Question

which atom has the largest radius
s
br
mg
b

Explanation:

Step1: Recall atomic radius trends

Atomic radius generally increases down a group and decreases across a period (from left to right). Also, for elements in different periods and groups, we compare their positions.
- Sulfur (S) is in period 3, group 16.
- Bromine (Br) is in period 4, group 17.
- Magnesium (Mg) is in period 3, group 2.
- Boron (B) is in period 2, group 13.

Step2: Analyze each element's position

- Boron (B) is in period 2, so it has a smaller radius than elements in period 3 or 4.
- Magnesium (Mg) and Sulfur (S) are in period 3. Since Mg is to the left of S in the period, Mg has a larger radius than S (as radius decreases across a period).
- Bromine (Br) is in period 4. Now, compare Mg (period 3) and Br (period 4). As we go down a group, the principal quantum number (n) increases, so the atomic radius increases. Br is in period 4, which is lower than period 3 (where Mg is). But wait, let's check the groups. Wait, Mg is group 2, Br is group 17. Wait, no, the trend down a group: for example, group 17: F (period 2), Cl (period 3), Br (period 4) – radius increases. Group 2: Be (period 2), Mg (period 3), Ca (period 4) – radius increases. Now, to compare Mg (period 3, group 2) and Br (period 4, group 17). The period number has a stronger effect? Wait, no, let's check the atomic radii values (approximate):
- B: ~85 pm
- S: ~100 pm
- Mg: ~145 pm
- Br: ~114 pm

So Mg has a larger radius than S, Br, and B. Wait, wait, no, wait Br is in period 4, but Mg is in period 3. Wait, maybe I made a mistake. Wait, the atomic radius of Mg is about 145 pm, Br is about 114 pm, S is about 100 pm, B is about 85 pm. So Mg is larger than Br? Wait, no, wait period 4 elements have higher n, so their atomic radii should be larger than period 3? Wait, no, for example, K (period 4, group 1) has radius ~227 pm, Ca (period 4, group 2) ~197 pm, while Mg (period 3, group 2) ~145 pm. So period 4 group 2 is larger than period 3 group 2. But Br is group 17, period 4. Let's check the electron configurations:

- Mg: [Ne] 3s² (n=3)
- Br: [Ar] 4s² 3d¹⁰ 4p⁵ (n=4)

The outermost electrons of Br are in n=4, but Mg is in n=3. Wait, but the effective nuclear charge also plays a role. For Br, the effective nuclear charge is higher because it has more protons (Br: 35 protons, Mg: 12 protons). Wait, maybe my initial thought was wrong. Let's re - evaluate the trends:

1. Across a period (left to right), atomic radius decreases because effective nuclear charge increases, pulling electrons closer.
2. Down a group (top to bottom), atomic radius increases because the principal quantum number (n) increases, so the electron cloud is larger.

Now, let's list the elements with their periods and groups:

- B: period 2, group 13
- Mg: period 3, group 2
- S: period 3, group 16
- Br: period 4, group 17

First, compare elements in the same period:

- In period 3: Mg (group 2) and S (group 16). Since Mg is to the left of S, Mg has a larger radius than S (because across period, radius decreases).

Now, compare elements in different periods:

- Mg is in period 3, Br is in period 4. Now, we need to see the balance between period (n) and group (effective nuclear charge). Let's check the atomic radii values (from standard data):

- Atomic radius of Mg: ~145 pm
- Atomic radius of Br: ~114 pm
- Atomic radius of S: ~100 pm
- Atomic radius of B: ~85 pm

So Mg has a larger radius than Br? Wait, that seems counter - intuitive because Br is in a higher period. But the effective nuclear charge for Br is much higher (35 protons) compared to Mg (12 protons). The increase in n (from 3 to 4) for Br is offset by the large increase in effective nuclear charge. So Mg (period 3, group 2) has a larger radius than Br (period 4, group 17), S (period 3, group 16), and B (period 2, group 13). Wait, but wait, another way: the elements in order of increasing atomic radius: B < S < Br < Mg? Wait, no, let's check a periodic table's atomic radius trend.

Wait, actually, the correct order from smallest to largest atomic radius among these is: B < S < Br < Mg? No, wait, no. Wait, let's check the positions again. Mg is in group 2, period 3. Br is in group 17, period 4. The general rule is that when comparing elements, if one is in a lower period and far to the left, and the other is in a higher period but far to the right, the left - most element (even in a lower period) can have a larger radius.

For example, Na (period 3, group 1) has a radius of ~186 pm, while Cl (period 3, group 17) has ~99 pm. K (period 4, group 1) has ~227 pm, Br (period 4, group 17) has ~114 pm. So Mg (group 2, period 3) has a radius of ~145 pm, which is larger than Br's ~114 pm. So among B, S, Br, Mg, Mg has the largest atomic radius.

Answer:

Mg (the atom with symbol Mg) has the largest radius.