A beam of hydrogen atoms is used in a Stern-Gerlach type experiment. The atoms emerge from the oven with a velocity \( v = 10^4 \, \text{m/s} \). They enter a region 20 cm long where there is a magnetic field gradient \( \frac{dB}{dz} = 3 \times 10^2 \, \text{T/m} \). The field gradient is perpendicular to the incident velocity of the atoms. The mass of the hydrogen atom is \( m = 1.67 \times 10^{-27} \, \text{kg} \). What is the separation of the two components of the beam as they emerge from the magnet?