1. Identify what is being asked

We need to compare the atomic radius of silver, Ag with the given elements:

• Au
• Cu
• Hg
• Ni

2. Use periodic trends

Silver belongs to group 11: $\text{Cu} \; (3d), \quad \text{Ag} \; (4d), \quad \text{Au} \; (5d)$

Normally, atomic radius increases down a group. So we may expect: $r(\text{Cu}) < r(\text{Ag}) < r(\text{Au})$

However, in heavier transition elements, especially 5d series, lanthanide contraction causes the size of 5d elements to become very close to the corresponding 4d elements.

Thus, Au and Ag have very similar atomic radii.

3. Check each option

• A: Au
  Due to lanthanide contraction, the atomic radius of Au is very close to that of Ag. This is the best match.

• B: Cu
  Cu is above Ag in the same group and is noticeably smaller.

• C: Hg
  Hg is in period 6, but not the closest comparison typically used here. Ag is closer in size to Au than to Hg.

• D: Ni
  Ni is a 3d transition metal and is much smaller than Ag.

4. Conclusion

The atomic radius of Ag is closest to Au.

$\boxed{\text{A: Au}}$

5. Comparison with stored correct answer

Stored correct answer = A
Derived answer = A

So, they agree.