Among the atoms listed, which one has the largest atomic radius based on periodic trends: Br, K, Na or Cl?

Introduction / Context:
Understanding trends in atomic radius across the periodic table is a key part of basic chemistry. Atomic size affects many properties, including ionisation energy, electronegativity and bonding behaviour. This question asks you to compare the atomic radii of four elements, bromine, potassium, sodium and chlorine, and identify which one has the largest atomic radius. Recognising how atomic size changes across periods and down groups makes such comparisons straightforward without needing exact numerical data.

Given Data / Assumptions:

• The elements to compare are Br, K, Na and Cl.
• Sodium and potassium are alkali metals in group 1, with Na in period 3 and K in period 4.
• We assume atomic radius trends follow the general rules: increases down a group and decreases across a period from left to right.

Concept / Approach:
Atomic radius generally decreases from left to right across a period because increasing nuclear charge pulls electrons closer, and increases from top to bottom within a group because additional electron shells are added. Alkali metals like sodium and potassium are large atoms compared with halogens in the same period. Potassium lies below sodium in the same group, so it has an extra electron shell and should be larger than sodium. Bromine is larger than chlorine but still a halogen, which are smaller than alkali metals in the same period. The approach is to apply these trends to compare sizes systematically and pick the largest.

Step-by-Step Solution:
Step 1: Compare sodium and potassium, both in group 1. Potassium is in period 4, below sodium in period 3, so potassium has an extra electron shell and therefore a larger atomic radius than sodium. Step 2: Compare chlorine and bromine, both in group 17. Bromine is in period 4, below chlorine in period 3, so bromine is larger than chlorine. Step 3: In any given period, alkali metals on the left are larger than halogens on the right, because atomic radius decreases from left to right across a period. Step 4: Therefore, in period 3, sodium is larger than chlorine, and in period 4, potassium is larger than bromine. Step 5: Among sodium and potassium, potassium is larger because it is in the period below and has more electron shells. Step 6: Thus, potassium has the largest atomic radius among Br, K, Na and Cl.

Verification / Alternative check:
If you look up approximate atomic radii in a data table, you will find values such as: K greater than Na, and Na and K both significantly larger than Cl and Br in their respective periods. Even without exact numbers, periodic trend diagrams clearly show that atomic size increases down each group and decreases from left to right. Visual periodic tables that code atomic radius by circle size also show potassium as one of the larger atoms in the fourth period. These alternative representations confirm that potassium has the largest radius among the listed elements.

Why Other Options Are Wrong:
Option A, bromine, is larger than chlorine but still smaller than potassium, because halogens are smaller than alkali metals in the same period. Option C, sodium, is larger than chlorine but smaller than potassium due to being in a higher period. Option D, chlorine, is one of the smaller atoms among the four because it is a halogen in period 3. Option E states that all have the same radius, which is incorrect and contradicts well established periodic trends. Only option B, potassium, matches the expected pattern of atomic radii and is the largest among the given atoms.

Common Pitfalls:
Students sometimes misremember the direction of atomic size trends or confuse them with trends for ionisation energy or electronegativity, which move in opposite directions. Another pitfall is to focus only on the number of protons and assume more protons means a larger atom, without considering the effect of additional electron shells and increased nuclear attraction. To avoid confusion, memorise the simple rules: atomic radius increases down a group and decreases from left to right across a period. Applying these rules step by step makes questions like this much easier.

Final Answer:
The atom with the largest atomic radius among the choices is Potassium (K), which lies in group 1, period 4 and has more electron shells than the others.