Question

Name the unit to measure the radius of an atom?

Answer 1

 Either is sufficient. There is a movement to use the picometer, since it is a SI unit and gives you values in the tens or hundreds. 

H = 0.37 Å, 0.037 nm or 37 pm 
Na = 1.86 Å, 0.186 nm or 186 pm 

As long as you indicate the measurement in the proper unit, people will understand it. Right now the Å is not being used that much since is not a SI unit, like the pm or the nm. The pm is becoming more popular.

Answer 2

Fermi(fm) is the practical unit for describing the radius of an atom. 1fm=10^-15m