According to special relativity, the length of a moving object is equal to its original length times an extra factor
L' = L [1 – (v/c)2]0.5.
Here, c is the speed of light, L' is the length of the object when it's moving, L is the length of the object when it's not moving, and v is the velocity at which it's moving. Our new length L' will be about 10-10 m or roughly the size of an atom. Our original length will be about 1.5 m. We can solve for v
v = c [1 – (L'/L)2 ]0.5
= (3.0×108 m/s)[1 – (10-10 m / 1.5 m)2 ]0.5
= 0.9999999999999999999977778 c.
You would need to move very close to the speed of light to be atom sized.
[1] This phenomenon is called "length contraction".
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