{r} = \Sigma Z_{p}$).  

3) $^{24}_{13}Al \rightarrow ^{24}_{12}Mg + ^{0}_{-1}e$      

The mass number of the reactant and the products is:

$A_{r} = 24$

$A_{p} = 24 + 0 = 24$

Now, the atomic number of the reactants and the products are:

$Z_{r} = 13$

$Z_{p} = 12 + (-1) = 11$      

This reaction does not meet the second condition ($\Sigma Z_{r} = \Sigma Z_{p}$) so this is not a balanced nuclear equation.

4) $^{23}_{12}Mg \rightarrow ^{24}_{12}Mg + ^{1}_{0}n$

The mass number of the reactant and the products is:

$A_{r} = 23$

$A_{p} = 24 + 1 = 25$  

This reaction is not a balanced nuclear equation since it does not meet the first condition ($\Sigma A_{r} = \Sigma A_{p}$).

Therefore, the correct option is 2.

I hope it helps you!