Step 1: Understanding the Question:
The question asks for the formal charge on the nitrogen (N) atom in the ammonium ion ($\text{NH}_4^+$).
Step 2: Key Formula or Approach:
The formal charge (FC) of an atom in a molecule or ion can be calculated using the formula:
$$\text{FC} = V - N - \frac{B}{2}$$
where $V$ is the number of valence electrons of the isolated atom, $N$ is the number of non-bonding valence electrons (lone pair electrons), and $B$ is the total number of bonding electrons (electrons shared in covalent bonds).
Step 3: Detailed Explanation:
For the nitrogen atom in the $\text{NH}_4^+$ ion:
1. Nitrogen belongs to Group 15 of the periodic table, so it has 5 valence electrons ($V = 5$).
2. In the ammonium ion, nitrogen forms 4 single covalent bonds with four hydrogen atoms, sharing a total of 8 electrons ($B = 8$).
3. There are no non-bonding lone pair electrons left on the nitrogen atom ($N = 0$).
Substituting these values into the formal charge equation:
$$\text{FC} = 5 - 0 - \frac{8}{2}$$
$$\text{FC} = 5 - 4 = +1$$
Step 4: Final Answer:
The formal charge on the nitrogen atom is +1, which corresponds to option (A).